# Retrieving total transpirable soil water in a rainfed vineyard using vine shoot growth, weather, and Sentinel-2 data

Yulin Zhang, Léo Pichon, Sébastien Roux, Anne Pellegrino, Guillaume Coulouma, Bruno Tisseyre

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To cite this version:

Yulin Zhang, Léo Pichon, Sébastien Roux, Anne Pellegrino, Guillaume Coulouma, et al. Retrieving total transpirable soil water in a rainfed vineyard using vine shoot growth, weather, and Sentinel-2 data. Agricultural Water Management, 2025, 318, pp.109760. 10.1016/j.agwat.2025.109760. hal-05223516

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# Retrieving total transpirable soil water in a rainfed vineyard using vine shoot growth, weather, and Sentinel-2 data

Yulin Zhang<sup>a, *</sup>, Léo Pichon<sup>a, *</sup> <sup>Δ</sup>, Sébastien Roux<sup>b</sup>, Anne Pellegrino<sup>c</sup>, Guillaume Coulouma<sup>d, Δ</sup>, Bruno Tisseyre<sup>a</sup>

## ARTICLE INFO

Handling Editor - Dr X Zhang

**Keywords:**

Inverse modeling (IM)

TTSW

Low-cost data

Soil water balance (SWB) model

Mediterranean climate

## ABSTRACT

Winegrowers must regulate grapevine water status, as it significantly influences plant vigor, yield, wine aroma, and ultimately the market value of the final product. Total Transpirable Soil Water (TTSW)—the maximum water available for grapevine extraction—plays a critical role in vineyard water management. However, direct measurement of TTSW is operationally challenging, lacks spatial representativeness, and is especially complex for deep-rooted, rainfed vineyards, which dominate Mediterranean regions. This study proposes a low-cost, scalable methodology for TTSW estimation, adapting an Inverse Modeling approach to incorporate accessible data sources: vine shoot growth indices based on simple visual observations, weather data, and Sentinel-2 imagery. The adapted model was evaluated in a rainfed vineyard in Southern France across six vine plots, achieving a mean absolute error of 30 mm compared to benchmark methods. Given the TTSW range, this error is considered acceptable. The method performed best in plots without dead or missing vines and required less than one hour of fieldwork per plot, offering substantial operational advantages over traditional soil profile analysis. Additionally, the method demonstrated lower estimation uncertainty than the traditional soil-based benchmark. This study highlights the potential of integrating TTSW inverse modeling with accessible data sources, particularly vine shoot growth indices, to develop a cost-effective and scalable protocol for TTSW estimation in rainfed vineyards. These findings address a critical gap in water management knowledge for non-irrigated vineyards and offer practical benefits for winegrowers in water-scarce regions.

## 1. Introduction

Total Transpirable Soil Water (TTSW) represents the maximum volume of water that a specific crop can extract from the soil, as defined by Ritchie (1981) and Pellegrino et al. (2005). It is a key parameter in Soil Water Balance (SWB) models, which helps simulating soil water that is available for plants (Celette et al., 2010). This parameter is of high interest for viticulture. Winegrowers must fine-tune grapevine water status over time to optimize yields and berry composition, which ultimately determines wine quality and prices (Leeuwen et al., 2009). Hence, a specific targeted wine can require a specific level of water deficit during defined phenology stages (Kang et al., 2023). Quantifying TTSW is indispensable for SWB models to make accurate vine water status simulation, thereby assisting vineyard water managements.

Identifying areas with low total transpirable soil water allows winegrowers to strategize against the impacts of climate change on vineyards (Santillán et al., 2019), by reducing soil labor, adopting drought-adapted grape varieties, anticipating deficit irrigation or adjusting planting densities and exposed leaf area (Leeuwen et al., 2019).

The most robust way to obtain the total transpirable soil water is through in-field measurements, by using probes to monitor soil water content within a wide range of depths. However, the main constraint is to capture sufficient soil water content variation within a year with sufficient rain to recharge the soil water storage and reach to TTSW. Furthermore, especially for deep-rooting species like grapevine, the reference protocol of measuring total transpirable soil water is prone to logistical constrains, especially in a production context. For instance,

<footnote><sup>a</sup> ITAP, Univ Montpellier, INRAE, Institut Agro, 2 Pl. Pierre Viala, Montpellier 34060, France</footnote>

<footnote><sup>b</sup> MISTEA, Univ Montpellier, INRAE, Institut Agro, 2 Pl. Pierre Viala, Montpellier 34060, France</footnote>

<footnote><sup>c</sup> LEPSE, Univ Montpellier, INRAE, Institut Agro, 2 Pl. Pierre Viala, Montpellier 34060, France</footnote>

<footnote><sup>d</sup> LISAH, Univ Montpellier, IRD, INRAE, Institut Agro, 2 Pl. Pierre Viala, Montpellier 34060, France</footnote>

<footnote>* Corresponding authors.</footnote>

<footnote>E-mail addresses: yulin.zhang@agro.au.dk (Y. Zhang), leo.pichon@supagro.fr (L. Pichon).</footnote>
soil water content sensors must be calibrated locally, requiring specific skills. The installation of sensors is difficult in rocky soils (Coppola et al., 2013; Ottoni Filho et al., 2014), which are yet often found in viticulture lands. In addition, only a small volume of soil is generally explored, thus lacking in spatial representativeness comparing to the scale of a commercial vineyard (Brillante et al., 2015). Hence, spatially scalable TTSW estimation methods could better address the spatial variability of vine water status (Acevedo-Opazo et al., 2008). The Digital Soil Mapping (DSM) approach has been largely used to estimate soil variables in space, generating maps on varying spatial scales (Mulder et al., 2016; Chen et al., 2022). This approach models total transpirable soil water under a soil-based scope, by estimating the total amount of water that a soil can store. This approach decomposes the TTSW into a set of Soil Available Water Capacity (SAWC) components like horizon thickness, bulk density and specific soil moisture contents, which are time-consuming to obtain (Cousin et al., 2022). However, such perspective does not account for plant-soil interactions, which makes it an approximative method for assessing the parameter. Moreover, accurately modeling these variables would require a large dataset as training data (Styc and Lagacherie, 2021). This high requirement of ground-truth measurements further increases the difficulty of applying the DSM approach to estimate TTSW.

In contrast, Cousin et al. (2022) advocated for Inverse Modeling (IM) as a versatile method to estimate TTSW across varying spatial scales. Inverse Modeling combines a process-based model with observations of the model's outputs to infer the model's inputs (Zhang et al., 2024a). Over the last two decades, the IM approach has been frequently employed to retrieve TTSW, while mainly focusing on annual crops (e.g., maize, wheat) by leveraging complex crop models (Morgan et al., 2003; Jiang et al., 2008; Todoroff et al., 2010; He et al., 2021). Concerning perennial deep-rooting crops like grapevine, authors have been developing methods to invert SWB models displaying lower requirement in model parameterization. For example, Campos et al. (2016) inverted a SWB model by using evapotranspiration measurements obtained from an Eddy Covariance tower. This data source allowed to obtain TTSW estimation on a farm level. Later, Gaudin et al. (2017) inverted a SWB model on a within-field level, by using predawn leaf water potential (PLWP) measurements. Notably, Gaudin et al. (2017) developed their inverse model specifically operating under dry conditions where the soil water balance model can be significantly simplified (An overview of their method will be given in Section 2.1). Such inverse model was shown to be particularly suitable for rainfed vineyards in Mediterranean regions. Nevertheless, the main limitation of that approach is the high data acquisition cost in order to obtain PLWP and the Basal Crop Coefficient (Kcb) measurements. While those data are commonly available in research projects, they are challenging to acquire in commercial vineyards. For instance, the protocol of collecting PLWP requires heavy and expensive equipment, specific skills and a very constraining measurement time window (Scholander et al., 1965). Consequently, despite its advantages, the applicability of the method of Gaudin et al. (2017) is limited in practice.

Thanks to modern sensing technologies (e.g., satellites) and digital devices (e.g., smartphones), it becomes increasingly easy to derive plant-based observations, like canopy reflectance data (Devaux et al., 2019) or plant height (Xie et al., 2021). In fact, some authors have paved the path for replacing predawn leaf water potential or Kcb measurements with other more accessible data sources and models. For example, Zhang et al. (2024b) predicted PLWP by using an index of vine shoot growth, obtained from visual observations, and weather data; Campos et al. (2010) created a Kcb regression model from Normalized Difference Vegetation Index (NDVI) derived from satellite images.

Notably, the vine shoot growth observations provide interesting potential. The index summarizing this information: iG-Apex, or the index of growth of “apex” (vine shoot), has been shown to be sensitive to vine water stress level (Pellegrino et al., 2005; Pichon et al., 2023), with lower values reflecting higher water deficit. This property may grant the index the possibility to become a proxy of soil water content, that is

commonly leveraged in other TTSW-retrieval studies (Alkassem et al., 2022), yet with a much lower cost. Indeed, this index is collectable in less than five minutes (Pichon et al., 2021), showing high cost-efficiency in the field. Its collection is integrated into a free mobile application installed by hundreds of users, which has gathered, on the French national scale, over 20,000 georeferenced iG-Apex observations by year 2021 (Pichon et al., 2022). Nonetheless, despite the potentials of this data source, no study has attempted to utilize it in inverse modeling, nor combining it with other accessible data sources like weather records and satellite images, to retrieve TTSW. While a methodology based on this information could greatly decrease the cost of obtaining the total transpirable soil water, it could provide a spatially scalable solution for commercial vineyards.

In this context, this study aims to explore the possibility to retrieve total transpirable soil water on a within-field scale by using vine shoot growth observations, weather information, and Sentinel-2 images. Specifically, the inverse model of Gaudin et al. (2017) was adapted for incorporating those data sources which are easily accessible for a production context, and available on a territorial spatial scale. Data were collected from six vine plots located in a rainfed vineyard in the Mediterranean region. The adapted model's accuracy, uncertainty, and required field work load were evaluated against validation approaches under both deep and shallow soil conditions ("deep/shallow soil" will be defined).

## 2. Materials and methods

### 2.1. Theoretical background

This part first outlines the theoretical basis for retrieving TTSW from plant-based observations and also weather data, highlighting the theoretical basis of using observations of vine shoot growth to retrieve TTSW. It then presents the inverse model of Gaudin et al. (2017), which provides the foundation for the methodology proposed in this study.

#### 2.1.1. Using plant-climate-based information to retrieve TTSW

Total Transpirable Soil Water (TTSW) represents the actual amount of water a crop can extract from the soil under specific environmental conditions and management practices. It inherently accounts for the interaction between soil properties (e.g. depth, critical humidity), plant genetic materials and physiology, and atmospheric demand (Cousin et al., 2022). Consequently, plant-climate-based observations provide a valuable means to inversely estimate TTSW, as they are intrinsically connected.

The relationship between plant physiological status and TTSW has been well established in the literature. One key indicator, the fraction of transpirable soil water (FTSW), is derived from TTSW and is frequently correlated with plant physiological variables such as predawn and midday leaf water potential, or stomatal conductance (Pellegrino et al., 2005). These strong statistical relationships provide a basis for using plant water status indicators to infer TTSW. Similarly, Coulouma et al. (2020) demonstrated that carbon isotope discrimination (δ¹³C) in grape must correlates with TTSW across a large range of soils, further supporting the potential of plant-based indicators to estimate TTSW. In parallel, Inverse Modeling (IM) studies commonly employ plant-climate-based observations, such as crop yield (He et al., 2021), leaf area index (LAI) and evapotranspiration (ET) (Alkassem et al., 2022), to retrieve TTSW. These methods also rely on the fundamental assumption that plant responses to soil water availability can be effectively used to infer TTSW. Therefore, linking the index of vine shoot growth to TTSW has a theoretical foundation (Pellegrino et al., 2005; Pichon et al., 2023).

However, several challenges must be considered when applying plant-climate-based approaches. First, other processes except plant transpiration, such as precipitation and soil evaporation, also contribute to soil water dynamics, potentially complicating the inversion process.
Second, the chosen indicator must be sufficiently sensitive to soil water availability, with its response to soil moisture changes outweighing the influence of other environmental factors such as nutrient availability or pest pressure. To address these challenges, Gaudin et al. (2017) proposed an IM approach that aims to simplify the system to be inverted, thereby improving the applicability of plant-climate-based TTSW inversion. The following section provides an overview of their methodology.

### 2.1.2. An overview of the inverse model of Gaudin et al. (2017)

The methodology proposed by Gaudin et al. (2017) is based on a simplification of the Soil Water Balance (SWB) equation, focusing exclusively on plant transpiration under dry conditions. By eliminating other water fluxes from the SWB equation, their approach simplifies the inversion process. To enable such simplification, the method is specifically designed for drought periods (i.e. a minimum of 10 days without rainfall), which are characteristic of Mediterranean summers when low soil water availability triggers stomatal closure in vines, enhancing plant's sensitivity to soil water availability. Hence, the applicability of this methodology relies on three key conditions:

1. **Prolonged dry conditions:** A minimum of 10 days without rainfall to ensure negligible soil evaporation and other water flux (except transpiration).

2. **Sufficient water deficit:** The water stress level must be high enough to activate stomatal closure in vines.

3. **No external water inputs:** No capillary rise from any water table or influence from deep soil layers beyond the vine root zone.

By reformulating the simplified SWB, Gaudin et al. (2017) derived an inverse model to estimate TTSW (expressed in mm or L/m²), requiring two primary inputs: the basal crop coefficient (Kcb) and the water status slope, as shown in the Eq. 1.

$$TTSW = -0.44 \times \frac{K_{cb}}{Slope} \quad (1)$$

The basal crop coefficient (Kcb) characterizes the ability of vines to extract soil water through transpiration (Doorenbos and Pruitt, 1977). Under common Mediterranean vine training systems (e.g. goblet training, vertical shoot positioning training), Kcb is assumed to remain constant during the mid-growth stage, typically ranging between 0.35 and 0.5 (Rallo et al., 2021).

The water status slope is obtained from a series of predawn leaf water potential (PLWP) measurements (in MPa) recorded alongside cumulative potential evapotranspiration (ET₀, in millimeter) (Allen et al., 1989). The accumulation of ET₀ starts from the date of the first PLWP measurement, and under the defined conditions, the relationship between PLWP and cumulative ET₀ is assumed linear (Roux et al., 2019). This linear trend reflects the progressive decline of PLWP with increasing climatic demand, with the fitted slope coefficient (expressed in MPa/mm) providing a quantitative measure of this relationship (see Appendix-A for an illustration). The slope coefficient is calculated once by using all available data, thereby is considered as temporally invariant.

The inverse model also incorporates a constant coefficient (0.44), which was derived through rigorous demonstration in Gaudin et al. (2017). This value is grounded in two key physiological assumptions: (1) stomatal closure occurs when the FTSW falls below 0.4 (Schultz, 1996; Pellegrino et al., 2006), and (2) the mathematical relationship between FTSW and PLWP follows the model proposed by Lebon et al. (2003), which has been shown to remain stable across different soil-climatic conditions and cultivars (Pellegrino et al., 2005).

In summary, by constraining the inverse model to a period where transpiration is the sole driver of soil water loss, the method of Gaudin et al. (2017) establishes a direct link between changes in predawn leaf water potential and the value of total transpirable soil water, requiring

only climatic demand (ET₀) and vine vegetation development (Kcb) data as inputs. Nevertheless, the required measurements could be expensive to obtain in a production context. The following section presents our adaptations for incorporating more accessible data sources.

## 2.2. Adaptations of the inverse model of Gaudin et al. (2017)

### 2.2.1. Incorporating the index of vine shoot growth and weather data

This study advocates leveraging the iG-Apex data to retrieve TTSW. Zhang et al. (2024b) proposed a predictive model, named Recursive-Duo-Model (RDM), that utilizes iG-Apex and weather variables as inputs to generate PLWP predictions with associated uncertainty. Consequently, the PLWP measurements required in the inverse model of Gaudin et al. (2017) were replaced by predictions generated by the RDM.

Raw iG-Apex and weather data were transformed into predictors (n = 30) by an algorithm included inside the RDM algorithm. The training data used to calibrate the RDM were obtained from the Mediterranean rainfed vineyard "Tavel" (Fig. 2a), collected from year 2008 to 2012 (cv. Grenache/R110). The detailed methodology related to the RDM was thoroughly described in Zhang et al. (2024b).

Thanks to the RDM, predictions of predawn leaf water potential were obtained for each studied plot and each date where iG-Apex observations were made. For each plot, a linear regression was fitted according to predicted PLWP and ET₀ information, using the Ordinary Least Square method. Detailed data acquisition methods will be presented in Section 3.2.3. The obtained slope coefficient was noted as Slope Predicted.

### 2.2.2. Incorporating Sentinel-2 imagery

Kcb was estimated with the regression model (Eq. 2) proposed by Campos et al. (2010), based on the Normalized Difference Vegetation Index (NDVI).

$$Kcb^{NDVI} = 1.44 \times NDVI - 0.1 \quad (2)$$

NDVI was computed from remote sensing data. The satellite imagery was sourced from the European Space Agency's Copernicus Program (www.esa.int). The harmonized Sentinel-2 Level-2 dataset (10 m resolution) was used to derive NDVI observations at studied locations. NDVI values were extracted from the four closest pixels to the center of each studied plot. An assumption was made that using four pixels allows to obtain a more robust description on the surroundings of a plot, while reducing the influence of data noise or missing data (Lang et al., 2023). Then, an average KcbNDVI was computed for studying plots at all image dates. These averages were aggregated across all dates for each plot, resulting in a final mean KcbNDVI and the corresponding standard deviation. The estimated Kcb was noted KcbNDVI.

### 2.2.3. Handling varying plot area

iG-Apex is measured from ten vines that form a plot. In Mediterranean vineyards, the occurrence of dead or missing vines may be frequent (Oger et al., 2023). If an iG-Apex observation plot contained dead or missing vines, the actual local plant density becomes lower, which could decrease the water competition. In order to compensate for this effect in the TTSW estimation, a plot-area-ratio standardization was proposed. This standardization adjusts the estimated TTSW to a uniform number of grapevines per square meter given a nominal plant density condition, allowing for the comparison of TTSW estimates obtained from different plots under the same unit (Bièvre, 2012). This correction factor was expressed as the ratio of the area (m²) of a reference plot, with no dead or missing vines, over the measured area of the vine plot under consideration (which may contain dead or missing vines). The factor was shown in Eq. 3.

### 2.2.4. The adapted inverse model

The adapted inverse model is presented below.
$$TTSW\_apex = -0.44 \times \frac{K_{cb}^{NDVI}}{Slope^{Predicted}} \times \frac{Referential plot area}{Measured plot area} \quad (3)$$

Where TTSW-apex is the estimated TTSW (mm). KcbNDVI stands for Kcb estimated from the model of Campos et al. (2010) and Sentinel-2 imagery (without unit). SlopePredicted is the slope coefficient predicted by using iG-Apex and weather data. The ratio of plot areas is used as a standardization operator. The deployed data sources were illustrated in Fig. 1.

Similar to the model of Gaudin et al. (2017), the adapted inverse model also must satisfy the three specific conditions. The following sections presented the verification of those conditions and detailed data acquisition schemes.

## 2.3. Field study and data acquisition

### 2.3.1. Studied area and vineyard

The rainfed vineyard under investigation, known as "Domaine du Chapitre", was situated in the Occitanie region of southern France (Fig. 2a). It was located approximately 10 km south of Montpellier and 4 km north of the coast (43.532103°N; 3.863947°E - WGS84). The vineyard's soil predominantly consisted of silty-clay to clay texture. The Mediterranean climate was typified by hot and dry summers (Joly et al., 2010). The vines were trained using a vertical shoot positioning system with three levels of trellising (maximum height of 1.6 m). The vineyard floor was periodically tilled. The grass cover between rows and vines was removed weekly during the growing season in order to reduce water competition.

The investigation took place in 2022 and 2023, and focused on two specific vine fields: Larzat (Fig. 2b) and Argèle (Fig. 2c). Both fields were planted with Vitis vinifera L. cv. Syrah (rootstock: Fercal). The plants were 7 years old and were both planted with a 2.5 m inter-row distance. Larzat field was planted with a 1.2 m inter-vine distance on the rows, while it was only 1 m in Argèle. Notably, the occurrence of dead or missing vines per hectare in Larzat was twice as high as that in Argèle (up to 30 %, Oger et al., 2023).

Within each field, three plots were selected. These plots were labeled from 1 to 6 (Fig. 2b&c). Additionally, all six plots were marked with the letter "D" or "S", indicating whether the plot had deep soil or shallow soil (Section 2.4.1.3). Each plot contained 10 productive grapevines, evenly divided between two adjacent rows, giving 5 productive vines per row. Measured Larzat plot areas were all larger than those of Argèle plots (Table 2), a result of both a lower planting density and the higher incidence of dead or missing vines mentioned previously (Section 2.2.3).

The plot 6 encountered an unusual event: it accidentally received gravity-fed water in early July in year 2022 (between the 8th and 11th) during three days from an overly irrigated neighboring block upstream. This plot was thus assigned an additional letter "I" to denote this inadvertent irrigation. The designations and implications of plot names are summarized in Table 1.

In order to utilize the adapted inverse model, the referential plot area was calculated based on the inter-vine and inter-row distances and the number of vines per plot (n = 10). The resulted area was 15 m² for the Larzat field and 12.5 m² for the Argèle field.

Together with actually measured plot areas (Table 2), the ratio of plot areas, which is the standardization operator, could be obtained for computing TTSW-apex.

### 2.3.2. Verification of the inverse model conditions

During the summer of 2022, an extended dry period from late June to mid-August, with no recorded rainfall, satisfied the first inverse model condition (Section 2.1.2). Throughout this period, weekly vine water status monitoring indicated at least a moderate water deficit across all studied plots, with PLWP values ranging between -0.5 and -0.3 MPa (Appendix A). This level of water deficit is expected to trigger stomatal closure in grapevines (Deloire et al., 2020), fulfilling the second condition. Additionally, the observed linear decline in PLWP values (Appendix A) supports the assumption of considering a simplified soil water balance (SWB), implying negligible available water in the root zone. Given the frequent historical droughts in the region and the exceptionally low water table levels recorded in Southern France in 2022 (www.brgm.fr), the third condition was also considered met.

Consequently, a 30-day window, from July 11th to August 9th of year 2022, was selected as the period which satisfies the three inverse model conditions. During this period, the sum of rainfall was zero, with the cumulative ET₀ of 231 mm and the mean daily temperature of 28°C (average min= 23°C; average max= 33°C). Data collected during this period were used as the inverse model's input.

As highlighted in Section 2.3.1, plot 6-SI experienced unintentional irrigation just prior to this selected period. This event violated the conditions of inverse model, as irrigated water could be equated to a rainfall occurrence or a capillary rise event. Despite this violation, plot 6-SI was retained in the experiment and subsequent analysis. This allowed for an investigation on the inversion outcome obtained when the inverse model conditions were not satisfied. It was also our intention to report the original experimental design. However, results from this plot should be interpreted with caution, because of their limited reliability.

### 2.3.3. Vine shoot growth and weather data

For each plot, five iG-Apex measurements were made during the selected period. It was confirmed that there was no nitrogen deficit post-flowering as SPAD measurements (SPAD-502 Chlorophyll meter) were well above 30 (Verdenal et al., 2023). It was also assumed that relevant vineyard management practices had mitigated the impacts of pests, thereby isolating water availability as the main limiting factor of vine shoot growth. The growth of vine shoot was assessed according to the method proposed by Pichon et al. (2021) and using the smartphone application Apex-Vigne (Brunel et al., 2019). During each observation of vine shoot growth, 50 apexes (5 per vine) were observed and categorized by the same human operator into three growth stages: i) full growth, ii) moderate growth, and iii) stopped growth (Appendix B). The iG-Apex index was computed for each plot at each date. During the studied period, a total of 30 iG-Apex observations (5 in each plot) were collected.

Weather data were provided by Météo France, and downloaded via the SICLIMA platform developed by AgroClim-INRAE. Six weather variables were downloaded at the daily scale and an 8-km spatial

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Data sources utilized for obtaining the adapted inverse model's inputs. (iG-Apex: the growth index of vine shoots; RDM: Recursive-Duo-Model (Zhang et al., 2024b); Kcb: Basal crop coefficient; Slope: Water status slope calculated from predawn leaf water potential and ET₀ time series; TTSW: total transpirable soil water).</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** (a) Location of the studied vineyard – “Domaine du Chapitre”, (b) Location of the studied plots in the field Larzat (“D” in plot ID signifies deep soils, while “S” signifies shallow soils), (c) Location of the studied plots in the field Argèle (“SI” in plot ID signifies shallow soils with irrigation).</figcaption></figure>

<table><caption>**Table 1**
The designations and implications of plot name.</caption><thead><tr><th>Plot ID</th><th>Description</th></tr></thead><tbody><tr><td>1-D</td><td>Larzat plots (N° 1 & 2) with deep soils</td></tr><tr><td>2-D</td><td>Larzat plot (N° 3) with shallow soil</td></tr><tr><td>3-S</td><td>Argèle plots (N° 4 & 5) with shallow soils</td></tr><tr><td>4-S</td><td>Argèle plot (N° 6) with shallow soils, which received inadvertent irrigation</td></tr></tbody></table>

<table><caption>**Table 2**
The area of the studied plots and their referential values.</caption><thead><tr><th rowspan="2">Plot ID</th><th colspan="3">Larzat field</th><th colspan="3">Argèle field</th></tr><tr><th>1-D</th><th>2-D</th><th>3-S</th><th>4-S</th><th>5-S</th><th>6-SI</th></tr></thead><tbody><tr><td>Referential area (m²)</td><td>15</td><td>15</td><td>15</td><td>12.5</td><td>12.5</td><td>12.5</td></tr><tr><td>Measured plot area (m²)</td><td>22</td><td></td><td>20</td><td>13</td><td>13</td><td>15</td></tr></tbody></table>

resolution during the selected period, including potential evapotranspiration (ET₀), mean, maximum and minimum temperature, precipitation, and relative humidity.

### 2.3.4. Extraction of NDVI from Sentinel-2 imagery

During the selected period, the Kcb was considered having reached its maximum potential. Extraction and pre-processing of Sentinel-2 images (resolution at 10 m) were performed with Google Earth Engine Code Editor. The four closest pixels to the center of each studied plot were extracted. Averaging these neighboring pixels may provide a more stable representation of vegetation development by mitigating single-pixel noise while preserving local values. Any images with cloud cover exceeding 30 % were excluded before extraction. Additionally, a cloud filtering process was applied to all selected images. This filter removed pixels that were identified as clouds or cirrus clouds by using information contained in the band QA60 (the cloud mask). Finally, a total of six satellite image dates were available within the selected period. The B2 (Near-infrared) and B4 (Red) spectral bands were used to compute NDVI, as suggested by Sozzi et al. (2020). The average NDVI values (Table 3) were then transformed into KcbNDVI using formula 2. (See

<table><caption>**Table 3**
The number of pixels associated to each studied plots and the averaged Normalized Difference Vegetation Index (NDVI) values with standard deviation.</caption><thead><tr><th>Plot ID</th><th>Number of pixels extracted</th><th>Average NDVI</th><th>Standard Deviation</th></tr></thead><tbody><tr><td>1-D</td><td>4</td><td>0.374</td><td>0.006</td></tr><tr><td>2-D</td><td>4</td><td>0.370</td><td>0.006</td></tr><tr><td>3-S</td><td>4</td><td>0.320</td><td>0.010</td></tr><tr><td>4-S</td><td>4</td><td>0.374</td><td>0.007</td></tr><tr><td>5-S</td><td>4</td><td>0.380</td><td>0.006</td></tr><tr><td>6-SI</td><td>4</td><td>0.394</td><td>0.007</td></tr></tbody></table>

Appendix C for viewing the temporal evolution NDVI values).

### 2.4. Validation method

The proposed approach was evaluated according to three criteria: accuracy of estimations, uncertainty of estimations, and required field work. To evaluate the accuracy of the estimations, validation data were chosen differently for plots with shallow and deep soils.

#### 2.4.1. Definition of validation data

#### 2.4.1.1. For shallow soil conditions.
In both fields, due to the hardness of soils and the presence of rocks, it was not possible to install probes to derived TTSW. Consequently, when the soil was relatively shallow for excavation, Soil Available Water Capacity (SAWC) was chosen as validation data. SAWC is obtained by observing physical properties of soils (Eq. 4), which should represent the maximum TTSW that could be physically attained by rainfed soils without capillary rise.

Soil available water capacity was measured by creating soil pits in the studied plots, and by following the methodology outlined by Cousin et al. (2022), as presented in Eq. 4.

$$SAWC = \sum_{i=1}^{i \leq \max N_b \text{Horizon}} Z_i \times BD_i \times (FC_i - PWP_i) \times (1 - R_i) \quad (4)$$

Where i represents each of the identified soil horizons. Z denotes the thickness of these horizons (dm). BD refers to the bulk density of each horizon (g. cm⁻³). FC stands for the Field Capacity, indicating the gravimetric soil water content held after rapid drainage (g. g⁻¹). PWP
stands for the Permanent Wilting Point, the gravimetric soil water content which causes an irreversible leaf wilt due to the lack of water (g. g⁻¹). Lastly, R represents the gravimetric proportion of rock fragments (diameter > 2 mm) within the soil (g. g⁻¹), which was assumed not to contribute SAWC.

In each identified soil horizon, multiple soil samples were collected and sent for laboratory analysis to determine the key parameters. For field capacity and permanent wilting point, the approach detailed by Klute (1986) was employed. This involved collecting undisturbed soil samples and determining their water retention at specific pressure potentials: -33 kPa for FC and -1500 kPa for PWP. The bulk density of the soil was measured using a photogrammetry method as described by Coulouma et al. (2021), which has been demonstrated to be more efficient than traditional core sampling, particularly for stony soils. For quantifying rock fragments, the procedure outlined by Algayer et al. (2020) was followed, which entailed sieving soil samples to isolate coarse elements larger than 2 mm in diameter, and obtaining their gravimetric ratio after drying at 105°C for 48 h. The detailed sampling information, averages, and standard deviations (when calculable) for all SAWC parameters were presented in Appendix D.

### 2.4.1.2. For deep soil conditions.
When the full depth of the soil could not be explored by soil pits, SAWC could not be used as validation data. In those cases, the method of estimating TTSW from actual PLWP observations proposed by Gaudin et al. (2017) was chosen as the best possible estimation of TTSW.

Predawn leaf water potential measurements used to estimate TTSW were made according to the method established by Scholander et al. (1965). Weekly measurements were performed with a pressure chamber between 3 a.m. and 5 a.m. in order to minimize the impact of transpiration. At each date and on each plot, five PLWP measurements were made on five different vines. Each measurement was obtained from one mature, healthy, and non-senescing leaf that was situated in the middle of a shoot. The PLWP value considered for a given plot at a specific date was the average of the five measurements. Water potential values were collected at five different dates over the selected period. All PLWP measurements were conducted by the same operator throughout the season.

The water status slope was then computed using the same methodology described previously (Section 2.1.2), which consisted of matching cumulative ET₀ with PLWP measurement dates, and fitting a linear regression model per plot. The same KcbNDVI values used for calculating TTSW-apex were deployed. The calculated TTSW was denoted as TTSW-plwp.

### 2.4.1.3. Evaluation of soil depth.
In total, six soil pits were created (Appendix D). Plots 3-S, 4-S, 5-S and 6-SI were excavated to their maximum depths (reaching rocks), which were respectively 0.9 m, 1.4 m, 1.4 m and 1.4 m. For these plots, the soil was considered “shallow” because the whole soil depth was analyzed. Four soil pits were realized, and SAWC was considered as the validation data.

In plot 1-D and 2-D, the excavation stopped at 1.5 m and 1.3 m respectively, because of the hardness of stony soil and the limited capabilities of the digging equipment. In these two plots, the deepest observed soils did not show any sign of approaching rocks, aligning with historical studies conducted in the same field which had indicated very deep soils (> 2 m) (Rouault, 2021). Hence, the soil pits in plots 1-D and 2-D were considered as truncated (“deep soil”), and TTSW-plwp was chosen as validation data.

### 2.4.2. Evaluating accuracy of estimations

The accuracy of the proposed approach was evaluated by comparing the TTSW estimations to corresponding observed validation data (SAWC or TTSW-plwp depending on the plot) and by calculating Mean Absolute Error (MAE) (Eq. 5) and Root Mean Square Error (RMSE) (Eq. 6), both expressed in mm.

$$MAE = \frac{\sum_{n=1}^{N} |E_n - O_n|}{N} \qquad (5)$$

$$RMSE = \sqrt{\frac{\sum_{n=1}^{N} (E_n - O_n)^2}{N}} \qquad (6)$$

Where N equal to 6, representing the total number of studied plots, E stands for estimated TTSW, and O stands for observed validation data.

### 2.4.3. Evaluating uncertainty of estimations

Estimation uncertainty was evaluated by an error propagation procedure based on the first-order Taylor expansion (Román Dobarco et al., 2019; Styc and Lagacherie, 2021). This technique enabled the transfer of uncertainties from a model’s inputs to its output. The uncertainty of each model input was represented by its standard deviation.

For soil available water capacity, the standard deviations of BD, FC, PWP were calculated from sample measurements. The standard deviation of KcbNDVI was calculated from NDVI values. The standard deviation of SlopePredicted was obtained by running multiple times (n = 100) the Recursive-Duo-Model. This could be done because the RDM model contains stochastic components, and predictions were associated with an uncertainty. Finally, the slope coefficients obtained from measurements were considered free of uncertainty.

The R package “errors” (Ucar and Henry, 2023) was used to realize the error propagation. The error propagation method generated a combined standard uncertainty, noted as σᵢ, which is specific to the underlying estimate (TTSW-apex, SAWC, or TTSW-plwp), noted as Ŷᵢ. These two elements were transformed to a statistically interpretable confidence interval, after defining a level of confidence (chosen to be 90 % in this study). Hence, for a given estimate, its limits of the 90 % confidence interval (CIL) could be computed (Eq. 7), where 'i' represents a specific plot.

$$CIL_i = \hat{Y}_i \pm 1.645\sigma_i \qquad (7)$$

The ratio between the width of confidence interval and its estimate was estimated, in order to obtain a relative description of an estimation’s uncertainty (Eq. 8).

$$CI ratio = \frac{2 * 1.645\sigma_i}{\hat{Y}_i} \qquad (8)$$

### 2.4.4. Evaluating required field work effort

Field work time required to make one TTSW estimation on a single plot by using each approach was quantified. It was expressed as the total time cost in hours (h).

$$Total time cost = \sum_{j=1}^{J} M_j * N_j * C_j \qquad (9)$$

Where M represents the number of repetitions required by a task, such as sampling M soil horizons in a plot or conducting M PLWP measurements (Table 4), N denotes the number of operators needed to complete the task and C is the time (in hour) needed to perform that task per operator. Additionally, J reflects the total number of different tasks required by a method. The variety of tasks and their respective time costs were described in Table 4.

For obtaining TTSW-apex and TTSW-plwp, J equaled one, suggesting only one task type was required. Conversely, SAWC required at least four different tasks (J=4). Five measurements of PLWP and iG-Apex were realized (M=5). While one person can efficiently gather iG-Apex data (N = 1), PLWP acquisition necessitates two operators (N = 2) due to nocturnal operations. To account for higher cost related to work during the night, each hour of night work was doubled in the calculation. Furthermore, the time required for certain tasks was affected by
<table><caption>**Table 4**
Field work hours and number of operators required for realizing the key tasks to implement the three methods.</caption><thead><tr><th>Purpose</th><th>Task</th><th>Number of operators</th><th>Hours of field work per operator</th><th>Work during the night</th></tr></thead><tbody><tr><td>Obtain TTSW-apex</td><td>Make one iG-Apex observation</td><td>1</td><td>0.1</td><td>No</td></tr><tr><td>Obtain TTSW-plwp</td><td>Make one PLWP measurement</td><td>2</td><td>0.3 (0.6<sup>a</sup>)</td><td>Yes</td></tr><tr><td rowspan="4">Obtain SAWC</td><td>Open and refill one soil profile</td><td>2</td><td>2.2</td><td>No</td></tr><tr><td>Analyse one opened soil profile</td><td>2</td><td>1</td><td>No</td></tr><tr><td>Collect and organize soil samples from one horizon for laboratory analysis</td><td>1</td><td>0.25</td><td>No</td></tr><tr><td>Collect soil samples of one horizon using the photogrammetric technique</td><td>1</td><td>0.25/0.5<sup>b</sup></td><td>No</td></tr></tbody></table>

<sup>a</sup>: One working hour during the night was considered to be two, for accounting for related high operational constraint.

<sup>b</sup>: 0.25 for soil horizons containing few rocks; 0.5 for soil horizons containing many rocks.

field conditions. For instance, plots with more soil horizons or higher rock fragment (Appendix D) necessitate increased field work hours.

## 2.5. Softwares

All analyses were performed using R Statistical Software (R Core Team, 2021). Spatial operations were carried out using QGIS 3.16.16-Hannover (QGIS Development Team, 2024). Agisoft Meta-shape® was employed for soil bulk density measurement by photo-grammetry as described by Coulouma et al. (2021).

# 3. Results

## 3.1. Inverse model inputs: Kcb<sup>NDVI</sup> and water status slopes

The Kcb<sup>NDVI</sup> values derived from satellite imagery ranged from 0.361 in plot 3-S to 0.467 in plot 6-SI, with the majority centered around 0.43 (Table 5). The standard deviation observed for each plot was low (0.009–0.060), indicating consistent vegetation levels during the studying period.

Fig. 3 depicts the predicted slopes with associated uncertainty at each plot illustrated by histograms. Mean slope coefficients and their standard deviations were indicated on the left (Fig. 3). Predicted slopes were generally distributed around −1.1*10<sup>-3</sup> MPa/mm, with those in

<table><caption>**Table 5**
Means and average standard deviations (n = 6) of basal crop coefficient (Kcb, no unit) used as inverse model input, estimated from NDVI time series for the six studied plots.</caption><thead><tr><th>Plot</th><th>Mean of Kcb<sup>NDVI</sup></th><th>Standard deviation of Kcb<sup>NDVI</sup></th></tr></thead><tbody><tr><td>1-D</td><td>0.438</td><td>0.009</td></tr><tr><td>2-D</td><td>0.432</td><td>0.033</td></tr><tr><td>3-S</td><td>0.361</td><td>0.047</td></tr><tr><td>4-S</td><td>0.439</td><td>0.060</td></tr><tr><td>5-S</td><td>0.447</td><td>0.020</td></tr><tr><td>6-SI</td><td>0.467</td><td>0.037</td></tr></tbody></table>

Larzat field globally higher than those in Argèle. The mean predicted slope value in plot 6-SI was notably low at −1.5678*10<sup>-3</sup> MPa/mm, while 1-D recorded the highest slope value at −8.3828*10<sup>-4</sup> MPa/mm. Predicted slopes in plot 4-S and 5-S were similar. The uncertainty of slope coefficients in each plot was rather constant.

## 3.2. Evaluation of inversion results

Fig. 4 shows the TTSW estimates from the adapted inverse model (TTSW-apex) alongside those obtained from validation methods, and their 90 % Confidence Intervals (CI). In average, validation data of TTSW varied around 140 mm. The overall Mean Absolute Error (MAE) between TTSW-apex and validation data (SAWC or TTSW-plwp) was 30 mm, with a Root Mean Square Error of 32 mm.

Specifically, plot 4-S and 5-S presented TTSW-apex values at 149 mm and 162 mm, with minor differences from validation data of 15 mm and 20 mm respectively. In these two plots, TTSW-apex estimates fell within validation data’s 90 % confidence interval. Larger discrepancies were observed in plot 3-S and 6-SI. Plot 3-S’s TTSW-apex stood at 117 mm, exceeding validation data by 53 mm. For 6-SI, TTSW-apex was 110 mm, 34 mm lower than the validation data, although with overlapping CIs. In plots 1-D and 2-D where TTSW-plwp was used as validation data, the errors of TTSW-apex estimates were respectively 19 mm and 37 mm, with both estimates being smaller than the validation data. In plot 1-D, TTSW-apex estimates fell within validation data’s 90 % confidence interval.

Fig. 5 complements the uncertainty information of estimations, by comparing the ratio of CI width. The CI ratios of TTSW-apex estimates varied, with the smallest ratio at 30 % (of the estimate) for plot 6-SI, and the largest at 56 % for plot 3-S. For TTSW-plwp, the CI ratios were relatively lower, notably 7 % for 1-D and 25 % for 2-D. Conversely, SAWC’s CI ratios spanned from 38 % in 4-S, to 67 % in 3-S, with SAWCs’ CI ratios generally surpassing those of TTSW-apex, except in plot 4-S.

Fig. 6 shows the field work hours necessary to perform each estimation method. In plots 1-D and 2-D, TTSW-plwp estimations consistently demanded 6 h of field work for each plot. SAWC estimates based on soil profiles required a minimum of 8.7 h of field work. Plot 3-S in the Larzat field demanded about 11 h due to its rockier soil, and plots in the Argèle required around 9 h. Comparatively, obtaining TTSW-apex estimates necessitated 30 min (0.5 h) of field work per plot for acquiring 5 measurements. Consequently, the TTSW-apex method necessitated substantially less field work: 12 times less than TTSW-plwp, and at least 17 times less than SAWC.

# 4. Discussion

## 4.1. Factors impacting inversion accuracy

The inverse model proposed by Gaudin et al. (2017) was adapted in this study to incorporate more accessible data sources—vine shoot growth, weather, and Sentinel-2 imagery—for retrieving Total Transpirable Soil Water (TTSW) in rainfed vineyards. The results yielded a Mean Absolute Error of 30 mm (RMSE= 32 mm), corresponding to 22 % relative to the validation data (≈140 mm), which falls within an acceptable range. Similar inverse modeling studies have reported error rates between 10 % and 30 % (Morgan et al., 2003; Jiang et al., 2008; Sreelash et al., 2017), as reviewed by Cousin et al. (2022). These non-negligible errors likely stem from factors such as oversimplified soil representations, unaccounted processes (e.g., farming practices or pest effects), and uncertainties in input data and measurements. While the proposed methodology achieves only moderate inversion accuracy, its primary value lies in balancing acceptable precision with cost-efficiency, making it suitable for practical implementation—a key aspect further discussed in Section 4.4.

In the context of viticulture, Alkassem et al. (2022) inverted a complex mechanistic model (STICS) in multiple vineyards, where the
<figure><img src="image_6.png" /><figcaption>Fig. 3. Predicted water status slope coefficients (in MPa/mm) representing the relationship between ET₀ and PLWP for the six studied plots, with means and standard deviations (SD). The variability of slope values was obtained by running repeatedly the predictive model (Recursive-Duo-Model) in each studied plot. (“D” in plot ID for “deep soils”, “S” for “shallow soils”, “SI” for “shallow soils with irrigation”).</figcaption></figure>

spatial variability in field conditions increased the difficulty of model parameterization. Focusing on 14 sites, their approach obtained a RMSE of about 50 mm. Comparatively, the adapted inverse model has maintained the parsimony from the model of Gaudin et al. (2017), without requiring extensive knowledge of model parameters. The lower error found in this study (RMSE of 32 mm) reinforce the interest of the adopted inversion strategy, which relies on the simplification of the Soil Water Balance (SWB) model by deliberatively constraining its applicability according to local climate conditions. The proposed approach also led to lower errors than the plant-based SAWC evaluation method based on carbon isotope discrimination (δ13 C) reported in Coulouma et al. (2020). In that study, the lowest RMSE was found at 35 mm. This outcome might further demonstrate the importance of integrating not only plant-based observations, but also other water-stress-related data sources (e.g. from remote and proximal sensing (Abbatantuono et al., 2024)) to retrieve TTSW.

Concerning the plot which received the accidental irrigation, the TTSW-apex estimate for plot 6-SI fell below the measured SAWC, underlying an underestimation. This may indicate that the vines had experienced important water deficit, which resulted in a low slope coefficient. Nonetheless, it was unexpected, because the irrigation should have increased the estimated TTSW in this plot. A possible explanation could be that the iG-Apex index, which reflects the cumulative water deficit over time, does not respond immediately to sudden changes in soil moisture (Pichon et al., 2023). This might have prevented the temporary increase of vine shoot growth index, even if the soil had received water, which has maintained the slope coefficient at a low level given the drought context. This observation demonstrated that the proposed methodology should only be applied on non-irrigated

vineyards to avoid unreliable results.

While plots with no dead or missing vines (DMV) showed generally high inversion accuracy (i.e., in plots 4-S and 5-S), the standardization ratio has significantly improved the accuracy in plots with a higher proportion of DMV. The standardization ratio adjusted the TTSW-apex estimates to 69 %, 66 %, and 75 % of the non-standardized values for 1-D, 2-D, and 3-S, respectively. Hence, the standardization played an important role in obtaining valid estimates of TTSW in those plots.

However, in plot 3-S, despite being adjusted by the ratio, the retrieved TTSW still appeared to lack physical plausibility because of the significant overestimation. This might suggest it was the plant growth itself that was fundamentally influenced by the presence of dead and missing vines: the true TTSW is indeed increased due to the reduced local vine density (0.5 vine/m²; nominal value: 0.7 vine/m²), which has strengthened the mismatch between plant-climate-based estimations and soil-based measurements (Brillante et al., 2015; Alkassem et al., 2022). Because of the rocky soils generally presented in the vineyard, probe-measured TTSW could not be obtained as validation data in this study. In addition, it was uncertain whether the weather trajectory within the studying period would allow the probe-based method to derive TTSW. Hence, in the future, the proposed inverse model could be tested and validated with in-depth probes in locations where such TTSW measurements are present, for instance, in the framework of On-Farm Experimentation (Lacoste et al., 2022).

The modeled KcbNDVI values align with the standard mid-season Kcb of 0.45 (± 10 %) for wine grapes trained under the vertical shoot positioning training system (Rallo et al., 2021). Modeled water status slope values are within the range previously reported by Gaudin et al. (2017) (from -3.9*10⁻³ to -1.3*10⁻⁴ MPa/mm), which was however derived
<figure><img src="image_7.png" /><figcaption>Fig. 4. Total Transpirable Soil Water (TTSW) retrieved from the adapted inverse model (TTSW-apex) compared with validation data (TTSW-plwp or SAWC) for the six studied plots, with 90 % confidence intervals represented as error bars. ("D" in plot ID for "deep soils", "S" for "shallow soils", "SI" for "shallow soils with irrigation").</figcaption></figure>

from a much higher number of plots. This allowed generating inversion results which were, in most of cases, physically interpretable. The data used for training the predictive model were sourced from a different vineyard ("Tavel") with distinct soil conditions and a different grape variety (Pichon et al., 2023). No model was therefore specifically trained to predict slopes within the context of this study. Nonetheless, current results might demonstrate the robustness of the proposed approach given the acceptable level of inversion error.

## 4.2. Challenges related to inversion uncertainty

Depending on the inversion methodologies, the retrieved TTSW's uncertainty could be very different. Among the studies that focused on grapevines to estimate TTSW by model inversion, this study showed a pioneering example of explicitly quantifying inversion uncertainty. Gaudin et al. (2017) and Alkassem et al. (2022) did not consider the estimation of uncertainty. Campos et al. (2016) proposed an estimation of TTSW uncertainty but they used an optimization method which was not designed for calculating a statistically interpretable confidence interval. Among inversion studies that focused on annual crops, the obtained estimation uncertainties were comparable to those reported by He et al. (2021). They assumed a 15 % variation in the input data of their inverse model, resulting in TTSW errors ranging from several millimeters to more than 50 mm.

In this study, the confidence intervals (CI) of inverted TTSW were as wide as about 40 % of the estimates, indicating a variation of ± 20 %, which seems acceptable to identify the global TTSW level. However, validation data fell within the 90 % CI only three times out of six (50 %). This showed that the current CI estimation method significantly

underestimated the TTSW-apex's uncertainty (Styc and Lagacherie, 2021). Indeed, some inputs in the inverse model, like slopes obtained from measured PLWP and the constant model coefficient (0.44), were assumed to be free of uncertainty in this experimental context. Future research should aim to incorporate the full spectrum of uncertainty across all inverse model inputs to offer a more robust description of estimation uncertainty.

Comparing retrieved TTSW's uncertainty with SAWC's should be done with great caution, given that there is a correlation between the CI width and the number of uncertain inputs used in each estimation method, aligning with findings of Styc and Lagacherie (2021). Specifically, TTSW-plwp, TTSW-apex, and SAWC methods require, respectively, 1, 2, and 3 uncertain inputs. This led to narrower CI widths for TTSW-plwp, intermediate widths for TTSW-apex, and wider widths for SAWC. Hence, inversion methods might not be inherently more certain than soil-based methods. Moreover, any errors arising from the inverse model or its misuse (e.g., plot 6-SI) are not necessarily captured within the confidence interval. This highlights the importance of verifying the inversion model conditions for future applications.

## 4.3. Limitations in method transferability

The study proposed an inversion workflow and tested it under a specific set of environmental conditions. As a result, the range of scenarios used for validating the method was narrow. In particular, the use of a single vineyard contrasts with the substantial local variability in soil and climate (Fernandez-Mena et al., 2023). Although the 2022 season provided suitable conditions for implementing the inversion approach, additional data from climatically contrasting years are needed to assess
<figure><img src="image_8.png" /><figcaption>Fig. 5. The ratio of width of 90 % confidence interval over estimates expressed in % of TTSW estimated from the adapted inverse model (TTSW-apex) and validation methods (TTSW-plwp or SAWC) for the six studied plots. ("D" in plot ID for "deep soils", "S" for "shallow soils", "SI" for "shallow soils with irrigation").</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 6. Field work hours required for the estimation of TTSW-plwp (validation method for "deep" soils), SAWC (validation method for "shallow" soils), and TTSW-apex (inverse model estimation) in each studied plot. ("D" in plot ID for "deep soils", "S" for "shallow soils", "SI" for "shallow soils with irrigation").</figcaption></figure>

the method's temporal robustness. Due to these limitations, the proposed inversion method, which is based on vine shoot growth, weather, and satellite data, should undergo further examination before operational deployment. Additional experiments and data collection are essential to define the range of conditions under which the method

remains valid. With this part of discussion, we aim to guide future research by highlighting key sources of variability across diverse management and environmental settings.

The proposed inversion model incorporates several empirical relationships. For instance, the constant coefficient (0.44) linking Fraction
of Transpirable Soil Water (FTSW) to Predawn Leaf Water Potential (PLWP) (Section 2.1.2) may require reevaluation when applied across a broader range of grape cultivars (Gaudin et al., 2017). Lebon et al. (2003) validated this relationship using four years of data for Gewürztraminer, and Pellegrino et al. (2005) confirmed it for Syrah. Both studies yielded similar constant values, suggesting limited variability. However, this apparent stability may mask cultivar-specific differences. Future research should more accurately characterize this coefficient's variability by incorporating a wider range of genotypes and root-stock–scion combinations.

Another potential source of variability lies in the predictive model used to estimate PLWP from iG-Apex and weather data (Section 2.2.1). The Recursive-Duo-Model developed by Zhang et al. (2024b) is a machine-learning-based model trained on data from two cultivars: Syrah and Grenache Noire. To generalize the model's applicability, new data must be incorporated as additional genetic materials are introduced. Although Pichon et al. (2023) reported that trimming and cultivar choice had little impact on the PLWP-iG-Apex relationship, their findings underscore the need to recalibrate the model using cultivars with more diverse responses to water stress (Gambetta et al., 2020).

Lastly, the model estimating the basal crop coefficient (Kcb) from NDVI (Section 2.2.2) also requires careful reevaluation. This relationship may introduce significant variability under differing soil management practices and training systems that alter canopy architecture. The original relationship derived by Campos et al. (2010) was developed under specific conditions and should not be considered universally applicable. In particular, the presence of inter-row vegetation may bias NDVI-based estimates. While in Mediterranean rainfed vineyards, such vegetation is typically removed before veraison due to water limitations (Kazmierski et al., 2011), its presence may still affect remote sensing measurements. However, Kazmierski et al. (2011) also observed that under dry conditions, inter-row crops had minimal impact on remote-sensing imagery, possibly because their shallow root systems limit growth, and even lead to desiccation during drought periods.

These sources of variability necessitate new experimental designs and, consequently, new research questions: both of which are critical for testing the method's transferability, thus assessing improvement to be performed before its generalization. Nevertheless, the method was not originally intended to retrieve TTSW under all circumstances. For example, the vine shoot growth index is specific to grapevines (Vitis vinifera), inherently limiting the inverse model's applicability to viticulture. However, the general strategy of applying the inversion approach only under dry conditions may be transferable to other perennial crops, for examples: 1 olives or nut trees, which also require high water-use efficiency under frequent drought stress, particularly in Mediterranean-type climates (Katerji et al., 2008).

## 4.4. Operational implications

For the inverse model to be valid, it requires a period of dry weather: a condition beyond the control of the practitioner. The method's application constraints are therefore strict. Unlike soil-based measurements, which can be conducted under a broader range of conditions, the plant-climate-based approach cannot be implemented at any time or location. Most importantly, it is limited to rainfed vineyards. Consequently, its use is unsuitable in humid or rainy viticultural regions, such as parts of Japan (Kobayashi et al., 2011); or regions where irrigation in viticulture is a common practice like in Australia or Brazil (Chaves et al., 2007). In contrast, the Mediterranean region, characterized by long, dry, and hot summers (Joly et al., 2010), offers more favorable conditions for applying the inverse model.

In comparison to soil-based methods, the plant-climate-based approach may be less effective for providing immediate estimates of TTSW, as it requires multiple field measurements over several weeks, in addition to favorable weather conditions. However, TTSW is typically used to support long-term strategic decisions, such as identifying

drought-prone zones, planning irrigation infrastructure, or updating plant materials, where the time required for data collection and model inversion is less constraining.

Dead or missing vines (DMV) are a common feature in older Mediterranean vineyards. To address this, the method includes a standardization operator intended to correct for irregular planting patterns. Nonetheless, our results indicate that this correction provides inconsistent improvements when the proportion of DMV is high, as observed in plot 3S. This introduces a significant limitation to the method's reliability in vineyards with frequent vine loss. The vine shoot growth index protocol requires measurements from ten contiguous vines, rather than from ten spatially scattered individuals. Thus, when the spatial distribution of remaining vines is too sparse, the method is not recommended.

Despite these operational limitations, the proposed inversion approach required the least field work among the three tested methods. This was expected because the approach was designed to rely on data relatively easy to collect. More field work hours imply not only increased effort for data collection in the field, but also additional preparatory activities, financial investments, and supporting operations. For instance, Styc (2020) reports an average cost of 1800 euros for conducting a single soil profile analysis. Similarly, one pressure chamber used for measuring water potentials costs about 2000 euros, and necessitates nocturnal measurements. In parallel, Tosin et al. (2022) reported advanced modeling techniques for predicting predawn leaf water potential using spectrometry data. However, access to the required digital instrumentation may pose a challenge for producers, particularly small-scale vineyard owners. Considering these externalities, the proposed method is highly cost-effective when compared to other existing approaches.

The proposed methodology still relied on human-based observations, which could be a significant factor contributing to the retrieval accuracy. According to Alkassem et al. (2022), remote sensing data, when combined with in-field soil moisture measurements, could achieve the highest inversion accuracy. This suggests that iG-Apex may play a similar role in providing valuable information to improve the accuracy of TTSW retrieval. Concerning human labor required by vine shoot growth data acquisition, the collection of iG-Apex itself could be an incentive action. As pointed out by Pichon et al. (2021), monitoring vine shoot growth before veraison provides insights into planning proactive vineyard management regarding unwanted water stress. For vineyard water management, measuring vine shoot growth and making inverse modeling may create some synergy scenarios. For instance, the data collected for water status monitoring can serve to make inverse modeling, and the obtained TTSW can be fed into a water balance model that replaces vine shoot data collection in following years. This allows growers to monitor other zones with the iG-Apex measurements and repeat such a procedure, while obtaining progressively TTSW estimations over the zone of interest.

The ability to gather iG-Apex data using a Farmsourcing mobile application, ApeX-Vigne, as described by Brunel et al. (2019), may significantly further enhance the interest of the proposed inversion approach. The Farmsourcing application has led to the accumulation of over 20,000 iG-Apex data points in Southern France by 2021, according to Pichon et al. (2022), and this number does not cease to grow. This citizen-science dataset offers opportunities for future research to evaluate the inverse model under a wide range of contrasting scenarios, providing valuable insights to refine the method's transferability. Combined with this dataset, the proposed methodology hold potential for mapping TTSW on varying spatial scales, and could contribute to a deeper understanding of TTSW spatial distribution across the region. However, current iG-Apex collection protocol in ApeX-Vigne does not verify the presence of dead or missing vines, a factor to which estimated TTSW might be sensitive. Future improvement of the application could incorporate this functionality.
## 5. Conclusion

Total Transpirable Soil Water (TTSW) is a crucial parameter for vineyard water management but is challenging to measure. In this study, TTSW was estimated in six vine plots in a Mediterranean rainfed vineyard using an inverse model that utilizes three types of easily accessible data: vine shoot growth observations, weather information, and Sentinel-2 imagery. The model was validated against soil-based measurements for shallow soils (soil depth range: 0.9 – 1.4 m) and against another established inversion method for deep soils. Compared to the validation data, the results showed a mean absolute error of 30 mm (RMSE = 32 mm), indicating acceptable inversion accuracy. Better inversion performance was observed in plots without dead or missing vines, while error increased in the presence of such vines, demonstrating the importance of carefully selecting the measurement plot. The proposed method demonstrated minimal operational constraints and moderate prediction uncertainty levels. However, this method requires several specific conditions to operate, which may necessitate regular vine shoot growth monitoring to increase the chance to be able to use this approach. In conclusion, the proposed inversion method significantly reduces the cost of obtaining TTSW estimations for rainfed vineyards and can be used to increase the accessibility of TTSW across extended spatial scales.

### CRediT authorship contribution statement

Bruno Tisseyre: Writing – review & editing, Supervision, Conceptualization. Guillaume Coulouma: Validation, Resources,

Investigation. **Anne Pellegrino:** Validation, Resources. **Sébastien Roux:** Validation, Resources. **Léo Pichon:** Writing – review & editing, Methodology, Conceptualization. **ZHANG Yulin:** Writing – original draft, Methodology, Investigation, Formal analysis.

### Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

### Declaration of Competing Interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Yulin Zhang reports financial support was provided by Digitag ANR-16-CONV-0004. Yulin Zhang reports financial support was provided by Région Occitanie.

### Acknowledgements

This work was supported by the French National Research Agency under the Investments for the Future Program, referred as ANR-16-CONV-0004. The ApeX-Vigne project was part of the DATI project, supported by the French National Research Agency under the Horizon 2020 PRIMA Program (ANR-21-PRIM-0001). The authors would like to thank Y. Bouisson, C. Enard, O. Huttel, L. Haon, P. Faure, for their technical assistance.

<figure><img src="image_10.png" /><figcaption>Appendix A. Figure, Predawn Lead Water Potential (Y axis) measured in the studied plots, compared with the cumulative ET₀ (X axis) recorded at the dates of measurement. The slope coefficient and the R² were obtained by fitting the linear regression model between the two variables. ("D" in plot ID for "deep soils", "S" for "shallow soils", "SI" for "shallow soils with irrigation")</figcaption></figure>
Appendix B. Images of vine shoots at three different growth stages: a) full growth, b) moderate growth and c) stopped growth. Image source: Institut Français de la Vigne et du Vin | Occitanie (https://www.vignevin-occitanie.com/fiches-pratiques/methode-des-apex/)

<figure><img src="image_11.png" /></figure>

Appendix C. Figure. Temporal evolution of the Normalized Difference Vegetation Index (NDVI) within the studying period in studied plots (the standard deviations were calculated from the four neighboring pixels.)

<figure><img src="image_12.png" /></figure>
<table><caption>Appendix D. Table. Measured parameters for computing soil available water capacity for each explored soil horizon of the six studied plots</caption><thead><tr><th>Profile ID<br>Unit</th><th>Horizon</th><th>Depth interval<br>dm</th><th>Field capacity<br>g/g</th><th>Permanent wilting point<br>g/g</th><th>Bulk density<br>g.cm<sup>-3</sup></th><th>Rock fragment<br>g/g</th><th>Calcium content<br>g/kg</th></tr></thead><tbody><tr><td rowspan="5">1-D</td><td>1</td><td>0-1</td><td>28.09 (0.01)</td><td>18.35 (0.01)</td><td>0.97 (0.01)</td><td>0.04</td><td>&lt; 0.1</td></tr><tr><td>2</td><td>1-5</td><td>17.63 (0.39)</td><td>11.93 (0.98)</td><td>1.56 (0.01)</td><td>0.02</td><td>&lt; 0.1</td></tr><tr><td>3</td><td>5-9</td><td>20.53 (0.4)</td><td>16.92 (0.6)</td><td>1.60 (0.12)</td><td>0.01</td><td>&lt; 0.1</td></tr><tr><td>4</td><td>9-11</td><td>21.32 (0.85)</td><td>16.02 (2.33)</td><td>1.64 (0.02)</td><td>0.02</td><td>&lt; 0.1</td></tr><tr><td>5</td><td>11-15 +</td><td>17.35 (1.91)</td><td>13.44 (1.98)</td><td>1.42 (0.04)</td><td>0.25</td><td>2.5</td></tr><tr><td rowspan="3">2-D</td><td>2</td><td>1-5</td><td>14.82 (0.29)</td><td>10.83 (0.72)</td><td>1.59 (0.03)</td><td>0.06</td><td>&lt; 0.1</td></tr><tr><td>3</td><td>5-8</td><td>15.93 (3.42)</td><td>9.86 (1.53)</td><td>1.64 (0.02)</td><td>0.02</td><td>&lt; 0.1</td></tr><tr><td>4</td><td>8-13 +</td><td>19.00 (0.65)</td><td>13.38 (2.00)</td><td>1.42 (0.04)</td><td>0.25</td><td>6</td></tr><tr><td rowspan="5">3-S</td><td>2</td><td>1-5</td><td>18.16 (1.25)</td><td>13.02 (0.81)</td><td>1.52 (0.09)</td><td>0.04</td><td>&lt; 0.1</td></tr><tr><td>3</td><td>5-7</td><td>21.32 (0.85)</td><td>16.02 (2.33)</td><td>1.61 (0.01)</td><td>0.08</td><td>&lt; 0.1</td></tr><tr><td>4</td><td>7-9</td><td>17.35 (1.91)</td><td>13.44 (1.98)</td><td>1.42 (0.04)</td><td>0.25</td><td>1.4</td></tr><tr><td>1</td><td>0-1</td><td>23.28 (0.01)</td><td>10.39 (0.01)</td><td>0.97 (0.01)</td><td>0.04</td><td>33.9</td></tr><tr><td>2</td><td>1-4</td><td>18.11 (1.14)</td><td>10.68 (0.62)</td><td>1.59 (0.09)</td><td>0.10</td><td>30.8</td></tr><tr><td rowspan="3">4-S</td><td>3</td><td>4-10</td><td>19.22 (0.87)</td><td>13.33 (1.26)</td><td>1.52 (0.04)</td><td>0.05</td><td>54.7</td></tr><tr><td>4</td><td>10-14</td><td>19.42 (0.64)</td><td>13.11 (0.66)</td><td>1.59 (0.01)</td><td>0.03</td><td>54.9</td></tr><tr><td>2</td><td>1-3.5</td><td>15.59 (1.27)</td><td>9.07 (0.86)</td><td>1.54 (0.09)</td><td>0.12</td><td>35.6</td></tr><tr><td rowspan="2">5-S</td><td>3</td><td>3.5-5</td><td>19.22 (0.87)</td><td>13.33 (1.26)</td><td>1.52 (0.04)</td><td>0.05</td><td>-</td></tr><tr><td>4</td><td>5-14</td><td>17.29 (0.84)</td><td>10.41 (0.99)</td><td>1.59 (0.01)</td><td>0.03</td><td>-</td></tr><tr><td rowspan="2">6-SI</td><td>2</td><td>1-5</td><td>15.66 (0.65)</td><td>10.23 (0.64)</td><td>1.46 (0.07)</td><td>0.09</td><td>36.3</td></tr><tr><td>3</td><td>5-14</td><td>15.15 (1.04)</td><td>7.70 (1.32)</td><td>1.59 (0.01)</td><td>0.03</td><td>54.2</td></tr></tbody><tfoot><tr><td colspan="8">Standard deviation is presented as number in brackets. The symbol "+" signifies "at least".</td></tr></tfoot></table>

## Data availability

Data will be made available on request.

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