Model sensitivity of simulated yield of winter oilseed rape to climate change scenarios in Europe

Winter oilseed rape (WOSR) is Europe ’ s prime oilseed crop and is grown for biofuel and edible oil production. To investigate the effects of climate change on the yield of winter oilseed rape, two crop models (HERMES and HUME-OSR) were used. This study investigated the sensitivity of crop model parameters (as a proxy of plant traits) under climate change. For both models, a global sensitivity analysis was performed under current temperatures, an increase of 2 and 4 ◦ C, in combination with (cid:0) 50 %, (cid:0) 25 %, current, + 25 % and + 50 % precipitation change, resulting in 15 combinations. The analysis was done for six different sites in Europe located in Germany, France, and the Czech Republic. The two models differ in model formalism; however, results show that the most sensitive parameters of WOSR for both models are associated with drought, both under current climatic conditions, and under changing temperatures and precipitation regimes. The sensitivity analysis shows that the most sensitive parameters for WOSR yield under climate change relate to plant traits affecting the growth of the vegetative phase.


Introduction
Winter oilseed rape (WOSR, Brassica napus L.) is Europe's prime oilseed crop and is grown widely across Europe (Tuck et al., 2006), where the majority of the winter oilseed rape area is located in Germany, Poland, Lithuania, Latvia, France and Italy (FAOSTAT, 2012;van Duren et al., 2015).WOSR is mainly grown in Europe for biofuel and edible oil production, but also for livestock feed supplements.The European Union has set a target of 20 % for the overall share of energy from renewable sources and a 10 % target renewable energy in transport by 2020 (European Parliament and the Council of the European Union, 2009; Thamsiriroj and Murphy., 2010;USDA Gain reports, 2018), in which biodiesel derived from WOSR plays a prominent role.To reach and maintain the contributions of WOSR to food, feed and biofuels, several measures can and have to be taken.While it is theoretically possible to increase the cropping area of WOSR, it will lead to a conflict with other crops, such as cereals (Rondanini et al., 2012) and root crops (e.g., sugar beet).Other measures to enhance production are optimizing the crop productivity through closing the gap between the potential and the actual yield (Diepenbrock, 2000;Berry and Spink., 2006;van Ittersum et al., 2013), reducing yield variability (Mendham et al., 1981;Berry and Spink., 2006;Rondanini et al., 2012;Weymann et al., 2015), and reducing susceptibility to diseases and pests (Fitt et al., 2006;Singh et al., 2017).To enhance productivity and reduce yield variability specific crop physiological traits can become increasingly important under climate change, such as the extension of the duration of the late reproductive phase, increasing the number of seeds per pod, which is the result a higher photoperiodic sensitivity in the vegetative phase (Diepenbrock, 2000;Gomez and Miralles., 2011;Rondanini et al., 2012), increase of the harvest index, for example by increasing the number of seeds per pod and pod length, and greater light use efficiency through changes in plant architecture (Habekotté, 1996;Rondanini et al., 2012;Böttcher et al., 2020).
These issues are already prominent under current climate conditions and might become increasingly important under climate change.An increase in air temperature will increase the rate of development of WOSR, which can make the crop more susceptible to low spring temperatures, but higher temperatures could also reduce the length of the growing season in northern latitudes and thereby expand the potential cropping area in Europe (Pullens et al., 2019).On the other hand, an increase in temperature may lead to supra-optimal temperatures in regions where the temperature is already high, i.e. at southern latitudes (Pullens et al., 2019).Although climate scenarios show a big variation in projected future air temperatures, consistent increases in temperature are seen over Europe (e.g.Ciscar et al., 2009;Bindi and Olesen., 2011;Iglesias et al., 2012;Flato et al., 2013;IPCC, 2014).However, climate change projections do not show consistent changes in future precipitation regimes (e.g.Ciscar et al., 2009;Bindi and Olesen., 2011;Iglesias et al., 2012;Flato et al., 2013;IPCC, 2014), and we have therefore simplified the analysis of changes in both temperature and precipitation in this study.
Under climate change, it can be expected that the WOSR production will encounter multiple weather events adversely affecting production, depending on the current climatic conditions (Pullens et al., 2019).Pullens et al. (2019) focused on the effect of climate change on the phenology of WOSR, the adverse effects of frosts, droughts and heat stress, and the occurrence of diseases, which indicated how and where in Europe WOSR will be affected by stress conditions under climate change.The effects of climate change on crop phenology and the adverse events on crop physiology is expected to negatively influence the crop yield and thus the profitability of arable farming.To further understand the effect of climate change on the yield of WOSR, we used two crop models, HERMES (Kersebaum, 1995) and HUME-OSR (Böttcher et al., 2020).Simulation models that capture the physiological responses of crops provide a tool for exploring how climate change may affect crop yield and which crop physiological responses are of greatest importance in various geographical settings (Wheeler and Von Braun., 2013;Corbeels et al., 2018;Rötter et al., 2018b;Kipling et al., 2019).
The current study aimed to explore which parameters of the crop models that are currently or will under climate change become the most sensitive with respect to WOSR yield.By pinpointing these parameters, we aim to identify 1) key plant traits of focus in plant breeding to mitigate negative effects of climate change, 2) management options of relevance for adaptation to climate change, and 3) issues for further research in support of adaptation to climate change.

Material and methods
The sites that were used in this study to support modelling were from Germany, France and Czech Republic, covering the major range of European cropping area with WOSR (Monfreda et al., 2008;van Duren et al., 2015), and experimental data from these sites were available from 1993 to 2014 with different varieties and nitrogen fertilization rates (Table 1).Three locations in Germany (Biestow, Christgrün and Forchheim), one location in France (Châlons-en-Champagne) and two in the Czech Republic (Domaninek and Lednice) were used to cover an East-West and North-South gradient, with a resulting gradient in mean annual temperature and annual precipitation.All data from German sites was from variety trials, while at the other sites only one variety was used (Table 1).Domaninek and Châlons-en-Champagne were the only sites where experiments with different nitrogen (N) fertilization rates were performed.The range of measured yields was from 3.27 to 5.97 Mg ha − 1 , for Domaninek in 1999 and Lednice in 2001, respectively.The standard deviation of all the yield measurements for all plots and all years was 0.5 Mg ha -1 .Phenological data for WOSR was available for all sites.
Two WOSR models (HERMES and HUME-OSR) were used to simulate the effects of climate change on the yield of winter oilseed rape.This study does not investigate the effect of climate change on simulated yield levels, but on the effects of climate change on the yield response, i. e. increasing and decreasing yield levels.No effects of pests or diseases are included in either model.Over the complete study, all presented yields are defined as the seed weight at 9% moisture content and for both models the default parameters are used (see Supplemental material S1 and S2).In both models, the sowing date was kept fixed, i.e. the sowing dates that were used in the field studies.

HERMES
HERMES is a generic crop model that simulates numerous crops and is capable of simulating crop rotations (Kersebaum, 1995).The model simulates only one-dimensional processes at a daily time step.The main processes are N mineralization, denitrification, transport of water and N, crop growth, phenological development, and N uptake.More details about the model can be found in Kersebaum (1995Kersebaum ( , 2007)).Based on preliminary runs, the values of AMAX (maximum CO 2 assimilation rate) was changed from 28 to 41 kg CO 2 ha − 1 leaf h − 1 , since the default value was too low; apart from this parameter, all sites were run with the default parameters for WOSR (Table 2).This adaptation was necessary since the model has so far not been intensively tested with detailed experimental data, and the parametrisation of the model is predominantly based on information from literature (Habekotté, 1996).All model simulations started in January of the first year of measurements; in this spin-up period, the soil water content had time to reach a state in which it did not depend on the assumed initial conditions.For each location, the mean minimum and maximum groundwater level were set to the lowest level (5 m) to exclude simulation of capillary rise and to ensure that the response of crop yields to variable water balance

Table 1
Sites that are used in the study, with the name of the site, location, the years for which data is available, which variety was used or if a variety trial was used and information about fertilization trials and yield.conditions derived from different climate settings.

HUME-OSR
The HUME-OSR model is based on a library (HUME) of general components for soil processes and a specifically designed component for simulating crop development (Böttcher et al., 2016) and growth of oilseed rape (Müller, 2009;Weymann et al., 2017;Böttcher et al., 2020).HUME-OSR simulates soil and crop processes on a point scale and also incorporates biomass loss due to frost.The model simulates all aboveand belowground plant structures, in combination with water and nitrogen dynamics on a one-dimensional scale.The phenology component is based on the BRASNAP-PH model (Habekotté, 1997), which was extended to simulate the BBCH values of WOSR (Böttcher et al., 2016).The model development is based on detailed experimental data from Hohenschulen, Germany and has proven to be able to represent yields over a variety of European experimental studies (Böttcher et al., 2020).A set of the data represented in the previously mentioned study for evaluation purposes is also used in this study.

Model application
Both models were run with their default parameter values for WOSR unless otherwise specified (Supplemental Material S1 and S2).An additional model calibration to the data used in the current study would have given a good fit to the specific target population, but has as the disadvantage that the resulting genotype-dependent parameters are difficult to interpret and to compare between studies (Casadebaig et al., 2020)."Also are the genotype-dependent parameters found by calibration to field data not the "true" parameters (i.e., the values that one would obtain by studying each individual process of the crop model individually, and in the limit of a very large amount of data) " (Wallach, 2011).A site-specific soil profile was used derived from data provided by the national reports and agencies.
For the current climate, the results of the models were compared with the measured yield to assess the performance of the models using the root mean square error (RMSE) between the modelled and harvested yield (Eq. 1) as a performance indicator: where s is the simulated value, o is the observed value and n are the number of data points.Furthermore, the R 2 (coefficient of determination), MBE (mean bias error) and NSE (Nash-Sutcliffe Efficiency (Nash and Sutcliffe., 1970)) were calculated, by using the following formulas: (2) where o and s are the observed and simulated values; o and s are the means of all the observed and modelled values, and ô are the predicted values.

Climate change
Both models were run for each site to analyse the sensitivity to changes in temperature and precipitations.Systematic changes in temperature and precipitation provided different climate scenarios to investigate the sensitivity of model parameters and hence crop traits to changing climatic conditions.The temperature scenarios used in this study were the current climate (the climate when the field trials were conducted), and 2 • C and 4 • C increase in air temperature.These temperature changes were combined with 5 changes in precipitation (50 % and 25 % decrease, current, and 25 % and 50 % increase in precipitation), resulting in a total of 15 scenarios.The CO 2 concentration was kept at 400 ppm since the current version of HUME-OSR is not sensitive to changes in CO 2 concentration.Although an increase in air temperature is related to a higher atmospheric concentration of CO 2 , in this study this correlation was not included.

Parameter sensitivity
The sensitivity of each model with the specific climate scenarios was investigated by running the model and changing one-parameter-at-atime (OAT-method), which is a Morris screening method (Morris, 1991), to calculate the elementary effect (EE, Eq. 2).For any given parameter set of X, the elementary effect of the ith input is defined as: where X ∈ ω, except that X ≤ 1 − Δ, Δ is a predetermined multiple of 1/ (d − 1), in which d corresponds to the number of intervals/levels that a parameter range is divided (Morris, 1991).This method calculates the deviation of the modelled yield compared to the yield of the original model run and computes the elementary effects.In this study we focus on the mean of the distribution of the absolute values of the elementary effects, μ* (Eq.6, Campolongo et al.

Table 2
Parameters used in the sensitivity analysis performed with different air temperatures for HERMES (Kersebaum, 1995).ETA is actual evapotranspiration and ETP is potential evapotranspiration.
In which R is p + 1, where p is the number of factors.Since μ* is the sum of all the absolute elementary effects, μ* on its own is sufficient to provide a reliable ranking (Campolongo et al., 2007).All analyses were performed in R statistical software v3.5.0 (R Development Core Team.R Foundation for Statistical Computing, 2018) using the sensitivity package v1.15.0 (Gilles et al., 2017), in which the improvements suggested by Campolongo et al. (2007) and Pujol (2009) are included.
For each model, model parameters were chosen based on expert knowledge (i.e. the model developers) and parameters that could potentially be changed through plant breeding.This also reduced the parameters that could change and result in less potential problems with equifinality/correlation and has a significant positive effect on the computational time.The parameters used for the sensitivity analysis and their meanings, minimum, maximum and default values for the sensitivity analysis are presented in Tables 2 and 3 for of HERMES and HUME-OSR, respectively, in total 14 parameters for HERMES and 23 parameters for HUME-OSR.For each parameter in both models, a uniform prior distribution was applied in the analyses.
After the sensitivity analysis for each climate scenario per location, the parameters were ranked based on the μ* to identify the most sensitive parameters per climate scenario (Campolongo et al. 2007, Specka et al., 2015;Jabloun et al., 2018).For each location the μ* was scaled, before the sum of the ranks over each location per climate scenario was calculated (Specka et al., 2015).

Results
Both models simulate the phenology of the crop and can be aligned with the measured phenological stages.The measured phenological stages are the first leaf stage (BBCH 11), start of flowering (BBCH 61), end of flowering (BBCH 69) and ripe (BBCH 89).The HERMES model is able to simulate the phenological stages slightly better (Fig. 1a, Table 4) than the HUME-OSR model (Fig. 1b, Table 4), however both models have a very high R 2 and NSE value indicating a good fit with the data.At the Christgrün site, the HUME-OSR model overestimates the rate of phenological development.In all model runs for both HERMES and HUME-OSR the harvest date was fixed to the recorded harvest date and therefore differences in phenological stages do not influence the yield level.

HERMES
The simulated and measured yield of each experiment in Table 1 for the default model parameters of HERMES is compared in Fig. 2a and  Table 5.The overall fit of the model compared to the measurements was poor (R 2 = 0.08), as HERMES does not seem to represent the high interannual variability, the variability in site, cultivar and management in measured yield of WOSR (Rondanini et al., 2012).The root mean square error between all observations and all simulations is 0.65 Mg ha − 1 .
The model can simulate those sites with single varieties significantly better with the default parameters than other sites with multiple varieties from variety trials, the model performance indexes for each sitespecific and all sites combined are shown in Table 5.
Table 6 shows the ranking of the sensitivity of the HERMES model parameters for each climate scenario.For all sites combined, the parameter AMAX is the most sensitive under current climate and all climate scenarios apart from the L scenarios, which are the scenarios where the precipitation is reduced by 25 %.Under 25 % lower precipitation parameter kc2 becomes more sensitive.Another sensitive parameter is Drought_stress_5, which is drought stress during grain filling.With increasing precipitation for all three temperature scenarios, the parameter Drought_stress_1 becomes increasingly sensitive, and this trend is also be seen for all parameters associated with drought stress.The parameters that are the least sensitive are inikc, kc3 and kc6, which represent the initial Kc factor for evapotranspiration and the Kc factor for evapotranspiration for the periods from stem elongation until the start of flowering and during senescence, respectively.Under all temperature scenarios with an increasing amount of precipitation, the sensitivity to drought stresses increases, while the sensitivity to kc is reduced.

Table 3
Parameters used in the sensitivity analysis performed with different air temperatures for HUME-OSR (Böttcher et al., 2020).

HUME-OSR
The HUME-OSR model, with its default model parameters, underestimates the yield compared to the measured yields (Fig. 2b and Table 7, R 2 = 0.143).It was developed using data from one high yielding experimental site (Böttcher et al., 2020) and inadequate prediction of stress responses may underestimate the high variation in measured yields (Rondanini et al., 2012;Böttcher et al., 2020).The RMSE between the modelled and simulated yield over all locations is 1.12 Mg ha − 1 .The model can simulate sites with varied N supply significantly better than other sites with the default parameters, the model performance indexes for each site-specific and for all sites combined are shown in Table 7.
Table 8 shows the ranking of the sensitivity of HUME-OSR model parameters for each climate scenario.The most sensitive parameters for HUME-OSR for all climate scenarios are SLAHST, reflecting specific leaf area before stem elongation starts, and gh, reflecting the allocation of leaf matter before stem elongation, indicating a key sensitivity of the biomass production before stem elongation.With increasing precipitation rates the parameters b and AT4 become increasingly sensitive; these are parameters for the allometric equation of pod dry matter and the developmental rate during pod development until maturation, respectively.The sensitivity of fSLAHST and AT2 decrease with increasing precipitation rate; these are functional parameters for the calculation of the variable specific leaf area before stem elongation starts and the developmental rate during leaf development, respectively.
Under all climate scenarios, minor change in parameter rankings are found; the top 10 sensitive parameters stay sensitive over all scenarios.Also, for all climate scenarios, AT2A and pfW are ranked the lowest, indicating that the model is not sensitive to changes in the developmental rate during inflorescence emergence and that the parameter describing a non-linear response to drought stress is not sensitive.

Simulated WOSR yield under current climate
The two crop models, HERMES and HUME-OSR, simulate similar variation in the modelled yield compared to the variation of the measured yield (Fig. 2).None of the models was calibrated to the specific sites and varieties, and the default parameters were used.Based on the simulation of the phenological stages the default parameters of both models appear to be able to simulate a range of varieties.For HERMES the AMAX was changed prior to the sensitivity analysis, the new value of AMAX was not calibrated for a specific site.Based on the model runs with the default parameters, it can be seen that the models perform differently (Tables 5 and 7).Both HERMES and HUME-OSR generally perform better when considering data from all sites, rather than evaluating each site separately, since in many cases the data was from variety trials.For the sites with variety trials, it should be noted that the interannual variability is strongly over-laid by the number of different varieties with inherent variability in each year and a genetic trend over 20 years, which canot be captured with only one parameter set.However, the default parameters of HERMES seem to be able to perform slightly better over each site-specific compared to the model output of HUME-OSR with default parameters.Only for Châlons-en-Champagne, a site where both models are performing well, did HUME-OSR perform better then HERMES.
The model simulations did not account for the specific cultivars grown in the experiments, and this may have contributed to the deviation between simulated and measured values since cultivars vary in biomass, harvest index and the N content of the plant (Mendham et al., 1981;Berry and Spink., 2006;Rondanini et al., 2012;Weymann et al., 2015).This potentially results in a mismatch between modelled and measured yield, especially on sites with data from variety trials showing an inherent high variation between varieties.However, the modelled

Table 6
Parameter ranking based on the μ* values of the Morris method for HERMES on all sites under different climate scenarios in which the percentages depict the change of precipitation.The colour scale ranges from the most sensitive parameter (green) to the least sensitive parameter (red).The parameter decscription is in Table 2. yields are in the same ranges as the measured yields.Another source of yield variability is the uncertainty related to the soil data.Soil profiles were mostly derived from regional soil types with no details obtained at the specific locations when inventory data is used.Variety trials are performed at the same farm area, but field vary from year to year which causes additional yield variability.HERMES is sensitive to soil information (Wallor et al., 2018), e.g., the estimation of soil dependent maximum effective rooting depth is critical, since an overestimation of rooting depth would result in a weaker response to water and nutrient limitation.The same holds if capillary rise from a shallow groundwater table is considered.Another mismatch between the modelled and measured yield can derive from biotic and abiotic stresses not covered by the models.These stresses were assumed not to be present in the data, because the field experiments were assumed to have been well managed.

Model parameter sensitivity to climate change
The climate change scenarios were used to systematically address the potential changes without using specific downscaled local climate change scenarios.By increasing the temperature by 2 and 4 • C we maintained the inter-annual variability in the observed temperature series; however, the inter-annual variability may also be affected by climate change (Racsko et al., 1991).In this study, the CO 2 levels were kept constant, because a CO 2 fertilization mechanism is not implemented in the HUME-OSR model, while HERMES considers an effect of CO 2 on both, photosynthesis and transpiration (Kersebaum and Nendel., 2014).Since this study focuses solely on the sensitivity of the model parameters to changes in temperature and precipitation, we consider this simplification to be of minor importance, although increased atmospheric CO 2 is known to enhance photosynthesis.Precipitation typically has high local and inter-annual variation, and this also applies to climate change projections, where climate models show large differences in projections (Racsko et al., 1991;Semenov et al., 2010;Madsen et al., 2012).Therefore, we used five different levels of precipitation to study the sensitivity of the model parameters to yield.
The different precipitation levels in combination with the different air temperature levels, as an indicator of climate change, can reveal patterns in the sensitivity of the crop parameters and/or plant traits (Trnka et al., 2011;Rötter et al., 2018a).For HERMES under all temperatures, the sensitivity of drought parameters 1, 3 and 6 increased with increasing precipitation level (Table 5).Over the whole growing season, more water was available and hence greater growth can be achieved, due to lower drought stress.However, when water is not a limiting factor, other factors will become limiting for crop yield (Jabloun et al., 2018), for example, the availability of nutrients.This correlates with an increase of the sensitivity of kc2, the Kc factor for evapotranspiration of the period from emergence to stem elongation, under a 25 % reduction of precipitation.The sensitivity of this parameter decreases when the amount of precipitation increases indicating lower drought stress during the period from emergence to stem elongation.The changes in the order of the sensitive parameters are related to the partitioning of plant biomass during the specific development stages, where seed yield is solely the result of partitioning during the seed filling phase.Therefore, crop yield depends very much on the timing of nutrient or water shortage.
In HUME-OSR, drought reduces biomass growth by a soil water deficit factor, SWDF (Böttcher et al., 2020), which is a ratio between potential and actual transpiration and a parameter to describe a non-linear response to drought, pFW (Ferreyra et al., 2003).In all climate scenarios, this parameter is not found sensitive, which matches Table 8 Parameter ranking based on the μ* values of the Morris method for HUME-OSR on all sites under different climate scenarios in which the percentages depict the change of precipitation.The colour scale ranges from the most sensitive parameter (green) to the least sensitive parameter (red).The parameter description is in Table 3.
the results of HERMES indicating no major drought stress in the studies applied here.In HUME-OSR the order of sensitivity does not change under the different temperature and precipitation scenarios; in all scenarios, the SLAHST and gh parameters associated with leaf area before stem elongation are the most sensitive parameters.Stem elongation corresponds to BBCH stages 30-39 (Weber and Bleiholder., 1990;Lancashire et al., 1991) and occurs just after winter dormancy.The parameters indicate that in HUME-OSR, the crop development before winter, the period from emergence to stem elongation, is of critical importance for seed yield (Habekotté, 1997;Böttcher et al., 2016).The stem elongation stage has been identified as important for crop growth and yield in many winter crops, since in this period the flowers are developing, branching occurs and the roots will grow deeper (Rapacz and Markowski., 1999;Robertson et al., 2002).Biomass accumulation later in the growing season will result in a higher yield, based on the sensitive fPW-exp parameter that represents the partitioning factor for hull/pods and the fixed harvest index (Böttcher et al., 2020).It is interesting that the stem elongation phase stays sensitive even when air temperatures increase and precipitation levels change, i.e. other parameters become more limiting/sensitive to crop yield.Over the whole range of climate change scenarios, the sensitivity of the top ten model parameters does not change significantly (Table 8), showing that the other parameters have a low importance measure and therefore have negligible relevance for the model output.
In both models, the sowing date was kept constant, while changes in sowing dates might have a large effect, by overcoming unfavourable hot and dry weather during flowering (Qian et al., 2018;Pullens et al., 2019).Because of an increase in temperature, the longevity of specific developmental stages might change, i.e. the seed filling period will shorten and hence reduce the amount of radiation intercepted during this period, thereby leading to lower yields (Berry and Spink., 2006).
The two models used in this study were not in complete agreement with respect to the plant parameters that will be the most sensitive under the modelled climate scenarios for WOSR, since the different crop models each simulate the crop in a different way and have different functions or responses integrated.Nevertheless, is it in both models clear that a sensitive period is the period from emergence to stem elongation (period 2 in HERMES and gh and SLAHST in HUME-OSR).Since we simulate a winter crop that is sown in autumn, it is important for the plant to establish well before winter starts.Winter oilseed rape is typically sown earlier than many winter cereals, and it has considerable above-and belowground growth before the onset of winter.In HUME-OSR the parameters associated with above-ground biomass (GH, Gf, HH and Hf) are more sensitive than the parameters associated with the root growth and rooting depth (ROOTI, ROOTS, K_Z and ZR MAX ).In future climate and with future cultivar the farmers have to make adjustments to the sowing date, to have a well-established crop before winter.
In HERMES drought stress during grain filling (Drought stress 5) is a sensitive parameter, which has been identified as a factor that reduces yield in field studies (Porter and Semenov., 2005), and under higher temperatures the parameter stays sensitive.Rashid et al. (2018) found that seed yield was reduced when winter oilseed rape was exposed to temperatures above 25 • C during grain filling, because the harvest index is affected by heat stress (Angadi et al., 2000;Faraji et al., 2009;Qian et al., 2018).

Implications
Only by implementing crop models and climate scenarios can the potential vulnerabilities of WOSR be identified; however, the results presented in this study might not be directly applicable in crop breeding.The presented results are from a theoretical point of view, while practically there might be difficulties to modify plant traits.Since, the traits found to be important in our study may correlate with other traits (potentially not represented in the models).Nevertheless, our results point at important traits for further development and testing of promising hybrid cultivars (Oghan et al., 2018).In this study, we focussed on the direct effects of climate change (without CO 2 fertilisation) on crop physiology.In practice, other factors, like inability to access the field due to flooding and/or diseases or pests will also affect crop growth and productivity (Pullens et al., 2019).However, the results stress the importance of considering the abiotic stress factors in plant breeding to ensure that WOSR cultivars have sufficient resilience to climate change.Development of crops that are less drought-sensitive and more tolerant to higher temperatures is needed for adaptation of WOSR production to climate change.Potentially, some varieties/wild types are already less susceptible to drought and can be used as a starting point to develop varieties that are more climate change resilient.The measured yield variability within years is high and can become more predominant in the future since breeding strategies are more focused on the amount of oil than yield stability (Rondanini et al., 2012).

Conclusion
The effects of climate change can only be adequately studied by models that simulate verifiable effects on the crop yield under climate change.In this study, two models were used to identify the plant traits of relevance for crop responses under climate change, which in the model are represented as crop parameters that are sensitive to changes in air temperature and precipitation.The sensitivity analysis of the two models with changes in temperature and precipitation shows that for HERMES the parameters associated with drought are sensitive, even under the current climatic conditions where no drought stress is present, while for HUME-OSR this effect was not seen.The models indicate that the period from emergence to stem elongation is the most sensitive period for the effects of climate change on yield.Both models identify model parameters for the vegetative growth period as important, suggesting that crop breeding and crop management needs to focus on WOSR varieties and management strategies that are less droughtsensitive and more tolerant to higher temperatures during vegetative growth to provide resilience of WOSR under climate change.

Fig. 1 .
Fig. 1.Simulated versus measured phenological stages of winter oilseed rape (Mg ha − 1 ) for six locations over Europe.The phenology are modelled with the default parameter setting of HERMES (a) and HUME-OSR (b), with a 1:1 line in red and the linear regression between the model and measurement (dashed line).

Fig. 2 .
Fig. 2. Simulated versus measured yield of winter oilseed rape (Mg ha − 1 ) for six locations over Europe.The yields are modelled with the default parameter setting of HERMES (a) and HUME-OSR (b), with a 1:1 line in red and the linear regression between the model and measurement (dashed line).

Table 4
Model performance of HERMES and HUME-OSR for different phenologic stages.

Table 5
Model performance for HERMES for yield levels at six locations individually and all locations together.

Table 7
Model performance for HUME-OSR for yield levels for six locations individually and all locations together.