# About drivers of performance for crop growth model calibration at the within-field scale

Daniel Pasquel, James A Taylor, Bruno Tisseyre, Sébastien Roux

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Daniel Pasquel, James A Taylor, Bruno Tisseyre, Sébastien Roux. About drivers of performance for crop growth model calibration at the within-field scale. European Journal of Agronomy, 2025, 170, pp.127773. 10.1016/j.eja.2025.127773. hal-05199121

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# About drivers of performance for crop growth model calibration at the within-field scale

Daniel Pasquel<sup>a,b,*</sup> <sup>ID</sup>, James A. Taylor<sup>a</sup>, Bruno Tisseyre<sup>a ID</sup>, Sébastien Roux<sup>c ID</sup>

## ARTICLE INFO

**Keywords:**

Predawn leaf water potential
WaLIS
Spatial calibration
Precision agriculture
Spatial pattern

## ABSTRACT

The calibration process is a necessary step to improve crop growth model (CGM) performances and to reduce the uncertainty related to model parameters. Modeling agronomic variables at the within-field scale needs to accurately reproduce the spatial pattern to enable a suitable spatial management. Spatial calibration is one efficient downscaling method for CGM spatialization. The objective of this study is to better understand the drivers of performance of spatial calibration by comparing it to an aspatial calibration (i.e. at field or site-specific scale) in various conditions. The impact of three driving properties was studied: the targeted variable variance, its level of spatial structure, and the correlation level of ancillary data. To this aim, a method was designed to simulate various spatial structures from the one of an existing vineyard whilst ensuring the temporal consistency of the simulated data. The method was applied to a vineyard CGM (WaLIS) aiming at estimating plant water restriction using predawn leaf water potential (Ψ<sub>PD</sub>) measurements. Results showed that spatial calibration improved the model performances at the within-field scale when Ψ<sub>PD</sub> was strongly structured and highly correlated to the ancillary data. When Ψ<sub>PD</sub> was either moderately or weakly spatially structured, the spatial constraint added more error instead of correcting errors, deteriorating the CGM performances. The ancillary data and the segmentation algorithm had a large impact on the spatial calibration performances.

## 1. Introduction

Crop growth models (CGM) are useful tools for predicting agronomic variables and interactions along the soil-plant-atmosphere continuum. CGM often require a huge number of parameters for their functioning that may involve unmeasurable values or values with large domains of uncertainty in their parametrization (Liu et al., 2018a). These uncertainties affect CGM outputs and thus reduce modeling performances (Wallach, 2011; Wallach et al., 2014). Improve the reliability of CGM is of primary interest and is mainly based on the way to parametrize models, it allows to reduce the sources of uncertainty (Wallach et al., 2016). The sources of uncertainty in predicting agronomic variables are well known and are based on (i) the model structure, (ii) the input data and (iii) the model parameters (van Oijen and Ewert, 1999). Seidel et al. (2018) highlighted that calibration process to parametrize CGM is an important source of uncertainty with still a potentiality to be improved.

In a precision agriculture (PA) context, CGM could be used to identify the most relevant management strategy to be applied at the within-

field scale. However, applying a CGM at the within-field scale involves using a model spatialization approach to adjust the native spatial footprint of the model to a finer-scale prediction of agronomic variables (Pasquel et al., 2022). Spatial calibration approaches can play a valuable role in modifying the spatial footprint of CGM as part of the spatialization process. In the case of prediction with CGM at the within-field scale, calibration of model parameters is performed to adjust for local site-specific variability without changing the model equations. In other words, spatial calibration approaches aims to spatialize CGM without modifying their point-based simulation formalisms. Modifying their formalisms could result in spatial GCM, but such models are out of the scope of this study.

Batchelor et al. (2002) presented various strategies for spatially applying CGM at the within-field scale, emphasizing the importance of applying CGM to homogeneous zones and the need to accurately define these zones. CGM can be applied spatially at within-field scale by employing either a point-based approach on a regular grid (Irmak et al., 2001; Wallor et al., 2018) or at specific measurement sites where

<footnote><sup>a</sup> ITAP, Univ. Montpellier, INRAE, Institut Agro, Montpellier, France</footnote>

<footnote><sup>b</sup> EMMAH, INRAE, Avignon Université, Avignon, France</footnote>

<footnote><sup>c</sup> MISTEA, Univ. Montpellier, INRAE, Institut Agro, Montpellier, France</footnote>

<footnote>* Corresponding author at: EMMAH, INRAE, Avignon Université, Avignon, France.</footnote>

<footnote>E-mail address: daniel.pasquel@inrae.fr (D. Pasquel).</footnote>
observed data are available for calibration (Pasquel et al., 2023). Both approaches, often referred to as site-specific modeling, represents the finest resolution for CGM application based on available data. Another approach involves spatially constraining the calibration process, aligning this later with within-field management zones and/or spatial characteristics of agronomic variables. Within-field zone delineation is common in PA (Corwin and Lesch, 2005; Tagarakis et al., 2018). Applying CGM on these defined within-field zones ensures spatial consistency in simulating agronomic variables (Thompson et al., 2024; Thorp et al., 2008). These homogeneous zones can also be delineated using ancillary data that capture spatial variability, such as soil properties or NDVI (Acevedo-Opazo et al., 2008; Bahat et al., 2024; Cammarano et al., 2021; Gaso et al., 2021; Leo et al., 2023; Maestrini and Basso, 2018; Ziliani et al., 2022).

An assumption behind this existing method is that constraining the spatial pattern of the agronomic variable will allow a spatially consistent smoothing of the calibration error relative to the measured data set. However, such data are either rarely available or may present a high level of noise to carry a calibration at a finer spatial scale. Thus, it is not immediately apparent if a calibration at a finer spatial scale will be able to efficiently reproduce the spatial pattern of the target agronomic variable. However, the effectiveness and achievable spatial resolution of such spatial calibration approach have not been extensively investigated. Comparison between site-specific scale, within-field zone and field scale has been rarely carried out (He et al., 2024; Trenz et al., 2024). Moreover, three potential drivers have a questionable impact on the spatial calibration process:

(i) the degree of the spatial structure/pattern of the agronomic variable to be predicted;

(ii) the total variance of the agronomic variable to be predicted;

(iii) the degree of correlation between the agronomic variable to be predicted and the ancillary data used to delineate within-field calibration zones.

Understanding their role can be a practical issue in order to predict performance of spatial calibration, but no such study has been carried out so far, probably because studying the effect of spatial structure requires many experimental data covering many spatial structures.

The objective of this study is to investigate how relevant it is to spatialize CGM by using spatial calibration for using a CGM at the within-field scale and in particular to identify in which situations the use of a spatial calibration is better than an aspatial calibration (i.e. at field or site-specific scale). To overcome the lack of data needed to

understand the sensitivity of the spatial calibration performance to the three drivers, an original hybrid approach using spatial perturbations of experimental data was specifically designed. This approach was applied to the CGM named WaLIS (Celette et al., 2010) which is designed to simulate predawn leaf water potential (Ψ<sub>PD</sub>) of vine during growing season (with the intention of managing water stress) and using real Ψ<sub>PD</sub> measurements.

## 2. Material and methods

### 2.1. Field data

The experimental vineyard used for this study was a 1.2 ha Syrah non-irrigated vineyard located in the south of France (43.144°N, 3.131°E, Gruissan, Aude) on the INRAE Pech Rouge experimental site. Spacing between each vines measure 1 m and between each row measure 2.5 m. The vineyard is cultivated on a limestone plateau and is characterized with clay accumulation at some locations impacting the soil spatial heterogeneity. The agronomic variable of interest was the predawn leaf water potential (Ψ<sub>PD</sub>) representative of the vine water stress. Ψ<sub>PD</sub> was manually measured for two consecutive years (2003 and 2004) on several dates (respectively 7 and 2 dates) at the within-field scale on 49 measurement sites using a pressure chamber (more details are available in Acevedo-Opazo et al. 2010 for this data set) (Fig. 1).

### 2.2. WaLIS and the predicted predawn leaf water potential (ΨPD)

The crop model Water baLance for Intercropped Systems - WaLIS, (Celette et al., 2010) was used to predict the Ψ<sub>PD</sub>. WaLIS is not exactly a CGM but a hydric model related to vine physiology, but it presents the same structure and the same characteristics than a CGM, reason why WaLIS was chosen. The main output of WaLIS is the vine water status represented by the Ψ<sub>PD</sub> and it has only few inputs, i.e. the weather data, the soil characterization and few parameter related to the vine physiology. The 2003 and 2004 weather data acquired through the weather station 11170004 (Gruissan) of the INRAE network at nearly 350 m of the experimental vineyard were used as WaLIS input data (Fig. 2). These weather data were collected via the INRAE CLIMATIK platform (Delannoy et al., 2022). They included the daily mean temperature (T<sub>mean</sub>), the daily precipitation (P) and daily evapotranspiration (ET). ET was computed using the Penman-Monteith equation (Allen et al., 1989; Pereira et al., 1999), for that purpose daily solar radiation, daily relative

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Location of the experimental Syrah vineyard at INRAE Pech Rouge (Gruissan, Aude, France) (left) and the distribution of the 49 sampling points within the vineyard, where each point represents the location of measured predawn leaf water potential (Ψ<sub>PD</sub>) on multiple dates during the season.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Weather conditions for the production season for (a.) 2003 and (b.) 2004 with the red line and the blue bars corresponding respectively to the mean temperature (T<sub>mean</sub>) and the daily precipitation (P). The dashed gray lines correspond to the dates of measurement of Ψ<sub>PD</sub> considered for this study in 2003 (June 18th, June 26th, July 8th, July 16th, July 23rd, July 30th and August 12th) and 2004 (July 8th and August 18th).</figcaption></figure>

humidity and the daily saturation vapor pressure were also recorded. WaLIS actually simulates the fraction of transpirable soil water (FTSW). Thus, Ψ<sub>PD</sub> were computed using predicted FTSW following Eq. 1 (refer to Lebon et al., 2003 for further details). Therefore, a relevant and realistic Ψ<sub>PD</sub> minimum had to be defined because this conversion contained a logarithmic expression and the resulting FTSW value could be equal to 0. This minimum was assumed to the lowest value observed within the 2003–2004 dataset, which was –1.1 MPa. Measured dates in 2003 were used to calibrate WaLIS. The prediction of Ψ<sub>PD</sub> was carried out in 2004 focusing primarily on the two measurement dates where the water stress in the vineyard was showing a high heterogeneity.

$$ \psi_{\text{PD.mod}} = \frac{\log(\text{FTSW}) - \log(C_a)}{C_b} \quad (1) $$

where C<sub>a</sub> is a constant equal to 1.0572 and C<sub>b</sub> is a constant equal to 5.3452 (from Lebon et al., 2003).

## 2.3. Data generation

### 2.3.1. Spatially rearranged field simulation

To investigate the impact of various spatial characteristics of vineyard management, simulated data was generated, allowing for accurate control over these characteristics. Thus, spatially rearranged fields (SRFs) were generated. These SRFs are defined in this study as simulated data obtained by spatially rearranging existing data, i.e. forming new simulated vineyards.

They were derived from the available 2004 observed data and their characteristics were constrained by the measurement dates in 2004, regarding their spatial structure of Ψ<sub>PD</sub> (SS<sub>Ψ</sub>) and their total variance of Ψ<sub>PD</sub> (σ<sub>Ψ</sub>). Characteristic of both available dates of measurements (July 8th 2004 and August 18th 2004) are detailed in Table 1. Note that in the followings, resulting simulated vineyards from July 8th 2004 and August 18th 2004 will respectively be referred as low σ<sub>Ψ</sub> and high σ<sub>Ψ</sub>. For these two measurement dates, the geographic locations of the sampling points were retained but the observed values were

<caption>**Table 1**</caption>

Characteristics of the predawn leaf water potential (Ψ<sub>PD</sub>) measured for possible evaluation dates related to their variability and spatial structure. The dates in bold correspond to the considered dates kept for the study having desired coupled characteristics. σ<sub>Ψ</sub> = standard deviation of Ψ<sub>PD</sub> (characterizing the variability), C<sub>i,Ψ</sub> = Cambardella index of Ψ<sub>PD</sub> (summarizing the variance spatially organized and the spatial structure).

<table><thead><tr><th>Date</th><th>σ<sub>Ψ</sub><br>(MPa)</th><th>σ<sub>Ψ</sub><br>characterization</th><th>C<sub>i,Ψ</sub><br>(%)</th><th>C<sub>i,Ψ</sub><br>characterization</th></tr></thead><tbody><tr><td>08.07.2004</td><td>0.10</td><td>Low</td><td>51</td><td>moderate</td></tr><tr><td>18.08.2004</td><td>0.16</td><td>High</td><td>32</td><td>moderate</td></tr></tbody></table>

redistributed to different sampling points to achieve different spatial structures and patterns. However, each measurement site kept its own temporal profile of Ψ<sub>PD</sub> using the 2003 dataset, i.e. the temporal profile of the seven measurement dates for 2003, in aim to relevantly calibrate WaLIS. Indeed, in non-irrigated vineyards, the spatial pattern of Ψ<sub>PD</sub> is known to show a temporal consistency over time as water stress increases (Acevedo-Opazo et al., 2010). In order to carry the spatial rearrangement of the measured sites, changes in Ψ<sub>PD</sub> values at neighboring locations were considered independent. However, by defining different levels of spatial structures for the spatially rearranged Ψ<sub>PD</sub>, we introduced intentionally varying degrees of spatial correlation in this study – a factor that we specifically aimed to evaluate in relation to spatial calibration.

Three different modalities to characterize the SS<sub>Ψ</sub> were chosen based on the Cambardella index (C<sub>i</sub>) (Cambardella et al., 1994). Thus, strong (S) (C<sub>i</sub> < 20 %), moderate (M) (40 % < C<sub>i</sub> < 60 %) and weak (W) (80 % < C<sub>i</sub>) SS<sub>Ψ</sub> were considered. To model the different SS<sub>Ψ</sub>, a reference spatial structure with known parameters was simulated using a theoretical variable. This theoretical variable was generated using Gaussian random fields (GRFs) on theoretical fields of size 500 × 500 pixels to ensure the targeted spatial structures were achieved and that the theoretical variogram approximated the experimental variogram (Fig. 3). These 500 × 500 GRFs were created because generated targeted SS<sub>Ψ</sub> is easier on larger number of units. Here, the size of each pixel was not a considered variable. The objective was to match both theoretical and experimental variograms to ensure the targeted spatial structures properties. Thus, the overall size of the GRF (500 × 500 pixels) was carefully chosen to meet this objective. Then, new 49-unit GRFs were generated (corresponding to the 49 initial measurement sites), with the same field shape as the real vineyard field (Fig. 3). These new GRFs were selected to approximate the targeted spatial structure (i.e. defined by the 500 × 500 GRFs) to ensure the spatial structure characteristic conservation of each considered SS<sub>Ψ</sub> modalities (S, M and W). Every spatial structure was estimated by theoretical variograms fitted with a REML method, more suitable when limited data are available to compute variograms (Kerry and Oliver, 2007). Thus, when both theoretical variograms of targeted GRFs and 49-unit GRFs were close (i.e. with a similar C<sub>i</sub> and a weak RMSE computed between each lag), spatial structures were assumed to be similar, i.e. the generated 49-unit GRFs were considered to have the desired SS<sub>Ψ</sub> modality and the considered 49-unit GRF was kept (Fig. 3). Then, the same approach was used to reassign the Ψ<sub>PD</sub> values from the 2004 dataset (Fig. 4) to the 49-unit GRFs. Reassignments were based on value ranking between the 49-unit GRF and the real 49 measurement sites. This reassignment ensured that the spatial structure/pattern characteristics were kept by sorting the values and attributing them according to their rank, i.e. real 49 measurement sites values were orderly reassigned to the 49-unit GRF
DATA GENERATION
Spatial structure rearrangement

<figure><img src="image_6.png" /><figcaption>Fig. 3. Data generation by rearranging the real measured sites to match with the targeted spatial structure corresponding to three spatial structure modalities. One example of each spatial structure modalities is illustrated with the rearrangement of the real measured sites. On each map, Voronoi tessellation was used to convert each of the 49 measurement sites of Ψ<sub>PD</sub> into polygons.</figcaption></figure>

values (this method aimed to conserve a similar spatial structure). Finally, there was 120 SRFs simulated (40 per SS<sub>ψ</sub>).

2.3.2. Ancillary data simulation

Ancillary data were also simulated for each generated SRF at three different levels of correlation with the corresponding Ψ<sub>PD</sub> (Q<sub>AD</sub>) at the evaluation dates. As a result, these ancillary data were spatially correlated with the SRF. For the record, it is very common to consider ancillary data in a PA context. Ancillary data are usually easier to get and are used to give information on the spatial structure/pattern of the considered agronomic variable (e.g. variables related to vine vigor, soil properties). Simulating auxiliary data thus allows the implementation of this common reasoning in PA while controlling Q<sub>AD</sub>. These simulated ancillary data were the only data used to delineate within-field zones. To be able to modify Q<sub>AD</sub>, the method from Oger et al. (2021) was adapted to simulate the ancillary data as needed for this study (Eqs. 2 and 3).

$$
AD_i = \Psi_{PD_i} + \varepsilon_{iwithi} N(0, \sigma_{AD}^2) \quad (2)
$$

$$
\sigma_{AD}^2 = \frac{\sigma_{\psi}^2}{(\mathrm{Cor}(\psi_{\mathrm{PD}}, \mathrm{AD}))^2} - \sigma_{\psi}^2 \text{with } \mathrm{Cor}(\psi_{\mathrm{PD}}, \mathrm{AD}) \in [0, 1] \quad (3)
$$

where ADᵢ is the ancillary data value at the location i, ψ<sub>PDᵢ</sub> is the Ψ<sub>PD</sub>
value at the location i, σ<sub>AD</sub><sup>2</sup> is the variance of simulated ancillary data,
σ<sub>ψ</sub><sup>2</sup> is the variance of predawn leaf water potential reassigned and Cor
(Ψ<sub>PD</sub>,AD) is the Pearson correlation between both variables.

In other words, with the assumption of second-order stationarity, the variance of Ψ<sub>PD</sub> and ancillary data corresponded to the sill values of the theoretical variogram. Thus, depending on the expected Q<sub>AD</sub>, the variance to be added to the Ψ<sub>PD</sub> values was determined by Eq. 2. The correlation levels considered were 94 %, 50 % and 10 % for Q<sub>AD</sub> within the SRFs. These three levels were selected based on correlations observed in the literature between normalized difference vegetation index and vine physiology parameters (Bramley et al., 2019; Hall et al., 2011) and to provide strongly contrasting levels.
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Predawn leaf water potential (Ψ<sub>PD</sub>) measured on the experimental vineyard on (a.) July 8th 2004 corresponding to the date with low total variance of Ψ<sub>PD</sub> (σ<sub>Ψ</sub>) and (b.) August 18th 2004 corresponding to the date with high σ<sub>Ψ</sub>. Voronoi tessellation was used to convert each of the 49 measurement sites of Ψ<sub>PD</sub> into polygons.</figcaption></figure>

## 2.4. Calibration approaches

### 2.4.1. Spatial calibration

The spatial calibration was defined as a calibration process based on the delineation of calibration zones from ancillary data that were representative of the spatial pattern of the considered agronomic variable. For further details about the spatial calibration approach please refer to Pasquel et al., (2023)). In that case, using spatial calibration implies applying a spatial constraint to the calibration process, driven by the use of within-field zones derived from a segmentation algorithm applied to spatial ancillary data.

**Step 1:** Parameter possibly spatially heterogeneous at within-field scale identification

The WaLIS parameters identified as likely to have some spatial variation were the total transpirable soil water (TTSW) and the maximum crop coefficient of the vine (K<sub>C</sub>) (McClymont et al., 2019; Verdugo-Vásquez et al., 2022). Note that in Celette et al. (2010) as there is 2 different crops, the authors chose to use K<sub>V</sub> and K<sub>IC</sub> respectively for crop coefficient of the grapevine and crop coefficient of the intercrop, here as only vine is considered, K<sub>C</sub> was used as generic term. Other WaLIS parameters were as spatially defined and their values were kept constant at a level representative of the environmental context from where the original data were measured (Celette et al., 2010). The TTSW and K<sub>C</sub> were spatially calibrated by finding the optimal parameter values on a 2-dimension grid using the measured data from Ψ<sub>PD</sub> 2003. The TTSW values ranged from 55 to 210 mm in increments of 5 mm and the K<sub>C</sub> values ranged from 0.35 to 0.5 in increments of 0.05, i.e. represent the possible parameter couple of TTSW and K<sub>C</sub> for the model calibration. These domain ranges were defined regarding expert knowledge and represent the diversity of cases which are possible to meet in the original environmental context (Roux et al., 2019). Calibrated values were those that minimized the mean absolute error (MAE) compared to all Ψ<sub>PD</sub> measurements realized in 2003.

**Step 2:** Delineation of the calibration zones

Within-field zones were delineated using a segmentation algorithm (Pedroso et al., 2010) included in the GeoFIS R package (Guillaume and Lablée, 2022) applied to the simulated ancillary data for each generated SRF. The considered number of within-field zones were between 2 and 5 zones. This number of within-field zone has been chosen because it

could be representative of a realistic management clustering in PA.

**Step 3:** Selection of the best within-field spatial modeling scale

Concerning the q<sub>AD</sub>, the hypothesis was that the higher the level of correlation of the ancillary data with the Ψ<sub>PD</sub>, the more relevant the delineation will be. Thus, the relevance of the delineation was evaluated by a one-way analysis of variance (ANOVA) linking Ψ<sub>PD</sub> with the delineated zones. The more the delineation explained the variation in Ψ<sub>PD</sub>, the more the delineation was considered relevant. Therefore, SRFs were kept depending on the delineation relevance, i.e. based on the proportion of variability explained by the delineated within-field zones. After the delineation of the calibration zones, the mean value of the measured sites within each zone was used for the spatial calibration, i.e. the modeling was performed at the spatial scale of the zones.

### 2.4.2. Aspatial calibration

The as spatial calibration approach was based directly on the simulated vineyards and applied at two scales, i.e. at field and at the site-specific scales. Calibration at field scale was performed on an as spatial calibration using field averages (i.e. average of all measurement points), which is the supposed original spatial footprint of CGM (Pasquel et al., 2022). Calibration at site-specific scale was performed on an as spatial calibration where each point was individually calibrated. This resulted in crop model outputs at either the field or the site-specific scale. The calibration at the site-specific scale is not considered as spatial calibration because each site is individually calibrated from the others. Thus, individually, each site-specific area corresponds to 0.25 ha.

## 2.5. Modeling performance evaluation

Crop model outputs resulting from both as spatial and spatial calibration approaches were compared to estimate which calibration approach was the most relevant. Thus, outputs of the spatial calibration approach were compared to the outputs of the as spatial calibration approach corresponding to the site-specific scale modeling and the field scale modeling. For all the modeling, outputs were disaggregated to the site-specific scale to assess the relevance of the spatial calibration. To evaluate outputs of spatialized WaLIS, the root mean square error (RMSE) (Eq. 4) and the spatial balanced accuracy (SBA) (Eq. 5) (Pasquel et al., 2023) were used. The SBA score was used to account for the
preservation of the spatial pattern of the outputs. It provides an assessment of both aspatial and spatial pattern errors. Thus, SBA was used on each spatial modeling scale.

$$RMSE = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(O_i - M_i)^2} \qquad (4)$$

where $O_i$ is the observed $\Psi_{PD}$, $M_i$ is the corresponding modeled $\Psi_{PD}$ and $n$ is the number of observation ($n = 49$).

$$SBA(O, M) = \frac{1}{100}\sum_{q=1}^{100} [1 - BA(O_{t(O,M,q)}, M_{t(O,M,q)})] \qquad (5)$$

where $O$ and $M$ are respectively the observed and modeled maps, $O_{t(O,M,q)}$ and $M_{t(O,M,q)}$ are respectively the observed and modeled maps at the threshold level $t(O,M,q)$ corresponding to percentile $q$ on the merging data distributions of $O$ and $M$.

The SBA score was used to determine the optimal scale for spatial calibration, specifically within-field zonal scales. For each simulated vineyard, the best-performing spatial scale (n-zones) was identified and compared to aspatial calibration approaches at both the field and site-specific scales. Since the SBA score is designed to compare spatial modeling within the same field (Pasquel et al., 2023), the difference in SBA score ($\Delta$SBA) was calculated to enable comparisons across different SRFs. The $\Delta$SBA evaluated the effectiveness of spatial calibration by comparing it to aspatial calibration at the site-specific scale ($\Delta$SBA$_{site}$) (Eq. 6) or the field scale ($\Delta$SBA$_{field}$) (Eq. 7). A positive $\Delta$SBA indicated that spatial calibration performed better, i.e. producing results with closer numerical values and spatial patterns, while a negative $\Delta$SBA indicated better performance by the aspatial approach.

$$\Delta SBA_{site} = SBA(O, M_{site}) - \min_{zone \in \{2.3.4.5\}} [(SBA(O, M_{zone})] \qquad (6)$$

where $M_{site}$ is the $\Psi_{PD}$ modeled using an aspatial calibration approach at the site-specific scale and $M_{zone}$ is the $\Psi_{PD}$ modeled using a spatial calibration approach for each considered within-field zones.

$$\Delta SBA_{field} = SBA(O, M_{field}) - \min_{zone \in \{2.3.4.5\}} [(SBA(O, M_{zone})] \qquad (7)$$

where $M_{field}$ is the $\Psi_{PD}$ modeled using an aspatial calibration approach at the field scale and $M_{zone}$ is the $\Psi_{PD}$ modeled using a spatial calibration approach for each considered within-field zones.

## 2.6. Statistical analysis

As the computational time was relatively high, 120 simulated vineyards were generated to have simulation within an acceptable computational power. Considering the 3 modalities of $Q_{AD}$, the selected best within-field spatial modeling scale and the aspatial calibration scales (i. e. field and site-specific scale), there were 1080 simulations for the whole study. All statistical analysis were performed using the R software (R Core Team, 2023). Multiple-way ANOVA was used to evaluate the significance of $SS_{\psi}$, $\sigma_{\psi}$ and $Q_{AD}$ in the determination of $\Delta$SBA. Before applying ANOVA, residual normality and homoscedasticity were tested using the Shapiro test and the Levene test respectively. A post hoc test, realized using a Tukey's Honest Significant Difference, was used to identify significant pairwise differences among the modalities and to identify which groups were different from the others.

## 3. Results

First results are about the performances of WaLIS to simulate $\Psi_{PD}$ at different spatial scales. The second part of the results highlights with which combination of the considered drivers the spatial calibration improves the model predictions.

### 3.1. Performance of WaLIS in predicting $\Psi_{PD}$

WaLIS performances were similar for both modeling dates (high and low $\sigma_{\psi}$). For the date with high $\sigma_{\psi}$, the mean of the different RMSEs obtained for each spatial modeling scale and each $Q_{AD}$, was equal to 0.16 MPa (Fig. 5). Thus, this corresponds to a relative error in predicting $\Psi_{PD}$ (for high $\sigma_{\psi}$) of 35%.

For the field scale modeling (i.e. using aspatial calibration), RMSEs were always equal to the average of all the measurement sites and is the same for all the simulated vineyards (Fig. 5b). Similarly, considering the site-scale modeling (i.e. using aspatial calibration), RMSEs were always equal regardless of the spatial arrangement of the measurement sites as the sites values are provided by the 2003 dataset. Indeed, only the measurement site locations were different between each of the simulated vineyards (modification of the $SS_{\psi}$) (Fig. 5b).

The spatialized WaLIS performances were dependent on the delineation level (only the results for the 2 and 5 within-field zones are shown in Fig. 5c) and the correlation between the ancillary data and the $\Psi_{PD}$ (refer to the Supplementary Fig. S.1, S.2 and S.3 to see the WaLIS performances for each level of delineation and each level of correlation for the considered simulated vineyards in Figs. 5b and 5c).

### 3.2. Relevance of using a spatial calibration approach

In Fig. 6, the more positive the $\Delta$SBA value, the more the spatial calibration approach was relevant compared to an aspatial calibration at field or site-specific scale. The $\Delta$SBA dispersion was different for both dates with high and low $\sigma_{\psi}$. The variability of $\Delta$SBA was higher for the date with a high $\sigma_{\psi}$ (August 18th). The results of Tukey's test (indicated by a letter on the top of the Figure) identify any significant differences between different combinations of spatial structure and ancillary data correlation. For both dates, $\Delta$SBA were higher when $Q_{AD}$ was higher, except for vineyards with weak spatial structures where the results were less contrasted, i.e. whatever the $Q_{AD}$, the difference in performance between aspatial and spatial calibration are similar. For moderate and strong $SS_{\psi}$, increasing $Q_{AD}$ increased significantly the relevance of using a spatial calibration approach. Using $Q_{AD}$ at 94 % for these $SS_{\psi}$ modalities showed significant relevance of using spatial calibration whatever the $\sigma_{\psi}$ of the data. The violin plots (Fig. 6) showed that most of the $\Delta$SBA values were relatively well grouped for all combinations of spatial structure and ancillary data correlations, but most did present some outliers.

Fig. 7 summarizes the effectiveness of spatial calibration compared to aspatial calibration. For a high $\sigma_{\psi}$, spatial calibration was highly effective compared to site-specific as spatial calibration (i.e. $\Delta$SBA$_{site}$ positive) when $SS_{\psi}$ was strong with $Q_{AD}$ was 94 %. However, its relevance decreased as $Q_{AD}$ dropped, with performances at 50 % and 10 % $Q_{AD}$ showing no improvement or even deterioration. For moderate or weak $SS_{\psi}$, spatial calibration was generally not effective at the site-specific scale, with no significant advantages over as spatial calibration. Compared to an as spatial calibration at the field scale, spatial calibration performed well when $SS_{\psi}$ was strong or moderate with $Q_{AD}$ at 94 %. At lower $Q_{AD}$ (50 % and 10 %), performance tended to decline, especially for moderate $SS_{\psi}$. When $SS_{\psi}$ was weak, spatial calibration provided no significant improvement, except for $Q_{AD}$ at 10 %, which showed a slight decrease in accuracy.

For a low $\sigma_{\psi}$, spatial calibration was effective when $SS_{\psi}$ was strong with $Q_{AD}$ was 94 % (Fig. 7). However, for $Q_{AD}$ at 50 % and 10 % with strong $SS_{\psi}$, and for moderate $SS_{\psi}$ with $Q_{AD}$ at 10 %, spatial calibration tended to reduce modeling performance. In other cases, the $\Delta$SBA$_{site}$ showed similar performances for spatial and as spatial calibration at the site-specific scale. For the $\Delta$SBA$_{field}$, spatial calibration was effective with strong and moderate $SS_{\psi}$ with $Q_{AD}$ of 94 %. In all other cases comparing to an as spatial calibration at the field scale, performances were better with spatial calibration. Overall, results for low $\sigma_{\psi}$ were less variable compared to those for high $\sigma_{\psi}$.
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Performances of WaLIS in predicting predawn leaf water potential (ΨPD) regarding each considered spatial structure of ΨPD (strong, moderate and weak) between the (a.) observed (simulated) ΨPD and modeling at different spatial scales: (b.) field and site-specific scale, (c.) at within-field scale (2-zone and 5-zone scales) for different level of correlation between ΨPD and the simulated ancillary data (10 % and 94 %). The presented modeling date were based on August 18th with a high ΨPD variability. Results are only shown for one simulated vineyard for each spatial structure modality. The dotted lines correspond to the delineated within-field zones for the considered simulated vineyard.</figcaption></figure>

# 4. Discussion

## 4.1. Spatial calibration performances compared to field and site-specific scale calibration

Spatial calibration generally outperformed as spatial calibration at the field scale, particularly with high σ<sub>ψ</sub> (Fig. 7), as it better captured within-field variability. Similar results have been reported in recent studies (He et al., 2024; Trenz et al., 2024). However, field-scale

calibration performed better for low σ<sub>ψ</sub> due to the low heterogeneity of the agronomic variable, which field-level data sufficiently represented. This aligns with the original design of crop growth models (CGM) for homogeneous field-scale areas. Compared to site-specific calibration, spatial calibration generally underperformed unless SS<sub>ψ</sub> was strong and ancillary data had a high Q<sub>AD</sub> (Fig. 7). Site-specific calibration treats each site independently, ignoring spatial relationships, which can limit its effectiveness for variables with within-field heterogeneity. Similar results were already observed in other studies
<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Change in the SBA distributions using a spatial calibration approach compared to an aspatial calibration approach (at field scale at the bottom and at site-specific scale on top) depending on the spatial structure of the agronomic variable (SS<sub>Ψ</sub>) (strong, moderate or weak), the variability of the agronomic variable (σ<sub>Ψ</sub>) (high variability on right and low variability on left) and the correlation between the agronomic variable and the ancillary data (Q<sub>AD</sub>) (Pearson's correlation of 10 %, 50 % and 94 %). A positive ΔSBA corresponds to better results with a spatial calibration approach, respectively a negative ΔSBA corresponds to a better result with aspatial calibration approach. Letters on the top are based on Tukey's test of significance. Modalities with the same letters are not significantly different at 0.05 probability level.</figcaption></figure>

(Batchelor et al., 2002; He et al., 2024; Trenz et al., 2024). In cases of weak or moderate SS<sub>Ψ</sub>, spatial calibration often deteriorated performances due to poorly defined calibration zones that introduced additional errors.

Previous studies already investigated using CGM at the within-field scale using either aggregated field data or site-specific measurements to calibrate the model (Batchelor et al., 2002; He et al., 2024; Thompson et al., 2024; Trenz et al., 2024). These studies mainly investigate if field or site-specific calibration better perform or if spatial calibration at the within-field scale could show better results. The innovation of this study lies in identifying conditions where spatial calibration is most effective and determining the optimal size of the specific unit (within-field zone). Here, the optimal size directly refers to the choice of whether or not to use spatial calibration. Indeed, adopting a spatial calibration approach involves the use of within-field calibration zones. Therefore, the trade-off between using an aspatial calibration (at the field or site-specific scale) and a spatial calibration approach (within-field calibration with 2–5 zones in this study) is directly related to the concept of optimal size. The optimal size is considered by computing the ΔSBA<sub>site</sub> and ΔSBA<sub>field</sub> between respectively the site-specific and the field scale with the optimal size within the within-field scale considered.

Even when spatial and aspatial calibration at the site-specific scale performed equally, spatial calibration offered the advantage of partially reproducing the spatial pattern of the agronomic variable. Furthermore, the most widely used CGM in crop modeling require dozens of input parameters. Using a spatial calibration approach, based on calibration zones, allows to reduce the number of parameters to calibrate and thus

reduce the effort and time needed in the calibration processes. By incorporating spatial constraints into the calibration process, spatial calibration helped mitigate a part of the calibration error that occurred when ignoring the spatial pattern of the agronomic variable. Thus, a trade-off must be found between the level of model downscaling (within-field zone calibration) and the aggregation of available data used for spatial calibration at field scale. In this context, downscaling by creating management zones, and potentially multiple levels of zones, may offer an effective strategy for achieving accurate model calibration. When carefully applied, spatial calibration can preserve the spatial structure of the variable while minimizing the influence of stochastic error in the measured data used as calibration dataset and in the modeling process. This approach aimed to reduce calibration uncertainty, particularly for poor-quality, high-resolution data. However, considering the spatial structure is only beneficial in the favorable conditions outlined by this study.

## 4.2. Spatial calibration performance and availability of ancillary data

The effectiveness of spatial calibration decreased with a decreasing of Q<sub>AD</sub>. It was most effective at high Q<sub>AD</sub> (94 %), where the spatial patterns of the ancillary data and target variable closely aligned, allowing accurate delineation and significant performance improvements. At Q<sub>AD</sub> of 50 %, commonly seen in agri-datasets, results varied and depended on the target variable variability. For very low correlations (Q<sub>AD</sub> = 10 %), delineation failed to create meaningful zones, and spatial calibration performed worse than field or site-specific calibration. Only one single
<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Relevance of using a spatial calibration compared to an aspatial calibration regarding the difference of SBA score for different spatial scales of modelling. Significances were estimated with a Tukey test (modalities with different letters) and correspond to a significant improvement or deterioration of the spatialized crop model (represented by *). Blue cases correspond to a better performance of a spatial calibration compared to an aspatial calibration. Red cases correspond to a better performance of an aspatial calibration compared to a spatial calibration. $\sigma_{\Psi}$ corresponds to the variability of $\Psi_{PD}$, S, M and W correspond to the spatial structure modalities $SS_{\Psi}$ (respectively strong, moderate and weak), 10, 50 and 94 correspond to the ancillary data correlation $Q_{AD}$ (respectively 10 %, 50 % and 94 %).</figcaption></figure>

ancillary data layer was chosen for this study to simplify the assumptions and the simulation of the ancillary data used. In reality, for a relevant and reliable use of ancillary data, several types of data should be used to better describe the spatial pattern of the agronomic variable (Derby et al., 2007). Data fusion is necessary to integrate several sources of ancillary data (e.g. soil and plant data) to have a more accurate delineation of within-field zones (Castrignano et al., 2019).

The aim of spatial calibration was to replicate the spatial pattern of the agronomic variable at a specific modeling date. This study assumed that the spatial patterns used to define within-field calibration zones remained static throughout the growing season and across production years. Similar assumptions have been adopted in other studies using static within-field zones (Hedley and Yule, 2009; Liu et al., 2018b; Stone et al., 2015). For the spatial calibration approach, the spatial pattern in the ancillary data must be available prior to the calibration process. Typically, such data are accessible at the beginning of the growing season, as they often originate from previous years, such as yield maps or relatively stable soil characteristics (e.g., soil texture, apparent soil electrical conductivity) (Nawar et al., 2017).

### 4.3. In-season dynamic within-field delineation

Spatial patterns, on which the calibration zones are assumed to be delineated, may be temporally dynamic for many agronomic traits (Anastasiou et al., 2019). Thus, spatial calibration might not account for changes over time within a growing season, as the within-field calibration zones are fixed at the beginning of the modeling process and then static. Here, delineation was based on a date where the $\Psi_{PD}$ was the more spatially heterogeneous. However, spatial calibration based on static calibration zones can be not relevant in case of field with strong time dependency. Many studies already investigated the relevance of using dynamic within-field zones for irrigation management (Cohen et al., 2017; Evans et al., 2013; Zhang et al., 2024). Such approach needs to have a strong spatiotemporal resolution, which can be achieved using

(low-cost) remote sensing data or sensors spread at within-field scale (Fontanet et al., 2020). However, using both kind of ancillary data with relatively stable spatial pattern characteristics (e.g. soil texture) and variables with changing spatial pattern from year to year depending on weather conditions (e.g. yield maps, crop coverage) has been identified as possible alternative to fully integrate the spatial pattern at the within-field scale (Nawar et al., 2017).

### 4.4. Spatial crop models: another spatialization process

Soil characteristics, and especially water fluxes, have a significant impact on CGM performances (Schmitter et al., 2015; Ward et al., 2018). However, CGM typically consider only vertical water fluxes, spatially constrained applications may integrate horizontal water fluxes by coupling CGM with hydrological models. Studies adopting this approach provide a more comprehensive representation of water dynamics (Huth et al., 2012; Shelia et al., 2018; Tenreiro et al., 2022; Xiang et al., 2020). Both input parameters considered to describe the within-field variability were related to the soil and the vine vigor. Climate data used were considered homogenous at the field level. However, microclimate in vineyard can have a huge impact on evapotranspiration and be heterogeneous at the row scale (Pereira et al., 2006; Torres et al., 2017). CGM are usually implemented with vertical water fluxes in the field. A more accurate representation of spatial interactions could be achieved by considering horizontal fluxes (e.g., runoff) to better capture within-field heterogeneity (Huth et al., 2012; Xiang et al., 2020).

## 5. Conclusion

This study examined the impact of spatial structure characteristics, total variance, and the level of correlation between an agronomic variable and ancillary data on the effectiveness of a spatial calibration approach. The findings demonstrated that spatial calibration significantly enhanced modeling performance when the agronomic variable
exhibited a strong spatial structure, a high variability, and a strong correlation with ancillary data used to delineate within-field zones (calibration zones). However, cases with moderate or weak spatial structure and high variability did not show similar benefits, highlighting the need for careful consideration of these conditions. For agronomic variables with low variability, no performance differences were observed between field or site-specific and spatial calibration approaches. This work provides new insights into spatializing CGM by downscaling predictions through the definition of within-field calibration zones. It advances understanding of how to increase the spatial resolution of crop models at the within-field scale, with the ultimate goal of improving agronomic practices to support more sustainable agriculture in a precision agriculture context.

## CRediT authorship contribution statement

**Bruno Tisseyre:** Methodology, Validation, Conceptualization, Writing – review & editing. **Sébastien Roux:** Writing – review & editing, Investigation, Methodology, Conceptualization, Validation. **Daniel Pasquel:** Methodology, Formal analysis, Writing – original draft, Investigation, Writing – review & editing, Conceptualization. **James A. Taylor:** Conceptualization, Validation, Funding acquisition, Writing – review & editing, Methodology.

## 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 was supported by the French National Research Agency under the Investments for the Future Program, referred as ANR-16-CONV-0004. This work has been realized with the support of MESO@LR-Platform at the University of Montpellier.

## Appendix A. Supporting information

Supplementary data associated with this article can be found in the online version at doi:10.1016/j.eja.2025.127773.

## Data availability

Data used in this study are available at this link: https://github.com/dpasquel/spatial Calibration_data

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