# Selecting crop variables and parameters for the calibration of a new cultivar in a crop model: A case study of winter wheat for STICS

Meije Gawinowski, Maël Aubry, Samuel Buis, Cécile Garcia, Jean-Charles Deswarte, Marie-Odile Bancal, Marie Launay

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## ► To cite this version:

Meije Gawinowski, Maël Aubry, Samuel Buis, Cécile Garcia, Jean-Charles Deswarte, et al. Selecting crop variables and parameters for the calibration of a new cultivar in a crop model: A case study of winter wheat for STICS. European Journal of Agronomy, 2025, 168, pp.127677. 10.1016/j.eja.2025.127677. hal-05135775

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Submitted on 30 Jun 2025

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# Selecting crop variables and parameters for the calibration of a new cultivar in a crop model: A case study of winter wheat for STICS

Meije Gawinowski<sup>a,b,*</sup>, Maël Aubry<sup>c,†</sup>, Samuel Buis<sup>d</sup>, Cécile Garcia<sup>b</sup>, Jean-Charles Deswarte<sup>b</sup>, Marie-Odile Bancal<sup>a,‡</sup>, Marie Launay<sup>c,§</sup>

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## ARTICLE INFO

Keywords:

Calibration

Estimation

Crop model

Winter wheat

Varietal parameters

## ABSTRACT

Crop models need to be regularly updated with parameterizations for new cultivars, but this requires calibration, which is a major challenge. Using the winter wheat cultivar Rubisko as a case study, we applied for the first time on experimental data a new calibration protocol to estimate the parameters of the STICS crop model for this new cultivar with multi-trial experimental data. We tested the calibration protocol in different conditions, with or without LAI and/or biomass experimental data, and we found that the resulting LAI and biomass dynamics strongly diverged. This study contributes to provide guidance to modelers for the calibration of a new cultivar in a crop model by focusing on the selection of variables and parameters to estimate as well as criteria for evaluating calibration strategies. With an application to winter wheat for the STICS crop model, this study has shown that the choice of calibration steps has a major impact on simulated outputs, but with a strong dependence on the structure of the experimental dataset. Firstly, this paper provides a methodology for the selection of calibration variables and associated parameters based on three criteria: 1) the relevance of the values of the estimated parameters, 2) the bias part of the mean square error, and 3) the analysis of the residuals. Secondly, by applying this methodology, we have shown that calibration based on LAI measurements is the most robust in the case of sparse observed data at the end of the cycle. Based on these results, we recommend caution when including parameters related to radiation-use efficiency; in particular, they should not be calibrated together with parameters related to leaf growth on biomass data alone. This study has enabled an appropriate calibration strategy to be defined, which will allow more modern French wheat cultivars to be parameterized in the STICS crop model.

## 1. Introduction

"Soil-crop" models are process-based models that simulate crop growth, soil water and nitrogen dynamics in response to environmental variability and agricultural practices. These models have been developed since the 1960s and are used worldwide for many purposes, such as yield forecasting (Chenu et al., 2017), supporting crop breeding (Chenu et al., 2017; Cooper et al., 2021), and assessment/prediction of climate change impacts (Lobell and Asseng, 2017). Uncertainty in crop model simulations is mostly due to model structure (i.e., the chosen formalisms of the different processes) and parameter values (Chapagain et al., 2022; Wallach and Thorburn, 2017). However, it should be noted that model

inputs, such as climate data or initial soil conditions, are also significant sources of uncertainty. Some plant parameters may be generic, while others may be species- or cultivar-specific (Casadebaig et al., 2020). For example, for winter wheat, one of the most important crops in the world and in France, phenology is highly heritable, well characterized by breeders, and usually calibrated first for new cultivars (Wallach et al., 2023). Since breeding progress is still increasing, newer cultivars with new characteristics are released each year. As choosing a cultivar is an important agricultural practice, it is important that crop models keep up with these new cultivars, as these new characteristics are of interest in terms of production potential or stress tolerance for example, which is particularly important when studying the effects of climate change on

<footnote><sup>a</sup> Université Paris-Saclay, INRAE, AgroParisTech, UMR Ecosys, Palaiseau 91120, France</footnote>

<footnote><sup>b</sup> Arvalis - Institut du Végétal, Villiers-le-Bâcle, France</footnote>

<footnote><sup>c</sup> INRAE, AgroClim, Avignon 84914, France</footnote>

<footnote><sup>d</sup> INRAE, UMR, EMMAH, Avignon 1114, France</footnote>

<footnote>* Correspondence to: 22 place de l'Agronomie, Palaiseau 99120, France.</footnote>

<footnote>E-mail address: meije.gawinowski@inrae.fr (M. Gawinowski).</footnote>
crops using simulation studies. Since crop models need to keep up with the evolution of agricultural practices, such as cultivar selection, it is therefore necessary to regularly include new cultivars in their parameterization. This requires the estimation of cultivar-dependent model parameters using measurements. In this study, we address the calibration of a new cultivar in a crop model, using winter wheat as a case study for the STICS crop model.

The aim of calibration is to improve parameter estimates by minimizing the error between model outputs and observed data. This is a challenging task, as the modeler has to make many decisions that can affect the results, as shown in the framework of the AgMIP initiative (Agricultural Model Inter-comparison Project; Rosenzweig et al., 2013) with the inter-comparison of calibration practices among crop modelers (Wallach et al., 2021): the choice of parameters to include and their range of variation, often based on the modeler's expertise and/or after sensitivity analysis; the choice of target output variables, some of which carry important experimental uncertainty; the choice of the algorithm (e.g. frequentist vs. Bayesian); the choice of the loss function; the choice of sequential vs all-together protocol; and the choice of the calibration vs. evaluation data sets. The inter-comparison of Wallach et al. (2021) showed that these different choices led to heterogeneous calibration results, even for groups of modelers using the same model and dataset. Consequently, Wallach et al. (2023) developed and tested a common calibration methodology for phenology with a given simplex algorithm and a given loss function for given target variables (phenological stages only) on observed French data. The modelers were allowed to choose the parameters to be calibrated with a detailed documentation of the process, distinguishing the major obligatory parameters from the candidate parameters, which are only included if their calibration reduces the AICc (Akaike Information Criterion corrected). The use of this common calibration methodology reduced the variability between modelers, but also the prediction error. The next step was to generalize this methodology to multiple types of data in crop models. To this end, a general methodology was recently developed and tested on synthetic data in Wallach et al. (2024), who developed a sequential approach for the calibration of different processes corresponding to different target variables and target parameters, with each step fed by the parameter values estimated in the previous step. In this study, we apply for the first time this methodology described by Wallach et al. (2024) to the calibration of a new winter wheat cultivar in the STICS crop model.

Parameter estimation is not straightforward because the number of parameters that can be optimized in crop models is important, while the number of observations is limited, which is a common restriction when crop models are calibrated (Seidel et al., 2018), with many interactions between parameters. Many authors have highlighted the importance of increasing the quantity and quality of the observations on which the quality of the model calibration depends (Basso et al., 2010; Beaudoin et al., 2008; Dumont et al., 2014; Hernández-Ochoa et al., 2024). In addition, the spatial and temporal patterns (especially in terms of soil, management and weather conditions) of the observations can be narrow, leading to larger errors in the validation or application of the model, as the calibration may not be representative in a wide range of environments (Hernández-Ochoa et al., 2024; Thorp et al., 2007). This highlights the importance of carefully selecting the measurements to be collected so that they can be carried out in a wider range of environments. Research by Guillaume et al. (2011) specifically addressed this issue, demonstrating that dynamic variables should only be included as target variables if the goal is to improve model predictions for both dynamic and end-of-season variables, rather than end-of-season variables alone. However, dynamic variables such as Leaf Area Index (LAI) and plant biomass are crucial for understanding carbon, nitrogen and water dynamics. For example, LAI has a strong influence on plant transpiration, which is a major concern when studying the effects of climate change on crops (Farooq et al., 2011). Therefore, an accurate simulation of these variables is crucial for the considered application framework. However, some of these dynamic variables are either

time-consuming to measure and therefore rarely available, or when measured, cover a range of variables with different ecophysiological meanings that are more or less consistent with the simulated variables from the model. This is particularly true for LAI, as this term groups very different variables such as GLAI (Green LAI), PAI (Plant Area Index, including stems and ears), or effective LAI (accounting for clumping effects), without a systematic definition (Fang et al., 2019). Moreover, LAI can be measured using different direct or indirect methods, some of which are known to underestimate LAI (Yan et al., 2019); they also integrate different spatial (from plot to field) and temporal (from day to cycle) scales. As a result, large uncertainties arise from LAI measurements, making it useful to explore different calibration strategies that may or may not include this variable. Even if the confidence level is higher for biomass measurements, it is also interesting to consider calibration strategies without this variable due to its high acquisition cost. Therefore, in this study we will explore different calibration strategies, including LAI and/or biomass observations.

In this paper, we adapted and applied for the first time the general method of Wallach et al. (2024) for the calibration of a new winter wheat cultivar in the STICS crop model based on experimental data provided by Arvalis, a French agricultural technical institute. In this method, we have investigated different calibration strategies, focusing on the availability of LAI and/or biomass observations. Our objective is to identify and prioritize the variables and parameters to be considered for the calibration of a new cultivar and to propose criteria for the evaluation of the tested strategies.

## 2. Materials and methods

### 2.1. Experimental data set

The target population was wheat fields in the main wheat-growing areas of France, sown with the winter wheat variety Rubisko and managed using standard agricultural practices with sufficient N fertilization to avoid N stress. Crop measurement and management data, as well as weather data, were provided by ARVALIS - Institut du vegetal, a French technical agricultural institute that conducts multi-year, multi-purpose trials, including variety trials, at several sites in France. Weather data came from weather stations close to each field and were supplemented by the SAFRAN meteorological reanalysis (Quintana-Seguí et al., 2008; Vidal et al., 2010) when missing. Daily variations of different climatic variables are shown in Figure S1. The Rubisko data (see Fig. 1 for the map) were divided into a calibration subset of 67 environments (17 sites, 6 years) and an evaluation subset of

<figure><img src="image_5.png" /><figcaption>Fig. 1. Map of France with the different sites of the multi-trial data from Arvalis. Point color represents the subset of each site and point size is proportional to the number of experimented years for each site.</figcaption></figure>
14 environments (12 sites, 6 years, details in Table S1). This separation was done manually by trying to maximize independence between the two subsets with respect to year and site; it was not possible to completely separate years and sites for the validation dataset, but there is no common year x site combination between the two subsets. In the following, we consider an environment to be a site x year combination.

Observed data were phenological dates for start of elongation (BBCH30), start of heading (BBCH 50), anthesis (BBCH 65) and harvest; in-season LAI from sowing to anthesis; in-season aboveground plant biomass (t/ha) from sowing to harvest; end-of-season grain number (per m²) and grain yield (t/ha) at harvest. Phenological stages were measured conventionally; ear 1 cm observations are made on multiple days by measuring ear length on 20 plants per plot over three blocks, then applying a correction model to determine the exact day the ear was 1 cm long; heading is measured when half of the ears have emerged from the sheaths, and anthesis is calculated with a correction model based on the heading date. Prior to 2020, LAI was measured using photographs taken at 57°, and from 2021 onwards measurements were done using the LITERAL device, which is composed of three high-resolution cameras and an integrated processing chain (DE Solan et al., 2024). Plant biomass is measured destructively on three samples per plot and per date after drying at 80 °C for 48 h. At harvest, grain yield is measured either directly on-board by the combine harvester or by weighing the resulting grain bags divided by the plot area. A correction coefficient for moisture is then applied to the grain yield based on a sample dried at 130 °C for 24 h. Grain number is then determined based on the thousand-kernel weight measured on several samples.

## 2.2. STICS crop model and model initial conditions

STICS (V10.1.0) is a dynamic 1D soil-crop model that integrates crop development, growth, and yield formation with the carbon, nitrogen, energy, and water cycles of the soil-crop system (Beaudoin et al., 2023). It operates on a daily time-step using input data on climate, crop species, soil conditions, agricultural management practices, and initial system states such as water and nitrogen content for each soil layer. Biomass growth is primarily driven by light interception, modeled using the big leaf approach based on leaf area index and Beer's law of light extinction, combined with radiation-use efficiency. Plant development is driven by thermal time, adjusted for vernalization and photoperiodic effects. Factors such as frost, nitrogen, sub-optimal temperatures or water deficiency can stress the crop, potentially affecting development, leaf area, growth and yield. General soil characteristics (depth, water content at field capacity and wilting point, bulk density and other physical and chemical properties) were provided by Arvalis and are shown in Figure S2. The simulations were restarted each year at the end of September (27th or 28th, i.e. day of year 270), a few weeks before sowing, with initial water availability set to field capacity on all horizons. Data from the Belgian white reports on cereals (https://livre-blanc-cereales.be/category/livreblanc/) and (Beaudoin et al., 2005) were used to determine the initial N availability after the previous crop.

## 2.3. Calibration method and protocol

### 2.3.1. Choice of parameters to estimate

The default values for the Rubisko parameters correspond to the already calibrated values for the cultivar Arminda, which is analogous to Rubisko in terms of precocity. Choosing model parameters to be estimated is a key decision for the modeler. This choice consists of deciding which parameters to calibrate and whether to include them as major or candidate parameters, as suggested by Wallach et al. (2024). This choice is primarily driven by data availability, but as crop models such as STICS have a high number of parameters (52), a choice has to be made (Wallach et al., 2021). The consensus is to calibrate the most sensitive parameters, which have been previously identified either through sensitivity analysis and/or by expert knowledge. However, when

calibrating new cultivars, the varietal specificity of model parameters should also be considered a priority. In fact, in STICS almost half of the parameters are considered as varietal (i.e. depending on the variety), while the others are specific; this suggests that only varietal parameters need to be calibrated to parameterize a new cultivar. The decision process for the parameters to be calibrated is shown as a decision tree in Figure S3 and detailed in Table S2. We therefore proceeded as follows: among the many parameters to be estimated, priority was given to those to which the model variables of interest are sensitive (Ruget et al., 2002). Parameters with low sensitivity were left at their default values, i. e. Arminda's parameters, in particular those parameters involved in the model's "satellite" calculations (i.e. those that do not have a direct impact on the functioning of the system in terms of growth and development). Among the sensitive parameters, the value of some is easily accessible through bibliography, measurements or expertise. Others are difficult to determine experimentally and must be estimated in some other way.

However, the varietal nature of the STICS plant parameters is regularly challenged and updated as knowledge of varietal behavior is gained, as is the case for radiation-use efficiency (efcroiveg, efcroirepro), particularly because some recent breeding efforts have targeted this trait (Govind et al., 2023; Stella et al., 2023). Indeed, for modern cultivars such as Rubisko, such a varietal specificity may be at play, so these parameters were added. In addition, some non-varietal parameters are routinely included in AgMIP exercises because their varietal status is discussed and they are sensitive (Wallach et al., 2024 and ongoing AgMIP calibration exercises); this is the case for cgrain and irmax, which we also included for grain number and yield prediction. For grain number, we chose to fix the varietal parameter nbgrmax (maximum grain number) to the observed experimental value plus 10%, as for AgMIP exercises; although it is highly sensitive, this maximum limit can be difficult to calibrate. In STICS, grain number is determined during a given period of time around anthesis with the varietal parameter nbjgrain usually set to 30 days and the non-varietal slope cgrain. However, Artru et al. (2018) found that this value is overestimated and should be set to 15 days. Accordingly, we decided to set nbjgrain to 15 days and rather calibrate the parameter cgrain. We therefore chose to calibrate 8 out of 52 parameters: 4 for phenology (step 1 of the calibration procedure; see Fig. 2), 2 for leaves (step 2), and 2 for yield formation (step 5). These parameters are listed in Table 1 with their definitions, units, limits and default values.

### 2.3.2. Application of the methodology of Wallach et al. (2024)

To calibrate the STICS model, we used the method developed by Wallach et al. (2024), following the recent calibration work done with AgMIP, using the R package CroptimizR (Buis et al., 2023) in combination with its wrapper function for STICS available in the R package SticsOnR (Lecharpentier et al., 2023) and the Nelder-Mead simplex algorithm that was used as in Wallach et al. (2024). Two types of parameters are considered in this protocol: major parameters, which are assumed to influence the simulated target variables in almost all environments, and candidate ones with a more uncertain and/or secondary influence (see Table 1 for the distinction). This protocol is divided into preliminary steps (gray boxes in Fig. 2) and a final step (red box in Fig. 2). Each preliminary step corresponds to the calibration of a given process with a loss function based on ordinary least squares (OLS, Eq. (1)) and parameter selection with the Akaike Information Criterion corrected (AICc, Eq. (2)) as described in Wallach et al. (2023):

$$OLS_v = \sum_{i,j} (Y_{ijv} - f_{jv}(X_i, \theta))^2 \# \quad (1)$$

$$\Delta = AICc_v = N_v \times \ln(MSE_v) + 2 \times \ln(N_v) \times p_v \# \quad (2)$$
<figure><img src="image_6.png" /><figcaption>**Fig. 2.** Flow diagram for the calibration protocol decomposed into different sequential preliminary steps focusing on single processes and target variables (gray boxes), here phenology (stlevamf, stamflax, stlevdrp, stdrmat + jvc as candidate), LAI growth (dlaimaxbrut, durvieF), biomass production (efcroiveg, efcroirepro), grain number (cgrain) and grain yield (vitircarb + irmax as candidate), and a final step with all the different variables (red box). Different calibration strategies including LAI and/or biomass data are explicit: 1) No LAI nor biomass data, 2) Only LAI data, 3) Only biomass data including A) Both RUE and LAI parameters, or B) Only LAI parameters, and 4) Both LAI and biomass data. Phenology includes dates of ear 1 cm, flag leaf, anthesis and harvest.</figcaption></figure>

<table><caption>**Table 1**
STICS parameters selected for calibration.</caption><thead><tr><th>Step</th><th>Parameter</th><th>Type</th><th>STICS name and unit</th><th>Range</th><th>Default value</th></tr></thead><tbody><tr><td rowspan="6">1) Phenology</td><td>TT emergence - BBCH30</td><td>Major</td><td>stlevamf (°Cd)</td><td>[150,1000]</td><td>700</td></tr><tr><td>TT BBCH30 - BBCH50</td><td>Major</td><td>stamflax (°Cd)</td><td>[100,500]</td><td>375</td></tr><tr><td>TT BBCH50 - BBCH65</td><td>Major</td><td>stlevdrp (°Cd)</td><td>[500,2000]</td><td>837</td></tr><tr><td>TT BBCH65 - BBCH90</td><td>Major</td><td>stdrmat (°Cd)</td><td>[500,1000]</td><td>700</td></tr><tr><td>Number vernalizing days</td><td>Candidate</td><td>jvc (days)</td><td>[40,60]</td><td>51</td></tr><tr><td>Maximum rate of gross daily increase of LAI</td><td>Major</td><td>dlaimaxbrut (m²/plant/°Cd)</td><td>[0.000005, 0.001]</td><td>0.00047</td></tr><tr><td rowspan="2">2) LAI growth</td><td>Maximum leaf lifespand</td><td>Major</td><td>durvieF (unitless)</td><td>[40,300]</td><td>200</td></tr><tr><td>Maximum RUE during vegetative phase</td><td>Major</td><td>efcroiveg (g/MJ)</td><td>[3,5]</td><td>4.25</td></tr><tr><td rowspan="2">3) Biomass production</td><td>Maximum RUE during reproductive phase</td><td>Major</td><td>efcroirepro (g/MJ)</td><td>[2,5]</td><td>4.25</td></tr><tr><td>Slope relationship between grain number and growth rate</td><td>Major</td><td>cgrain (grains/g/day)</td><td>[0.03, 0.04]</td><td>0.036</td></tr><tr><td>4) Set of grain number</td><td>Rate of increase of C harvest index versus time</td><td>Major</td><td>vitircarb (g grains/g plant/day)</td><td>[0.00005, 0.002]</td><td>0.0007</td></tr><tr><td>5) Grain filling</td><td>Maximum C harvest index</td><td>Candidate</td><td>irmax (unitless)</td><td>[0.45, 0.6]</td><td>0.55</td></tr></tbody></table>

$$ MSE_v = \frac{1}{N_v} \times \left( \sum_{i,j} (Y_{ijv} - f_{jv}(X_i, \theta))^2 \right) \# \quad (3) $$

where $Y_{ijv}$ is the observed value for the $i^{th}$ time point in the $j^{th}$ situation, $f_{jv}(X_i, \theta)$ is the corresponding model prediction for variable v with $X_i$ the inputs, $\theta$ is the vector of parameters to be estimated, $MSE_v$ is the mean square error for variable v computed as the difference between observed and simulated values across all environments for variable v, $N_v$ is the number of data points and $p_v$ is the number of estimated parameters. For each process, a set of major parameters is estimated. The parameter selection process is applied to an additional set of candidate parameters that explain some of the remaining variability. Calibration is first performed with the major parameters only, then again with additional candidate parameters, and if the corresponding corrected AIC criterion is lower, then the candidate parameter is selected; otherwise it is set to its default value. In each step, the estimated parameters are then forced for calibrating the next process; for example, the phenological parameters estimated in step 1 are used for the next steps. Then, in the final step, all the different processes and their target variables are included to calibrate the major and previously selected candidate parameters with a loss function based on weighted least squares (WLS), with initial parameter values set to previously estimated ones and weight values set to the error variances as estimated after the preliminary steps.

$$ WLS = i.j.v \left( \frac{Y_{ijv} - f_{jv}(X_i, \theta)}{\omega_v} \right)^2 \# \quad (4) $$

$$ \omega_{i,j,v} = \frac{\sum_{i,j} (Y_{ijv} - f_{jv}(X_i, \theta))^2}{N_v - p_v} \# \quad (5) $$

where $\omega_{ijv}$. The different calibration steps have been chosen following the work of Wallach et al. (2024). They are chosen according to the availability of observed data and their order is based on their chronology and level of dependence according to the model structure (chosen formalisms of the different processes). Here these steps correspond to phenology, LAI growth, production of plant biomass, grain number and grain yield at harvest. Since LAI and biomass data are not systematically measured in Arvalis trials due to their higher acquisition cost, we explored different options for the steps corresponding to these variables (LAI growth and biomass production):

* Strategy 1 - No LAI, no biomass data available

* Strategy 2 - Only LAI data available

* Strategy 3 - Only biomass data available

A) Estimation of both RUE and LAI parameters

B) Estimation of LAI parameters only

Strategy 4 - Both LAI and biomass data available

## 2.4. Evaluation criteria of the tested calibration strategies

In order to assess the quality of the calibration for the different
strategies studied, we propose to examine three criteria:

* Comparison of the estimated values for the different parameters, paying particular attention to the parameter values estimated at the lower and upper bounds and to the physiological plausibility of the estimated values

* Comparison of errors by calculating the mean square error (MSE<sub>v</sub>, Eq. (5)) and the root mean square error (RMSE<sub>v</sub>, Eq. (6)) for each variable v, where vobs<sub>i</sub>(t) and vsim<sub>i</sub>(t) are the observed and simulated values for environment i, time t and variable v, and N<sub>v</sub> is the number of observed values for this variable v (across environments and time):

$$MSE_v = \frac{1}{N_v} \times \sum_{i,t} (vobs(t) - vsim(t))^2 \quad (5)$$

$$RMSE_v = \sqrt{MSE_v} \quad (6)$$

In particular, MSE can be decomposed into bias and difference in variability, as in Guillaume et al. (2011):

$$MSE_v = bias_v^2 + SDSD_v + LCS_v \quad (7)$$

$$bias_v^2 = ( \overline{vobs} - \overline{vsim} )^2 \quad (8)$$

$$SDSD_v = (\sigma_{obs_v} - \sigma_{sim_v})^2 \quad (9)$$

$$LCS_v = 2 \times \sigma_{obs_v} \times \sigma_{sim_v} \times (1 - r) \quad (10)$$

where $\overline{vobs}$ ($\overline{vsim}$) is the mean of the observed (simulated) values, $\sigma_{obs}$ and $\sigma_{sim}$ are the standard deviations of the observed and simulated values and r is the correlation between observations and simulations. As detailed in Guillaume et al. (2011), the bias component expresses the mean difference between observations and simulations, the SDSD component expresses variance error, i.e. the difference in variability between observations and simulations and the LCS component is the remainder with no interpretation, corresponding to noise/-irreducible error.

* Evaluation of residuals, calculated as the difference between observed and simulated values for environment i, time j and variable v such as:

$$res_{ijv} = vobs_{ij} - vsim_{ij} \quad (11)$$

Residuals can be examined according to time or observations; they should be close to zero, and they should be similar across time or observations. Therefore, residual smooths should be as flat as possible and close to 0. Positive biases indicate underestimation in the simulations, while negative biases indicate overestimation.

Mean square errors and residuals are examined for both the calibration and evaluation subsets; analysis of the calibration subset assesses the quality of the calibration methodology whereas analysis of the evaluation subset assesses the effectiveness of prediction.

## 2.5. Data availability

The experimental dataset provided by Arvalis is not made available for confidentiality reasons, but the calibration methodology we applied is based on the open-access model STICS (Beaudoin et al., 2023), the open-access R packages SticsOnR (Lecharpentier et al., 2023) and CroptimizR (Buis et al., 2023), and the application of the calibration methodology from Wallach et al. (2024) is also open-access.

# 3. Results

## 3.1. Values of estimated parameters

Phenological parameters (stlevamf, stamflax, stlevdrp, stdrmat and jvc) are estimated similarly between the different strategies (Fig. 3), but this is not the case for LAI and biomass parameters, leading to contrasting simulations between strategies (Fig. 4). LAI parameters (dlaimaxbrut, durvieF) are estimated at different values between the different strategies; leaf lifespan durvieF is notably estimated at the upper bound of 300°Cd for the strategy “Biomass (no RUE)”. There is also a limit issue for the vegetative radiation-use-efficiency parameter efcroiveg at the upper bound of 5 g/MJ with the strategy “Biomass (with RUE)”. Moreover, with this strategy, besides estimating efcroiveg at the upper bound, LAI parameters dlimaimaxbrut and durvieF are also estimated at lower values than the other strategies, resulting in lower LAI dynamics (Fig. 4A). However, for the “LAI+Biomass” strategy, the LAI parameters are estimated at similar values to the “LAI” strategy, and efcroiveg is estimated at 4.5 g/MJ, closer to the default value. For the reproductive radiation-use-efficiency parameter efcroirepro, there is no limit issue, but the estimated values are quite low at 3.25 and 2.4 g/MJ for the “Biomass (with RUE)” and “LAI + Biomass” strategies respectively.

## 3.2. Comparison of square errors

Firstly, the different strategies reduced the mean error compared to the default parameterization of the Arminda cultivar for all the considered variables (Table 2 for phenological stages, Table S3 for the other variables), despite their similarity. The RMSE values are similar for phenological stages between calibration strategies (Table 2), in line with the similarity of the estimated parameter values. Errors are quite low and acceptable for the different phenological stages, with similar values between the calibration and evaluation subsets.

For the other variables, the results are more contrasted (see Table S3 for RMSE values and Fig. 5 for MSE decomposition), still with error reduction for all the calibration strategies compared to Arminda’s default parameterization for both the calibration and evaluation subsets (except for grain number for evaluation). For plant biomass, grain number and grain yield, bias and variability components are strongly reduced compared to Arminda’s parameterization; the MSE is mostly explained by the remaining component. This is not the case for LAI, where bias and variability persist for both subsets. For LAI, the MSE is the lowest for the strategies that include LAI data, i.e. “LAI” and “LAI + Biomass”, and the MSE is particularly high for the strategy “Biomass (with RUE)” with large bias. For plant biomass, the MSE values are similar between strategies but still slightly lower when LAI and/or biomass data are included in the calibration procedure. For the evaluation subset, there is some persistent bias for plant biomass for all strategies except for “LAI + Biomass”. For grain number and grain yield, the MSE is the lowest for the “No LAI, no biomass strategy”. However, the “LAI + Biomass” strategy is not too far behind; in fact, it is the strategy with the lowest bias values for the different variables of interest. There is also some persistent bias for grain yield with the calibration strategy for both subsets.

## 3.3. Analysis of residuals

Analysis of the residuals allows us to assess how the variables of interest are either underestimated, overestimated or well estimated over time (Fig. 6). For LAI, residuals are similar between the calibration strategies and always positive (underestimated simulations), furthermore they increase with observations similarly for both the calibration and evaluation subsets. The flattest LAI residuals are obtained with the “LAI” and “LAI + Biomass” strategies. For plant biomass, residuals also increase with observations (underestimated simulations), with strong deformations for the “LAI + Biomass” strategy. Residuals are similar
<figure><img src="image_7.png" /><figcaption>Fig. 3. Estimated values of calibrated parameters for each calibration strategy and default Arminda values. Black dashed lines represent lower and upper bounds.</figcaption></figure>

between the other strategies, centered around zero with low de-
formations, until 12 t/ha where they start to increase; residuals remain
the flattest for the “LAI” strategy.

4. Discussion

4.1. Evaluating calibration strategies: what is the best option?

Firstly, the calibration improved the fit of the model to the experi-
mental data across all strategies compared to Arminda’s default
parameterization. Phenology is well estimated across all strategies, with
almost identical estimated parameter values and error values; this sta-
bility in the estimation of phenological parameters is reassuring as it
shows that there is no compensation between phenology and other
processes, regardless of the choice of calibration steps. However,
parameter estimates related to LAI growth and biomass production are
contrasted across strategies, resulting in divergent simulated outputs,
raising the question of the best option based on three criteria: the values
of the estimated parameters, the error values and their bias components,
and the residuals.

4.1.1. Comparing estimated parameter values

When comparing estimated parameter values between different calibration strategies, attention must be paid to their physiological plausibility. In particular, parameters estimated at upper or lower bounds need to be closely analyzed; they may indicate that either the chosen ranges of variation for these parameters are too restricted, the optimization algorithm is not performing well, or the available experimental observations are not suitable for calibrating these parameters. In this study we have chosen large ranges, based on Wallach et al., (2024) and ongoing AgMIP calibration exercises. In addition to bound issues, it is also important to analyze parameters estimated at values significantly different from the default values considered, especially when considering wide ranges of variation. These wide ranges make it possible to check that a parameter is estimated at a plausible value, even if its variation is not too restricted. As the parameter values are very specific to each model, even for generic parameters such as RUE, they cannot always be related to the existing literature, so the plausibility of the parameter values is mostly based on expert knowledge. In our study, some of these issues can be raised:

* In the strategy “Biomass (with RUE)”, the vegetative RUE parameter *efcroiveg* is estimated at the upper bound of 5 g/MJ, which is not considered physiologically reasonable and too high compared to the default value of 4.25 routinely used in STICS. This shows that when LAI and RUE parameters are calibrated together on biomass data, the algorithm favors the adjustment of RUE as the easiest (i.e. most

direct) way to impact biomass. However, with the strategy “LAI + Biomass”, where these parameters are calibrated separately, *efcroiveg* is estimated at a reasonable value of 4.45 g/MJ.

* The reproductive RUE parameter *efcroirepro* is estimated at low values for the strategies “Biomass (with RUE)” and “LAI + Biomass”, respectively at 3.24 and 2.35 g/MJ. Even if the lower bound is not reached, this decrease in reproductive RUE is not physiologically plausible; it is very unlikely that this trait, if varietal, has decreased in modern cultivars. These estimates are likely due to the lack of biomass data at the end of the growing season, but difficulties in estimating *efcroirepro* could also be due to the structure of the model; if LAI and biomass are linearly related during the vegetative phase, this is not the case during the reproductive phase (Varlet-Grancher et al., 1981). There is also a risk that these low values for *efcroirepro* lead to underestimated biomass simulations during the reproductive phase, although this cannot be assessed due to the lack of data.

* For the strategy “Biomass (no RUE)”, the leaf lifespan parameter *durvieF* is estimated at the upper bound of 300, which is not considered physiologically reasonable with respect to the default value of 200 routinely used in STICS. In addition, some complementary simulations (data not shown) showed that when extending the upper bound to 400, *durvieF* is still estimated at the upper bound. Moreover, all strategies lead to high values of *durvieF* even if the upper bound is not reached (except for “Biomass (with RUE)” as mentioned above), likely due to the lack of LAI data during senescence.

Overall, there were some difficulties in estimating the parameters *efcroiveg*, *efcroirepro*, and *durvieF*; for *efcroiveg* this is due to the structure of the model and the choice of calibration, but for *efcroirepro* and *durvieF* this is most likely due to a lack of data. There is a likely propagation of error between the two parameters with possible compensation; in Wallach et al. (2024) *efcroirepro* was also estimated at a lower value than the true value used to generate synthetic data, but this was likely due to the fact that some other candidate parameters were not selected and were therefore set at values different from the true ones; this was notably the case for *durvieF* with a higher value of 260°Cd. The concerns expressed about the estimated parameter values raise red flags for several strategies: “Biomass (with RUE)”, “Biomass (no RUE)” and “LAI + Biomass”.

Beyond the comparison of the considered calibration strategies, for
grain number *cgrain* values were estimated similarly across strategies,
most likely due to the fact that grain number depends on plant biomass
around anthesis when simulated biomass is still similar between the
strategies. However, the calibrated *cgrain* values are lower than the
default value for Arminda; this is due to the different value of the
parameter *nbjgrain*, which controls the time period before anthesis for
<figure><img src="image_8.png" /><figcaption>**Fig. 4.** Observed and dynamic variables observed and simulated by STICS for the calibration and evaluation data sets A) LAI and B) Plant biomass (in t/ha). Black points represent observations, colored lines represent the average of the variables over the different simulations for each calibration strategy and the colored ribbon represents the standard error around the mean.</figcaption></figure>

grain number determination, which we set at 15 days instead of the default 30 days according to Artru et al. (2018). For grain yield, the estimated values of *vitircarb* are higher than the default Arminda and *irmax* values are lower than the default specific value, almost reaching the lower limit due to the compensation between the two parameters. Indeed, for the preliminary calibration step on grain yield *vitircarb* is

estimated at values closer to the default around 0.011, and the candidate parameter *irmax* is selected and calibrated to a lower value around 0.45 as it improves the AICc selection criteria, but during the final calibration step, *vitircarb* is ultimately estimated at higher values around 0.015. This compensation questions the relevance of including the specific parameter *irmax* in the calibration procedure, even if it was selected with an
<caption>**Table 2**</caption>

RMSE values (in days) for the different phenological stages (ear 1 cm, flag leaf, anthesis and maturity) for the calibration and evaluation datasets for each calibration strategy.

<table><thead><tr><th rowspan="2">Calibration option</th><th rowspan="2">Dataset type</th><th colspan="4">Phenological stage</th></tr><tr><th>Ear 1 cm</th><th>Flag leaf</th><th>Anthesis</th><th>Harvest</th></tr></thead><tbody><tr><td rowspan="2">Arminda</td><td>Calibration</td><td>10.78</td><td>17.62</td><td>16.24</td><td>12.31</td></tr><tr><td>Evaluation</td><td>10.93</td><td>15.09</td><td>13.24</td><td>11.36</td></tr><tr><td rowspan="2">No LAI, no biomass</td><td>Calibration</td><td>5.62</td><td>4.28</td><td>4.08</td><td>6.33</td></tr><tr><td>Evaluation</td><td>5.17</td><td>4.33</td><td>5.06</td><td>7.10</td></tr><tr><td rowspan="2">LAI</td><td>Calibration</td><td>5.55</td><td>4.34</td><td>4.18</td><td>6.23</td></tr><tr><td>Evaluation</td><td>5.24</td><td>4.26</td><td>5.57</td><td>7.29</td></tr><tr><td rowspan="2">Biomass with RUE</td><td>Calibration</td><td>5.57</td><td>4.21</td><td>4.12</td><td>6.38</td></tr><tr><td>Evaluation</td><td>5.26</td><td>3.47</td><td>5.31</td><td>7.53</td></tr><tr><td rowspan="2">Biomass no RUE</td><td>Calibration</td><td>5.50</td><td>4.23</td><td>4.13</td><td>6.18</td></tr><tr><td>Evaluation</td><td>5.20</td><td>4.37</td><td>5.57</td><td>7.29</td></tr><tr><td rowspan="2">LAI + Biomass</td><td>Calibration</td><td>5.50</td><td>4.22</td><td>4.19</td><td>6.14</td></tr><tr><td>Evaluation</td><td>5.13</td><td>4.29</td><td>5.71</td><td>7.32</td></tr></tbody></table>

improvement in AICc and error. Between the calibration strategies, *vitircarb* values also depend on the simulated biomass dynamics during grain filling, so they are estimated at higher values for the strategies resulting in lower biomass during grain filling “No LAI, no biomass” and “LAI + Biomass”.

### 4.1.2. Comparing squared errors

The divergence in LAI and plant biomass simulated by the different strategies is not necessarily well accounted for by the calculation of errors. The obtained results are similar between the calibration and evaluation subsets regarding error values and strategies comparison.

The LAI error is indeed lower when LAI data are included in the calibration process. However, this is not the case for plant biomass, with very similar errors between the different strategies; this is explained by the fact that the divergence in the simulations occurs late in the growing season when there are few observations, so errors cannot be calculated during this critical period of time. The strategy “Biomass (with RUE)” was previously mentioned for the issue in the estimation of *efcroiveg* to the upper bound and lower values for the LAI parameters; this also leads to higher error in LAI with important bias. However, despite the issues previously mentioned regarding parameter values for the strategy “Biomass (no RUE)” and “LAI + Biomass”, errors are low for LAI and plant biomass. For grain number and grain weight, errors are lower for the strategy “No LAI, no biomass”; this is consistent with the findings of Guillaume et al. (2011) that end-of-season variables such as yield are better predicted when dynamic variables are not included in the calibration process. Among the different strategies, “LAI + Biomass” is the one with the lowest errors for both the calibration and evaluation subsets.

### 4.1.3. Analysis of residuals

Looking at the residuals provides more insight into how the errors are distributed across the observations for the different strategies. Residuals behave similarly between the calibration and evaluation subsets. Here, residuals tend to deform with wider confidence intervals when data is scarce. Strategies resulting in the flattest residuals across observations should be preferred. Here the LAI residuals for high LAI values (near the maximum) are the least positive for the “LAI” and “LAI + Biomass” strategies, so the simulated LAI is the least underestimated with these strategies. For plant biomass there is a strong increase in

<figure><img src="image_9.png" /><figcaption>**Fig. 5.** Decomposed MSE into bias (bias2, in turquoise), difference in variability (SDSD, in orange) and residual (LCS, in mauve) and total MSE (sum of the other components, in pink) faceted for LAI, plant biomass, grain number and grain yield for the different calibration strategies computed on the calibration and evaluation datasets.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Fig. 6. Residuals between observations and simulations in function of observed values for LAI and plant biomass (t/ha). Point shape correspond to the dataset type (calibration or evaluation), colors correspond to the different calibration strategies and lines correspond to Loess non-parametric regression with ribbons as their confidence intervals.</figcaption></figure>

residuals near maturity, with consequent uncertainty due to data scarcity, for all strategies except “LAI”: for this one, residuals remain flat and close to zero over time with limited underestimation.

### 4.1.4. Determining the best calibration strategy

Based on these different criteria, we recommend the “LAI” strategy for this dataset, as there are no major physiological issues in the estimated parameter values, the errors for the target variables remain acceptable even though there is some bias for grain yield, and this strategy provides the flattest residuals for LAI and plant biomass. Given these results, we tested two complementary strategies based on “LAI + Biomass” but (i) without *efcroirepro* for biomass, and (ii) without *durvieF* for LAI and *efcroirepro* for biomass. There was no bound issue for the estimated parameter values and residuals were flatter when both *efcroirepro* and *durvieF* were excluded but these strategies did not perform better than the LAI strategy (data not shown). There is a trade-off in the quality of the calibration of in-season versus end-of-season variables (i.e. LAI and biomass versus grain number and grain yield). The “LAI” strategy is especially relevant when considering LAI and biomass dynamics but with some bias on grain yield; however, if the sole purpose of the model is to predict yield, the LAI and biomass should be excluded from the calibration process to obtain the lowest error and bias (but the error will be larger for LAI and plant biomass).

## 4.2. Limitations in the application of the calibration protocol of Wallach et al. (2024)

Although the calibration improved the fit of the model to the experimental data and allowed to choose an adequate strategy, some limitations can be raised. Regarding the experimental dataset, as mentioned in the previous section, the comparison of the calibration strategies was considerably impacted by the structure of the dataset, as some estimation issues stem from the lack of experimental LAI and plant biomass data. Besides, we settled for the “LAI” strategy even though there is more uncertainty on the measurements than for biomass. Here LAI measures were performed with direct methods, known to be more precise than indirect ones, but there was a change in the acquisition method in 2020; this change is assumed to be minor since acquisition still relies on photographs, but with higher precision with the newer LITERAL method (DE SOLAN et al., 2024). Three points are raised regarding the application of the calibration methodology:

* No cross-validation was performed; more robust results could be obtained with a leave-one-out (LOO) method, which usually results in the lowest prediction error (Hernández-Ochoa et al., 2024; Wallach et al., 2021), leading to overfitting when randomly applied, as some situations may be used many times in both the calibration or evaluation subsets. Seidel et al. (2018) underlined that modelers often underestimate prediction errors due to the frequent overlap of experimental sites between calibration and evaluation steps. To avoid this, Casadebaig et al. (2020) proposed to divide the dataset into five parts and perform a cross-validation loop without repeating the data for the evaluation step on each of the five parts successively. Finally, Hernandez-Ochoa et al. (2024) examined the best way to combine seasons and years for calibration and evaluation dataset; they found that phenology was estimated similarly between combinations but LAI and plant biomass were not as stable. Such approaches are feasible for our case study with additional computational resources.

* The selection of candidate parameters could be more largely exploited as this is a specificity of the methodology we did not explore. Indeed, we only considered two candidate parameters (*jvc*, *irmax*), as we wanted to test a restricted set of strategies based on the type of included variables, and this number increases consequently when considering combinations with the candidate status of the parameters.

* The choice of parameters to be included: we decided to include some non-varietal parameters due to ongoing discussions on their potential varietal specificity in STICS (*efcroiveg*, *efcroirepro*, *cgrain*, *irmax*). The results were not concluding for radiation-use-efficiency, which prevents the evaluation of potential breeding progress on this parameter for modern cultivars. The same consideration can be raised for parameters related to heat and/or drought tolerance since these characteristics are of major importance under climate change. However, we did not even try to calibrate such parameters since, like the RUE parameters, they affect biomass production very directly. Estimating these parameters would rather require dedicated experiments with one-on-one and combined stress with varying intensity.

## 4.3. Contributions of the study and recommendations

This study is the first application of the protocol for the whole crop model presented in Wallach et al. (2024); indeed, there are ongoing AgMIP exercises aimed at inter-comparing the application of this methodology across a range of wheat crop models. This study contributes to giving guidance to modelers for the calibration of a new cultivar in a crop model by providing insight into the selection of variables and parameters to estimate as well as criteria for evaluating calibration strategies. This study demonstrated that the choice of calibration steps has a major impact on simulated outputs, with a strong dependence on the structure of the experimental dataset. We also provide valuable feedback on the application of this methodology to our case study for the winter wheat cultivar Rubisko in STICS. For our case study, the scarcity of LAI and biomass data was indeed limiting and affected the calibration performance; we found that strategies including biomass data were not robust enough to the lack of end-of-season observations but with a more
complete dataset the conclusions might be different. Nevertheless, we
recommend systematic data acquisition throughout growth for both LAI
and biomass, particularly near the maximum for LAI and near maturity
for biomass for calibration purposes. For plant biomass this can be
achieved by measuring this variable more systematically at maturity,
just before harvest. For LAI, this requires increasing the number of
measurements around the maximum and measuring LAI senescence;
although senescence is usually measured by the percentage of green
area, this is not completely analogous to LAI. We also recommend
caution when including some parameters if they relate to processes that
are not necessarily well observed in the data, for example here param-
eters related to reproductive growth and LAI senescence with few data
on these periods of time. We strongly recommend that both LAI and RUE
parameters are not calibrated together on biomass data, as this is often
considered when LAI data is lacking (Wallach et al., 2024).

Regarding more practical aspects, calibrating Rubisko is relevant so that this cultivar can be used in STICS simulations. Rubisko is not amongst the most popular French cultivars right now - though it used to be with 14 % of the French wheat cultivated area in 2016, so there is a lot of multi-trial data for this cultivar. The data provided by Arvalis includes twelve cultivars, but in this study, we chose to focus on Rubisko to explore calibration strategies because it has the highest number of environments. Now that we have found a suitable calibration strategy, it can be applied to the other eleven cultivars in the multi-trial dataset, including more modern cultivars such as Chevignon and Kws Extase, representing 14.5 % and 4.8 % of the French wheat cultivated area in 2024. Furthermore, the estimation of phenological parameters alone is valuable for other purposes, such as the calculation of pheno-climatic indices as in (Beauvais et al., 2025; Le Roux et al., 2024).

4.4. *Perspectives for the calibration of crop models*

As previously mentioned, the recommended “LAI” calibration strat-
egy can be applied to other cultivars of the multi-trial dataset provided
by Arvalis; the calibration strategies considered in this study could also
be explored for the other cultivars, despite the lower numbers of envi-
ronments. It would also be interesting to apply this strategy to other
datasets, but also to explore the different calibration strategies on other
datasets with different structures. Finally, we used a frequentist cali-
bration approach as proposed in Wallach et al. (2024), as Bayesian ap-
proaches were not necessarily recommended by Wallach et al. (2021),
but this would still be interesting to assess the varietal specificity of
parameters by comparing parameter distributions rather than point es-
timates. Hierarchical models could be used to estimate all the cultivars
together, thus allowing for more robust parameter estimation (Baey
et al., 2018; Viaud et al., 2022).

CRediT authorship contribution statement

**Buis Samuel:** Writing – review & editing, Supervision, Methodology, Conceptualization. **Deswarte Jean-Charles:** Writing – review & editing, Funding acquisition, Conceptualization. **García Cécile:** Writing – review & editing, Data curation. **Launay Marie:** Writing – review & editing, Supervision, Methodology, Funding acquisition, Conceptualization. **Bancal Marie-Odile:** Writing – review & editing, Supervision, Methodology, Funding acquisition, Conceptualization. **Aubry Maël:** Writing – review & editing, Methodology, Formal analysis, Conceptualization. **Gawinowski Meije:** Writing – original draft, Visualization, Methodology, Formal analysis, Data curation, 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.

**Appendix A. Supporting information**

Supplementary data associated with this article can be found in the
online version at doi:10.1016/j.eja.2025.127677.

Data availability

Data will be made available on request.

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