Forcing the SAFY Dynamic Crop Growth Model with Sentinel-2 LAI Estimates and Weather Inputs from AgERA5 Reanalysis and CM SAF SARAH-3 Radiation Data for Estimating Crop Water Requirements and Yield

Abstract

The continuous development of both numerical weather model outputs and remote sensing-derived products has enabled a wide range of applications across various fields, such as agricultural water management, where the need for robust gridded weather data and recurring Earth Observations (EO) is fundamental for estimating crop water requirements (CWR) and yield. This study used the latest reanalysis dataset, AgERA5, combined with the up-to-date CM SAF SARAH-3 Satellite-Based Radiation Data as meteorological inputs of the SAFY dynamic crop growth model and a one-step evapotranspiration formula for CWR and yield estimates at the farm scale of tomato crops. The Sentinel-2 (S2) estimates of Leaf Area Index (LAI) were used to force the SAFY model as soon as they became available during the growing stage, according to the satellite passages over the area of interest. The SAFY model was calibrated with ground-based weather observations and S2 LAI data on tomato crops that were collected in several farms in Campania Region (Southern Italy) during the irrigation season, which spans from April to August. To validate the method, the model estimates were compared with field observations of irrigation volumes and harvested yield from a monitored farm in the same region for the year 2021. Results demonstrated that integrating AgERA5 and CM SAF weather datasets with S2 imagery for assimilation into the SAFY model enables accurate estimates of both CWR and yield.

1. Introduction

In recent decades, the increasing occurrences of drought events and intensification of climatic variability have posed crucial challenges in the definition and implementation of sustainable and resilient agricultural practices [1], particularly in water-scarce regions. Since irrigated agriculture accounts for approximately 70% of the global freshwater withdrawals [2,3], all the efforts toward a more efficient and rational use of water in the agricultural sector are significant for both ensuring food security and mitigating environmental impacts. In response to these challenges, the European Union, with the Water Framework Directive (2000/60/EC) and, later, Italy, with the Ministerial Decree of the Ministry of Agricultural Food and Forestry Policies, issued on 31 July 2015, have emphasized the foundational role of information, i.e., the knowledge development of irrigated areas and irrigation volumes in the agricultural context for current concerns over the past years. This knowledge is indeed central to (i) the design of appropriate hydraulic systems and interventions, (ii) the proper management of the exiting infrastructures, (iii) the wise prioritization of investments and interventions in areas identified as the most vulnerable and at risk of water scarcity and, finally, (iv) the creation of historical data series that can inform climate-oriented studies.

Nonetheless, as noted in several studies, direct measurements of irrigation volumes remain scarce, often constrained by logistical and economic limitations [4,5]. In this context, the integration of advanced meteorological datasets and Earth Observation (EO) datasets into crop monitoring and modeling frameworks offers promising solutions for improving both the awareness of the water needs for agriculture as a picture of the present and past years over a region as well as irrigation scheduling and crop management at farm level for actively optimizing water consumption in the near future [6,7,8,9,10].

In the literature, three primary methodological approaches have been established for estimating irrigation needs based on EO data, ancillary meteorological inputs and, possibly, in combination with agro-hydrological modeling [11,12,13]. The first approach relies on satellite-derived soil moisture data and applies an inverse soil water balance model to infer irrigation volumes at a monthly resolution following procedures suggested by [14]. The second and third approaches share the common step of estimating crop evapotranspiration (ETc), which corresponds to the combined water loss from plant transpiration and soil evaporation, which are some of the key factors that determine water demand on a daily scale. The main difference between them lies in the method used to estimate evapotranspiration: one approach explicitly applies surface energy balance models, using remotely sensed radiometric surface temperature to estimate the sensible heat flux, and derives evapotranspiration as the residual of the surface energy balance [12]; the other approach relies on satellite-derived crop biophysical variables, such as Leaf Area Index (LAI) and/or fractional vegetation cover, which are then used as inputs in crop evapotranspiration empirical modeling [15]. According to the two latter approaches, irrigation needs for open field crops are calculated by means of the net crop water requirements (CWR), using a local water balance model [11] as the difference between ETc and water gained from rainfall together with variations in soil water storage and groundwater contributions [11]. Net CWR can be considered a reliable approximation of actual irrigation needs, which are critical in aiding informed determination of irrigation volumes to be applied. Irrigation volumes are then inherently influenced by many other factors that include irrigation technology, system performance, specific agronomic practices, water use efficiency in irrigation (e.g., drip or sprinkler systems), and the manner in which farmers use different crop management practices at their disposal [11]. These factors argue for the need to reliably estimate irrigation volumes by using tested and tried techniques that account for system losses and field-level heterogeneity.

In this study, irrigation needs were estimated through ETc modeling based on satellite-derived crop parameters in the hypotheses of standard crop management, high-efficiency irrigation systems, and absence of environmental stress and diseases [15]. A central issue in this context remains the accurate estimation of ETc, which, according to empirical approaches such as that one proposed by the Food and Agriculture Organization’s FAO-56 model [11,15], is highly dependent on meteorological variables, which include temperature, humidity, solar radiation, wind speed, and atmospheric pressure as well as on crop-specific parameters, like the Leaf Area Index (LAI). The accuracy of these estimates is indeed dependent on spatial representativeness and scalability of weather data at a regional scale, which are critical because weather data are usually available at a restricted number of sites where ground-based weather stations are installed as part of a monitoring network. Although spatial interpolation techniques can be used to obtain weather data over large regions that are covered by monitoring networks, these techniques introduce errors that depend on the density of the monitoring network itself and the spatial variability of the interpolated variables [4,16]. The advent of high-resolution gridded weather datasets from atmospheric numerical modeling has, however, significantly enhanced the spatial coverage and representativeness of weather data [17]. This advancement has led to a significant improvement in agricultural monitoring and prediction systems and allowed for a more dynamic and spatially explicit characterization of weather [18]. These datasets offer spatial and temporal continuity and could be readily integrated into Decision Support Systems (DSS), especially in regions or contexts where ground-based measurements are limited, unavailable, or difficult to access.

Among the most recent developments in meteorological numerical gridded data, the AgERA5 database stands out as a high-resolution (hourly, about 10 km) agro-meteorological reanalysis that is specifically tailored for agricultural applications [19]. This database is based on the ERA5 reanalysis from the European Centre for Medium-Range Weather Forecasts (ECMWF) and it was made publicly available for the first time in year 2020 on the Copernicus Climate Change Service’s (CDS) online data portal [20], with data being available from 1979 up to the present. The AgERA5 dataset is provided together with other reanalysis ECMWF products, such as ERA5, ERA5-Land and the Copernicus European Regional Reanalysis (CERRA), all of which are available on the CDS platform. These datasets have been proven to be reliable proxies of ground-based reference evapotranspiration (ET₀) and weather observations [11]. They have to date been widely used in crop evapotranspiration assessments in many parts of Southern Europe [5,16,21,22,23,24] whose climates are similar to long-term trends in Italy’s Campania region and other areas worldwide [25,26,27,28].

Additionally, in some recent studies, the possibility of exploiting satellite-based radiation combined with reanalysis data for improving the performance of evapotranspiration estimates has been evaluated by using gridded products developed by the European Organization for the Exploitation of Meteorological Satellites (EUMETSAT). These products are specifically provided by two independent Satellite Application Facilities (SAFs) that include (i) the Satellite Application Facility on Climate Monitoring (CM SAF) [16] and (ii) the Satellite Application Facility on Land Surface Analysis (LSA SAF) [29]. More recently, CM SAF released the SARAH-3 dataset, an updated satellite-based climate record of surface solar radiation [30]. In this study, SARAH-3 was employed together with AgERA5 reanalysis data for the first time to provide ETc estimates as a basis for computing net CWR.

Concerning satellite-derived crop indices, this study used Sentinel-2 (S2) multispectral imagery to interrogate LAI dynamics. The use of S2 multispectral imagery for crop monitoring is well-documented [31,32] and widely recommended because of its high spatial resolution (10–20 m) and short 5-day revisit period [33]. In particular, S2-derived LAI estimates play a central role in crop model assimilation by enabling more accurate representation of different phenological characteristics [34,35]. However, the effective use of satellite-based LAI requires validation against in situ observations and careful temporal alignment with model time steps. Although the revisit period is technically adequate for informative and timely assessment of crop dynamics, it should be noted that specific atmospheric conditions may prevent the use of the imagery for the reliable characterization of crop parameters.

This limitation can be addressed by coupling satellite-based LAI estimates with crop growth modeling to continuously simulate crop growth dynamics under varying environmental conditions and at a regional scale for extensive studies [36]. In this study, the Simple Algorithm For Yield (SAFY) dynamic crop growth model [37] was judged to be suitable for such integration due to its simplified structure, which enables it to rely on a limited set of parameters and inputs, including LAI and weather data. SAFY simulates the time evolution of green LAI and biomass accumulation, and it has been successfully applied in various agro-ecological settings by other researchers [36,38]. Other examples of integration of satellite-based crop parameters and crop growth modeling can be found in [34,35,39], where the authors used the AquaCrop model instead of the SAFY model. The AquaCrop model simulates the net CWR by describing the canopy cover evolution [40,41].

In this study, we proposed a cutting-edge approach for estimating both net CWR and the yield of tomato crops by integrating AgERA5 and CM SAF SARAH-3 weather datasets with Sentinel-2-derived LAI into the SAFY model, which we calibrated and validated using field data from farms in Southern Italy’s Campania Region. The tomato (Solanum lycopersicum) was purposefully selected because it is a high-value crop with significant water demand, particularly in Mediterranean regions where evapotranspiration rates are high during the growing season. Accurate CWR estimates are essential to optimize irrigation, improve water productivity [42] and our understanding about the actual water needs, and to develop a historical dataset capable of supporting climate-oriented analyses.

To the best of our knowledge, this is the first study in the scientific literature that employs both AgERA5 and CM SAF SARAH-3 weather datasets for the estimation of CWR and yield. Furthermore, a distinctive feature of this research lies in the application of the SAFY crop growth model using reanalysis and remotely sensed weather data as inputs. The study plays an important role in advancing knowledge in the field of agro-hydrological modeling, as it explores the use of the most up-to-date freely available gridded weather datasets and evaluates their impact on model-based estimates. By assessing how different types of meteorological inputs influence the accuracy and reliability of CWR and yield predictions, this research contributes to a deeper understanding of the potential and limitations of large-scale data sources for agricultural monitoring and DSS.

2. Study Area, Data and Methods

2.1. Study Area and Field Data

The study focused on the Campania region in Southern Italy (Figure 1), where approximately 4000 hectares of farmland are dedicated to the cultivation of tomatoes, with this area representing around 13% of the total area used for open-field vegetable farming. This delineation allowed the study area to be representative of intensively cultivated tomato systems that offered a suitable testbed for the proposed modeling approach.

The field campaigns were carried out during the irrigation seasons (from April to July) of the years 2019 and 2021 on a farm situated in the northwestern part of the region (yellow circle in Figure 1, i.e., D’Amore farm), specifically targeting tomato crops. The robust and accurate data collected during the 2021 campaign in this farm were already analyzed in a previous study [35], which focused on the application of the AquaCrop crop growth model combined with ERA5-Land reanalysis and CM SAF SARAH-2.1 satellite-based radiation data, along with Sentinel-2-derived crop parameters (i.e., canopy cover) in estimating CWR and yield for the targeted tomato crop. Here, the same experimental dataset was used to validate the results of this study’s analysis by comparing them with the previous outcomes.

The Campania region has a Mediterranean climate that is characterized by (i) warm springs, (ii) mild, wet winters and autumns, and (iii) hot and dry summers with average monthly temperatures reaching up to 30 °C and low rainfall with average monthly values of about 50 mm. In the farm’s immediate vicinity is a ground-based automatic weather station (AWS) that has been delivering accurate measurements of precipitation, wind speed at 10 m above ground level, atmospheric pressure, solar radiation, and air temperature and relative humidity at 2 m above ground level since 2008. This AWS belongs to the regional monitoring network managed by the Regional Hydrometeorological Service that publishes daily weather data on a freely accessible web platform: https://centrofunzionale.regione.campania.it, accessed on 10 January 2025 [35,43], which we used to acquire the data reported in

Table 1. Main statistics from the weather observations in April–September of 2008–2024.

Weather Variable	Mean	Standard Deviation	Coefficient of Variation (−)
Daily mean air temperature at 2 m (°C)	19.4	5.1	0.27
Daily maximum air temperature at 2 m (°C)	25.7	5.9	0.23
Daily minimum air temperature at 2 m (°C)	13.5	4.7	0.35
Daily mean air relative humidity (%)	69.8	12.3	0.18
Daily mean wind speed at 10 m (m s−1)	2.5	0.9	0.38
Daily solar radiation (W m−2)	258	75	0.29
Total Accumulated Precipitation in the period Apr–Jul (mm)	195	113	0.58

.

Table 1 shows the statistics of the weather observations that we selected from the AWS’s records for the 2008–2024 irrigation periods between April and July, during which tomatoes are grown. Irrigated agriculture is a very common practice in the region during the period from April to July or until September, depending on the specific crop types and agricultural practices [35]. The cultivation of tomatoes usually takes place from April/May to July/August (growing period ranging from 100 to 140 days).

The farm where our field campaign was conducted in 2021 cultivated the Solanum lycopersicum Heinz 5108 cultivar in all of its 9 hectares, after which, it was rotated with wheat in the following years. The experiments were conducted by transplanting the crops on April 8 and harvesting them on July 20. Prior to harvesting, an efficient drip irrigation system was used to supply water to the crops, with each irrigation event consisting of a fixed application of water to a depth of 14 mm. Following typical farming practices, irrigation was optimally scheduled to ensure that the depletion of water in the root zone (RZD) consistently exceeded 50% of the readily available water (RAW) [34,35]. During the considered growing seasons, tomato leaves did not show significant and extensive anomalies attributable to nutritional deficiencies or symptoms linked to pathogens, which could significantly compromise the vegetative development of the plants.

Table 2. Observational datasets compiled in 2021 and later used to validate this study’s results.

Field Data	Value
Cumulative net irrigation volume (9 April–17 July)	294 mm (2940 m3/ha)
Total yield at harvesting date	121 t/ha

shows the two key datasets that were compiled and used to validate the results of our CWR and yield modeling.

Due to technical limitations, it was not possible to measure LAI with ground-based techniques during the 2021 campaign. However, during the 2019 campaign at the same farm, ground-based non-destructive measurements of LAI on tomato crops had been successfully conducted over a 2-hectare portion of the total farm area (Figure 2b). The measurement protocol included 10 sampling points, each corresponding to a 20 m × 20 m Sentinel-2 pixel, covering the selected area (Figure 2a), in order to enhance spatial correspondence between ground and image-based measurements. This was accomplished by making sure that the compilation of ground-based LAI measurements coincided with Sentinel-2’s satellite acquisitions or within 1–2 days of satellite imagery acquisition (Section 2.2). For 2019, the crops were transplanted on 8 April and harvested on 5 August.

Table 3. LAI field measurements by date and values.

Dates	Mean Value	Minimum Value	Maximum Value
21 May 2019	0.78	0.58	0.97
17 June 2019	1.78	1.27	2.24
25 June 2019	1.80	1.45	2.16
7 July 2019	1.92	1.50	2.31
27 July 2019	1.50	1.21	2.19

shows the crop field mean, minimum, and maximum LAI measurements and the dates on which they were conducted.

LAI measurements were made with the LICOR LAI-2000 Plant Canopy Analyzer, produced by LI-COR Environmental (Lincoln, NE-United States of America) (Figure 2c), which operates by comparing the intensity of diffuse incoming radiation measured at the base of the crop to that at the top [44]. The LAI-2000 instrument was used with all five optical rings and shielded with a 180° view cap to avoid the inclusion in the measurements of extraneous elements present in the immediate vicinity, such as the operator himself [31,44]. To further reduce the influence of multiple scattering on measurements, measurements were exclusively taken early in the morning or at the end of the afternoon between 6:30 and 9:30 AM and 6:30 and 8:30 PM, respectively. A single sensor was used for both above- and below-canopy measurements following suggestions by [7] and by [45].

2.2. Sentinel-2 LAI Estimates

The ground-based non-destructive measurements of LAI conducted in 2019 were used here to validate the satellite-based LAI estimates. The satellite multispectral imagery used to estimate the LAI was acquired by the Sentinel-2 satellites, part of the European Space Agency’s (ESA) Copernicus program [46]. The Sentinel-2 constellation is composed of three satellites that include Sentinel-2A, Sentinel-2B and the more recent Sentinel-2C, which was launched in 2024. During the period in which this project was conducted, Sentinel-2C was not working. The tile used in this investigation is T33TVF. This title is related to the 122 and 79 orbits of the Sentinel-2A and Sentinel-2B satellites, allowing the acquisition of images approximately every 2–3 days. Both satellites have multispectral cameras that record 13 bands at different spatial resolutions: 4 bands at 10 m, 6 at 20 m, and 3 at 60 m. S2 LAI was calculated using different bands with spatial resolutions of 10 and 20 m. The bands that were used to estimate LAI are the visible spectrum (VIS-B3, B4), the “red edge” (B5, B6, B7), the near-infrared (NIR-B8a), and the shortwave infrared (SWIR-B11, B12), together with their corresponding solar and viewing angles that were retrieved from the metadata of each considered S2 acquisition [47].

The LAI estimates were derived by using the SentiNel Application Platform (SNAP) toolbox [48]. SNAP is a free and open-source software platform designed for processing Earth Observation data from various satellite missions, including Sentinel-2. This software uses algorithms that employ artificial neural networks, trained by using simulated reflectance from physically based models. These models simulate Top of Canopy (TOC) reflectance, precisely for the pertinent Sentinel-2 spectral bands. The calculation of LAI utilizes the reflectance measured by Sentinel-2 in the said spectral bands, along with observed geometry information, as inputs for the trained neural network-based algorithm. The algorithm derives Level 2B biophysical products, like LAI, by primarily using Level 2A products as inputs. Level 2A products, which represent surface reflectance, are derived from the L1C imagery (TOA–Top Of Atmosphere reflectance), through an atmospheric correction procedure that is performed by means of the Sen2Cor processor. This correction is necessary because atmospheric effects must be reduced in order to accurately estimate ground vegetation properties. An important consideration is that the LAI estimated from satellite data refers specifically to the so-called green LAI (GLAI), which accounts only for the photosynthetically active leaf surfaces, excluding senescent and dead leaves. This estimate is derived from the analysis of canopy reflectance in the visible (VIS), near-infrared (NIR), and shortwave infrared (SWIR) regions of the electromagnetic spectrum, which are particularly sensitive to the presence of green biomass [49]. As a result, the presence of senescent or necrotic tissues, which are characterized by lower reflectance in the NIR and higher reflectance in the VIS compared to active leaves, leads to lower LAI values in satellite-derived observations (Figure 3).

2.3. AgERA5 Reanalyisis and CM SAF SARAH-3 Satellite-Based Radiation Data

AgERA5 is the latest reanalysis dataset, freely provided by the ECMWF on the CDS web platform [20]. The database is specifically developed for agricultural applications and consists of a set of daily weather variables, such as atmospheric pressure, wind speed, solar radiation, air temperature, relative humidity, and precipitation [19]. These daily weather data are derived from the ECMWF global reanalysis, ERA5 [50], by statistically downscaling ERA5 outputs over a 0.1° × 0.1° longitude–latitude grid, in the fashion of ERA5-Land reanalysis [51]. AgERA5 reanalysis extends all over the globe and from 1979 to the present. It provides a continuous and consistent database of gridded weather data that was employed here as a proxy of in situ weather observations to overcome the problematic issue of data scarcity that is related to the sparse distributions of monitoring stations and difficulties in accessing fragmented country and regional-level datasets [4].

Since radiation data from atmospheric numerical modeling are affected by major errors [16,21,43], an integration of AgERA5 data with other weather data from other sources that are related to solar radiation was proposed and used to address this limitation. In particular, surface incoming shortwave radiation products belonging to the third edition of the Surface Solar Radiation Data Set-Heliosat (SARAH-3) delivered by the Satellite Application Facility on Climate Monitoring were used. The SARAH-3 database is a satellite-based climate data record derived from satellite observations in the visible channels of the Meteosat Visible and InfraRed Imager (MVIRI) and the Spinning Enhanced Visible and Infrared Imager (SEVIRI) instruments onboard the geostationary Meteosat satellites [30]. SARAH-3 data covers the time period from 1983 to 2020 in the form of a climate data record (CDR) that has been operationally extended as the Interim Climate Data Record (ICDR) with a latency of 5 days to the present. These data cover the region of ±65° longitude and ±65° latitude at a daily spatial resolution of a 0.05° × 0.05° latitude-longitude grid [30]. The products are freely available on the CM SAF Web User Interface (CM-SAF, www.cmsaf.eu). This third edition of data was released in 2023, updating the SARAH-2.1 database [52], used in [16].

In this study, both AgERA5 and CM SAF products were downscaled at the site of interest by using a triangle-based bilinear interpolation method [53]. For daily mean, maximum and minimum air temperature, an Environmental Lapse Rate (ELR) correction was also applied to account for elevation differences between grid points and the farm [4]. Thereafter, bias correction was applied by using a complete regional-scale time series of observed weather data (18 time series of the AWSs for the Campania Region) from 2008 to 2024 [4,43]. The bias correction scheme concerned correcting data with the regional mean monthly biases between AgERA5 or CM SAF outputs and ground-based measurements [4]. Hereinafter, the integrated database of AgERA5 weather data with CM SAF solar radiation is referred to as AgERA5 + CMSAF.

2.4. The Dynamic Crop Growth Model: SAFY

2.4.1. SAFY Implementation: Input Data and Parameters

The Simple Algorithm for Yield Estimation (SAFY) is a parsimonious crop growth model designed to estimate key biophysical variables, such as LAI, dry above-ground biomass (DAM), and crop yield, using minimal inputs [37]. The model is structured to operate on a daily time step from plant emergence (D₀) to full senescence, making it suitable for both local and regional-scale applications, especially in data-scarce contexts. The weather input variables are the daily incoming solar radiation, RS, and the daily mean air temperature, T.

Rooted in the light-use efficiency theory, SAFY simulates biomass production as a function of (i) climatic efficiency, ε_c, i.e., the ratio of incoming photosynthetically active to global radiation, (ii) absorbed photosynthetically active radiation (APAR), i.e., the fraction of photosynthetically active radiation that is absorbed by the crop, (iii) effective light-use efficiency (ELUE), i.e., the ratio of photochemical energy produced as DAM from APAR and (iv) a temperature stress function (F_T), which accounts for the role of temperature stress on DAM production. Equation (1) shows the temporal evolution of DAM from day j-1 (D₀ at the beginning of the algorithm) to the following day j, while Equation (2) specifies the daily increment of DAM (${∆}_{DAM;j-1,j}$) as follows:

$${{\mathrm{D}\mathrm{A}\mathrm{M}}_{\mathrm{j}}={\mathrm{D}\mathrm{A}\mathrm{M}}_{\mathrm{j}-1}+∆}_{\mathrm{D}\mathrm{A}\mathrm{M};\mathrm{j}-1,\mathrm{j}}$$

(1)

$${∆}_{\mathrm{D}\mathrm{A}\mathrm{M};\mathrm{j}-1,\mathrm{j}}=\mathrm{E}\mathrm{L}\mathrm{U}\mathrm{E}·{\mathrm{A}\mathrm{P}\mathrm{A}\mathrm{R}}_{\mathrm{j}-1,\mathrm{j}}·{\mathrm{F}}_{\mathrm{T}}\left({\mathrm{T}}_{\mathrm{j}}\right)$$

(2)

where

$${\mathrm{A}\mathrm{P}\mathrm{A}\mathrm{R}}_{\mathrm{j}-1,\mathrm{j}}=\left(1-{\mathrm{e}\mathrm{x}\mathrm{p}}^{-\mathrm{K}·{\mathrm{L}\mathrm{A}\mathrm{I}}_{\mathrm{j}-1}}\right)·{{\mathrm{\epsilon }}_{\mathrm{c}}·\mathrm{R}\mathrm{S}}_{\mathrm{j}}$$

(3)

$${\mathrm{F}}_{\mathrm{T}}\left(\mathrm{T}\right)=\left\{\begin{array}{l} 1-{\left({\displaystyle \frac{{\mathrm{T}}_{\mathrm{o}\mathrm{p}\mathrm{t}}-\mathrm{T}}{{\mathrm{T}}_{\mathrm{o}\mathrm{p}\mathrm{t}}-{\mathrm{T}}_{\mathrm{c},\mathrm{m}\mathrm{i}\mathrm{n}}}}\right)}^{\mathsf{\beta }}\mathrm{i}\mathrm{f} {\mathrm{T}}_{\mathrm{c},\mathrm{m}\mathrm{i}\mathrm{n}}<\mathrm{T}<{\mathrm{T}}_{\mathrm{o}\mathrm{p}\mathrm{t}} \hspace{1em}\\ 1-{\left({\displaystyle \frac{{\mathrm{T}}_{\mathrm{o}\mathrm{p}\mathrm{t}}-\mathrm{T}}{{\mathrm{T}}_{\mathrm{o}\mathrm{p}\mathrm{t}}-{\mathrm{T}}_{\mathrm{c},\mathrm{m}\mathrm{a}\mathrm{x}}}}\right)}^{\mathsf{\beta }}\mathrm{i}\mathrm{f} {\mathrm{T}}_{\mathrm{o}\mathrm{p}\mathrm{t}}<\mathrm{T}<{\mathrm{T}}_{\mathrm{c}.\mathrm{m}\mathrm{a}\mathrm{x}}\\ 0\mathrm{i}\mathrm{f} \mathrm{T}<{\mathrm{T}}_{\mathrm{c},\mathrm{m}\mathrm{i}\mathrm{n}} \mathrm{o}\mathrm{r} \mathrm{T}>{\mathrm{T}}_{\mathrm{c},\mathrm{m}\mathrm{a}\mathrm{x}}\end{array}\right.$$

(4)

with T_c,min, T_opt and T_c,max representing, respectively, the minimum, optimal and maximum temperatures that govern the plant growth.

The temporal evolution of LAI (Equation (6)) is then simulated as the cumulative result of two opposing processes, growth and senescence, after which a positive component (${∆}_{LAI}^{+}$) associated with leaf development is added to LAI at the previous day during the growth phase, while a negative component (${∆}_{LAI}^{-}$) accounting for leaf loss is added during the senescence phase. These two phenological stages are determined using a degree-day approach, which identifies the onset of senescence based on the attainment of a threshold thermal sum (i.e., STT). This threshold is reached through the accumulation of daily mean air temperatures (i.e., SMT), starting from the crop emergence date, D₀.

Let SMT at step j be:

$${\mathrm{S}\mathrm{M}\mathrm{T}}_{\mathrm{j}}=\left\{\begin{array}{l}{\displaystyle \sum _{{\mathrm{D}}_0}^{\mathrm{j}}}\left({\mathrm{T}}_{\mathrm{j}}-{\mathrm{T}}_{\mathrm{c},\mathrm{m}\mathrm{i}\mathrm{n}}\right)\hspace{1em}\mathrm{i}\mathrm{f} {\mathrm{T}}_{\mathrm{j}}>{\mathrm{T}}_{\mathrm{c},\mathrm{m}\mathrm{i}\mathrm{n}}\\ 0\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\end{array}\right.$$

(5)

then,

$${{\mathrm{L}\mathrm{A}\mathrm{I}}_{\mathrm{j}}={\mathrm{L}\mathrm{A}\mathrm{I}}_{\mathrm{j}-1}+∆}_{\mathrm{L}\mathrm{A}\mathrm{I};\mathrm{j}-1,\mathrm{j}}$$

(6)

where ${∆}_{\mathrm{L}\mathrm{A}\mathrm{I};\mathrm{j}-1,\mathrm{j}}={∆}_{\mathrm{L}\mathrm{A}\mathrm{I};\mathrm{j}-1,\mathrm{j}}^{+}$ until ${\mathrm{S}\mathrm{M}\mathrm{T}}_{\mathrm{j}}<\mathrm{S}\mathrm{T}\mathrm{T}$

$${∆}_{\mathrm{L}\mathrm{A}\mathrm{I};\mathrm{j}-1,\mathrm{j}}^{+}={∆}_{\mathrm{D}\mathrm{A}\mathrm{M};\mathrm{j}-1,\mathrm{j}}·{\mathrm{P}}_{\mathrm{L}}\left({\mathrm{S}\mathrm{M}\mathrm{T}}_{\mathrm{j}}\right)·{\mathrm{S}}_{\mathrm{L}\mathrm{A}}$$

(7)

$${\mathrm{P}}_{\mathrm{L}}\left(\mathrm{S}\mathrm{M}\mathrm{T}\right)=1-{\mathrm{P}}_{\mathrm{L}\mathrm{a}}·{\mathrm{e}\mathrm{x}\mathrm{p}}^{{\mathrm{P}}_{\mathrm{L}\mathrm{b}}·\mathrm{S}\mathrm{M}\mathrm{T}}$$

(8)

while, as ${\mathrm{S}\mathrm{M}\mathrm{T}}_{\mathrm{j}}\ge \mathrm{S}\mathrm{T}\mathrm{T}$, ${∆}_{\mathrm{L}\mathrm{A}\mathrm{I};\mathrm{j}-1,\mathrm{j}}={∆}_{\mathrm{L}\mathrm{A}\mathrm{I};\mathrm{j}-1,\mathrm{j}}^{-}$

$${∆}_{\mathrm{L}\mathrm{A}\mathrm{I};\mathrm{j}-1,\mathrm{j}}^{-}={-\mathrm{L}\mathrm{A}\mathrm{I}}_{\mathrm{j}-1}·{\displaystyle \frac{{\mathrm{S}\mathrm{M}\mathrm{T}}_{\mathrm{j}}-\mathrm{S}\mathrm{T}\mathrm{T}}{{\mathrm{R}}_{\mathrm{s}\mathrm{e}\mathrm{n}}}}$$

(9)

Equations (7)–(9) describe the crop phenology that is controlled by the following parameters: biomass partitioning (P_La, P_Lb), onset of senescence (i.e., STT), and its progression (i.e., rate of senescence R_sen). What is worth noting from these calculations is that SAFY requires the definition of 13 parameters, categorized into three groups. The first group includes parameters derived from the literature or direct measurement, such as the light extinction coefficient (K), climate efficiency (ε_c), specific leaf area (S_LA), initial dry above-ground mass (DAM₀), and cardinal temperatures (i.e., minimum, T_c,min; optimal, T_opt; maximum T_c,max) governing plant growth. The second group consists of the four parameters that control crop phenology, such as those regulating biomass partitioning and the onset and rate of senescence. The third group includes parameters that are highly sensitive to local agro-environmental conditions: the day of emergence (D₀) and the effective light-use efficiency (ELUE), the latter accounting for cumulative stress factors related to water availability, nutrient levels, and management practices. SAFY has been proven to be useful because of its simplicity and flexibility and is especially useful for operational crop monitoring and decision-support applications in irrigated systems, such as those used for tomato cultivation in water-stressed areas [36].

2.4.2. Assimilation of Sentinel-2 LAI into SAFY

In this study, the LAI dynamic produced by the model (Equation (6)) was corrected by sequentially assimilating the S2 LAI estimates as soon as satellite images were available. The assimilation technique was a direct insertion of satellite-based data in place of the value simulated by the model.

This sequential direct insertion was applied under the assumption that a continuous update of one crop model state based on remotely sensed observations would reduce the biases induced by the model simplifications of the processes and environmental conditions influencing the crop growth dynamics [34,35].

2.5. The One-Step Approach for Evaluating Evapotranspiration (SAFY-E)

Crop evapotranspiration under standard conditions, i.e., evapotranspiration from disease-free, well-fertilized crops grown in large fields under optimum soil water conditions and achieving full production under the given climatic conditions [11]. ETc computed according to the Penman–Monteith formula and reported in the FAO-56 paper as the preferred method to evaluate ETc when a complete set of weather data is available [11]. The application of the formula was carried out by following the one-step approach [4,15,42] that consists of inputting weather data and crop parameters directly into the formula itself to explicitly account for the aerodynamic, r_a, and surface, r_s, resistances as follows:

$$\mathrm{E}{\mathrm{T}}_{\mathbf{c}}={\displaystyle \frac{1}{\mathsf{\lambda }}}{\displaystyle \frac{\mathsf{\Delta }\left({\mathrm{R}}_{\mathrm{n}}-\mathrm{G}\right)+{\mathrm{c}}_{\mathrm{p}}{\mathrm{\rho }}_{\mathrm{a}}\left({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}}\right)/{\mathrm{r}}_{\mathrm{a}}}{\mathsf{\Delta }+\mathsf{\gamma }\left(1+{\mathrm{r}}_{\mathrm{s}}/{\mathrm{r}}_{\mathrm{a}}\right)}}$$

(10)

$${\mathrm{r}}_{\mathrm{a}}={\displaystyle \frac{\mathrm{l}\mathrm{n}\left(\frac{{\mathrm{z}}_{\mathrm{m}}-\mathrm{d}}{{\mathrm{z}}_{\mathrm{o}\mathrm{m}}}\right)\mathrm{l}\mathrm{n}\left(\frac{{\mathrm{z}}_{\mathrm{h}}-\mathrm{d}}{{\mathrm{z}}_{\mathrm{o}\mathrm{h}}}\right)}{{\mathrm{k}}^2{\mathrm{W}\mathrm{S}}_2}}$$

(11)

$${\mathrm{r}}_{\mathrm{s}}={\displaystyle \frac{{\mathrm{r}}_{\mathrm{l}}}{{\mathrm{L}\mathrm{A}\mathrm{I}}_{\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}}}}$$

(12)

where λ is the latent heat of vaporization; Δ is the slope of the saturation vapor pressure curve at air temperature T; R_n is the net incoming solar radiation; G is soil heat flux density; c_p is the specific heat at constant pressure; ρ_a the mean air density at constant pressure; (e_s – e_a) is the vapor pressure deficit; γ is the psychrometric constant. At the daily scale, all these variables depend on the following daily weather inputs: incoming solar radiation, RS, mean, maximum and minimum temperatures, T, T_max and T_min respectively, air relative humidity, RH, and atmospheric pressure. For details on the formulations of their calculations from weather inputs, please refer to [11].

From an operational standpoint, what specifically determines the calculation of r_a and r_s:z_m is the height of wind measurements, i.e., 2 m, z_h is the height of humidity measurements, i.e., 2 m, d is the zero plane displacement height, which is generally assumed to be equal to 2/3 of the crop height, h_c, z_om is the roughness length governing the momentum transfer, which is equal to 0.123 h_c, z_oh is the roughness length governing the transfer of heat and vapor, equal to z_om, k is the von Karman’s constant, WS₂ is the wind speed at height 2 m, computed from WS at 10 m by applying a logarithmic profile [11], r_l is the bulk stomatal resistance of the well-illuminated leaf, which is 100 s m⁻¹, LAI_active is the active (sunlit) leaf area index, which is 0.5 LAI. When LAI is greater than 4, the surface resistance should be set at 50 s m⁻¹. For cultivating tomatoes, the crop height is assumed to be 0.4 m [31,34,35]. In this study, the ETc assessment was performed by using daily weather data, alternatively from ground-based observations and the AgERA5 + CMSAF database, while the LAI was obtained from the SAFY dynamic forcing model outputs with S2 LAI estimates as available.

2.6. Assessing Net CWR and Yield

FAO defines crop water requirement (CWR) as “the depth of water needed to meet the water loss through evapotranspiration of a disease-free crop, growing in large fields under non-restricting soil conditions, including soil water and fertility, and achieving full production potential under the given growing environment” [54]. Although CWR equals ETc in numerical values, the latter denotes the actual water loss via crop evapotranspiration while CWR indicates the quantity of water required to compensate for this loss and ensure optimal crop growth; this implies that the water that must be supplied through the irrigation system to ensure that the crop receives its full crop water requirements. When irrigation is the major source of water obtained by the crop, the irrigation supply must be at least equal to or greater than the CWR. The irrigation supply is then difficult to accomplish because of losses and inefficiencies within the irrigation system. Conversely, if the crop obtains part of its water from alternative sources, such as rainfall, soil moisture reserves, or groundwater contributions, the irrigation requirement may be significantly lower than the total CWR.

In this study, it was assumed that (i) throughout the irrigation seasons the soil moisture reserve was unchanged, so that the water stored in the soil does not contribute to reduce the crop water loss, (ii) there are no subsurface contributions and (iii) rainfall fully contributes to offsetting evapotranspiration losses. Under these assumptions, broadly acknowledged in the scientific literature [55], the difference between losses for crop evapotranspiration and rainfall (i.e., the net CWR) was judged to be a reliable proxy of irrigation needs that was calculated as follows:

$$\mathrm{net} \mathrm{CWR}={\mathrm{E}\mathrm{T}}_{\mathrm{C}}-{\mathrm{P}}_{\mathrm{n}}$$

(13)

where P_n is the effective precipitation that accounts for canopy interception. Runoff and percolation are here considered negligible, considering the low amount of rainfall during the growing season, as common practice [31,55] and as also verified for the same field and period in a previous study by [35]. So, P_n depends on canopy development, through LAI and fractional vegetation cover, f_vc, and an empirical factor, a, is equal to 0.28 mmday⁻¹, according to the following empirical formulation, which is broadly used for similar purposes [31,55]:

$${\mathrm{P}}_{\mathrm{n}}=\mathrm{P} -\mathrm{a}·\mathrm{L}\mathrm{A}\mathrm{I}·\left(1-{\displaystyle \frac{1}{1+\frac{{\mathrm{f}}_{\mathrm{v}\mathrm{c}}·\mathrm{P}}{\mathrm{a}·\mathrm{L}\mathrm{A}\mathrm{I}}}}\right)$$

(14)

Yield estimation requires the conversion of DAM from the simulations (i.e., DAMmax, from Equation (1)) into fresh yield by means of conversion factors that are able to account for the portion of biomass allocated to the harvestable product and its water content, as follows:

$$\mathrm{Y}=\mathrm{Fresh} \mathrm{Yield}={\displaystyle \frac{ {\mathrm{DAM}}_{\max }·\mathrm{HI}}{{\mathrm{F}}_{\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{h}}}}·\mathrm{c}$$

(15)

where HI is the harvest index, i.e., the fraction of dry biomass allocated to the harvestable organ in the form of fruit or grain, with this function being set at 0.5 as suggested by [11] for the cultivation of tomatoes, while F_fresh is the conversion factor from dry to fresh weight, whose value is set at 0.055 [34,35,36] with c being a unit conversion factor, that is set at 0.01, to account for the difference in measurement units between the model output DAM_max (g m⁻²) and the farm’s observed fresh yield (t ha⁻¹, Table 2).

2.7. Statistical Indices for Evaluating Performance

The performances of the proposed methodology were determined by using two dimensionless statistical indices, PBIAS, which stands for percent bias, and PRMSE, which stands for percent root mean square error. These indices were calculated as follows:

$$\mathrm{PBIAS} (\%)={\displaystyle \frac{1}{\overline{\mathrm{O}}}}{\displaystyle \frac{{\sum }_{\mathrm{j}=1}^{\mathrm{m}}\left({\mathrm{P}}_{\mathrm{j}}-{\mathrm{O}}_{\mathrm{j}}\right)}{\mathrm{m}}}100$$

(16)

$$\mathrm{P}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}\left(\%\right)={\displaystyle \frac{1}{\overline{\mathrm{O}}}}\sqrt{{\displaystyle \frac{{\sum }_{\mathrm{j}=1}^{\mathrm{m}}{\left({\mathrm{P}}_{\mathrm{j}}-{\mathrm{O}}_{\mathrm{j}}\right)}^2}{\mathrm{m}}}}100$$

(17)

where j denotes the day index, P_j and O_j represent the predicted and observed values of the variable under evaluation, respectively; $\overline{\mathrm{O}}$ is the average of the observed values over the considered time period, here covering m days. The use of PBIAS and PRMSE to evaluate performance is widely adopted and recognized in scientific literature and allows for comparability with previous works and for a more rigorous benchmarking of our results.

3. Results

This section presents (i) the validation of the S2 LAI estimates against ground-based LAI measurements, (ii) the performance assessment of AgERA5 reanalysis and CM SAF radiation datasets by comparing them with ground-based weather observations at the nearest weather station in the surroundings of the farm of interest (Figure 1), and (iii) the main results regarding the proposed methodology’s ability to reliably estimate CWR and yield.

3.1. Validation of the S2 LAI Estimates with Ground-Based LAI Measurements

For the year 2019, a set of both Sentinel-2 multispectral images for LAI estimation (Section 2.2) and ground-based LAI measurements (Section 2.1) were available for the analyzed farm. This allowed us to validate the S2 LAI estimates that were assumed as a benchmark for evaluating performance in the following analyses.

The Sentinel-2 imagery from April until mid-May and 20 June, 1 July, and 21 July was discarded due to very cloudy atmospheric conditions. This elimination left us with five usable images for the irrigation season.

Table 4. S2 LAI estimates.

Dates	Mean Value	Minimum Value	Maximum Value
22 May 2019	0.76	0.69	0.89
17 June 2019	1.63	1.27	1.94
25 June 2019	1.71	1.02	2.36
5 July 2019	1.74	1.36	2.29
27 July 2019	1.17	0.79	1.58

shows the mean, minimum and maximum values of the study plot’s 10 pixels.

Figure 3 shows the box plots of LAI data for comparison between the ground-based measurements, i.e., LICOR-2000 LAI (Table 3), and the S2 estimates listed in Table 4. In the boxplots of Figure 3, the circle represents the mean value for the 10 pixels within the study plot’s 2 hectares, the central line is the median, and the box is delimited by the 25th and 75th percentiles of the sample. Whiskers go from the end of the interquartile range to the furthest observation within the whisker length. Values beyond the whisker length are defined as outliers and appear as cross markers. The mean values of the ground measurements are always greater than the S2 estimates, with a PBIAS—given by the average difference between mean S2 estimates and mean observations over the mean of the observations—being equal to −1%. The PRMSE is equal to 12%. These performances encourage the use of satellite-based estimates as proxies for ground-based LAI measurements.

As shown in Figure 3, the tendency of ground-based LAI measurements to overestimate the Sentinel-2-derived LAI becomes more evident during the senescence phase. This discrepancy arises from the fact that optical instruments such as the LAI-2000 are unable to discriminate between photosynthetically active and inactive tissues. As a result, senescent and necrotic leaves, along with reproductive organs (e.g., fruits), contribute to radiation interception in ground-based measurements, potentially leading to an overestimation of LAI. In contrast, the Sentinel-2 LAI represents only the photosynthetically active leaf area (as discussed in Section 2.2) and therefore excludes senescent and dead tissues.

3.2. Performance of AgERA5 and CM SAF SARAH-3 Data

The following statistics, which were computed by benchmarking them to the ground-based observations at the farm’s nearest AWS, refer to the performance of AgERA5 + CMSAF daily weather data, bias corrected and downscaled at the site of interest.

Table 5. Statistical indices for weather variables from AgERA5 and CM SAF databases.

Dataset	Weather Variable	PBIAS (%)	PRMSE (%)
AgERA5	T	−7.0	6.1
	Tmax	−0.024	3.4
	Tmin	−11.1	10.7
	RH	6.5	10.1
	WS	21.0	24.2
	P 1	−17.7	234.8
	RS	−3.4	11.7
CM SAF	RS	0.16	4.7

¹ The statistics refer to the daily value of precipitation.

provides a synoptic overview of these statistics.

As shown in Table 5, the weather variables most affected by errors are (i) precipitation, with a PRMSE of 234.8%, which is consistent with findings by [56] who reported that the numerical models tend to perform poorly when data that were compiled under cloudy conditions are used, and (ii) wind speed, with PBIAS and PRMSE equal to 21.0% and 24.2%, respectively. The estimates of temperatures are affected by acceptable errors, along with air relative humidity. The most reliable estimates made by reanalysis products regard T_max. The CM SAF radiation dataset exhibits a lower PBIAS compared to the AgERA5 radiation dataset, and it outperforms AgERA5 in terms of PRMSE, which is almost one third (Table 5). Therefore, the AgERA5 RS was substituted by the CM SAF RS in the AgERA5 + CMSF database. Overall, it was demonstrated that the quality of AgERA5 data is very similar to the quality of ERA5-Land reanalysis [23,24], which was used for similar purposes in a previous study in the region [35].

3.3. Calibration of the SAFY Model

Although SAFY is a parsimonious crop growth model, it still requires the estimation of 12 parameters and knowledge of the crop’s day of emergence or transplantation (D₀).

In this study, the seven parameters described in

Table 6. SAFY parameter values.

Parameter	Value	Measurement Unit	Source of Data
DAM0	4.1	g m−2	As in [36] calibrated under comparable climatic conditions at tomato-growing fields in a neighboring region.
εc	0.46	-
K	0.26	-
ELUE	3.7	g MJ−1
SLA	0.0175	m2 g−1
PLa	0.29	-
PLb	0.00167	-
STT	400	°C	Locally calibrated at tomato-growing fields in the study area.
Rsen	9000	°C day−1
Tc,min	11	°C
Topt	25	°C
Tc,max	32	°C

were derived from the Capitanata area in Apulia Region of Southern Italy, where a similar study also monitored the growing of tomatoes under comparable climatic conditions [36]. The remaining parameters were locally calibrated using available data collected at tomato fields within the study region during 2023. In particular, S2 LAI values gathered at several farms in the neighborhood of D’Amore farm were used for calibrating both the temperature governing the senescence beginning and development of the senescence process as well as the temperature stress function, along with the ground-based weather observations at the monitoring AWSs in the surroundings of the analyzed fields, which provided the input weather data of daily mean temperature, T, and incoming solar radiation, RS. Table 6 reports the estimated parameter values, while Figure 4 illustrates the LAI evolution simulated by the calibrated SAFY model, compared with the average S2 LAI values on the days of the satellite passages in the year 2023, recorded at the analyzed tomato fields.

In Figure 4, the tomato fields and their associated average LAI were grouped according to two different transplantation dates: (a) G1, 19 April and (b) G2, 29 April. This distinction was refined by using a single set of calibrated parameters that were obtained by optimizing the model against data from both groups, each of which had its own dynamics.

Performance evaluation in terms of PBIAS between SAFY LAI estimates and S2 LAI estimates for G1 data gives an average value of 19%, but 4% for the G2 data; the very low PBIAS of the second group is due to the circumstance that the model underestimation at the first stages of canopy development compensates the overestimation at the senescence phase. PRMSE is equal to 34% and 30% for G1 and G2 groups, respectively, which corresponds to average RMSE of 0.45 and 0.33, in agreement with similar studies [36]. Overall, the LAI dynamics are well described by the SAFY simulation, which is able to fill the gaps between two successful satellite passages. Indeed, the cloudiness in the month of June 2023 made possible only one S2 LAI estimate (Figure 4).

3.4. LAI Dynamics

This section assesses the extent to which the calibrated SAFY model was able to reliably reveal LAI dynamics in the same area of calibration but for a different year of analysis, based on input weather data from different sources. The year of interest was 2021 (Section 2.1), when a field campaign allowed us to validate the proposed methodology’s ability to estimate CWR and yield. Figure 5 shows a snapshot overview of the SAFY simulated LAI dynamics compared with S2 LAI under four different conditions by using (i) only weather observations as input data, (ii) both weather observations and S2 LAI estimates for forcing the simulation as soon as a satellite-derived product was available, (iii) AgERA5 + CMSAF as weather inputs and (iv) AgERA5 + CMSAF in combination with the S2 LAI estimates.

The benchmark scenario was based on LAI dynamics derived from SAFY simulations with the combined use of weather observations and S2 LAI data, representing the most accurate estimates available. This scenario outperformed the SAFY outputs in terms of LAI when only weather observations were employed. Moreover, Figure 5 also shows that the use of the AgERA5 + CMSAF dataset alone leads to SAFY LAI estimates that are highly biased with respect to the S2 LAI estimates. However, when SAFY was forced by assimilating S2 LAI estimates, the model outputs are in good agreement with the benchmark scenario values. This alternative scenario is assumed as a proxy of the benchmark scenario that requires in situ weather observations; on the contrary, it relies on gridded numerical and satellite products, freely available on the web.

The two scenarios (represented by the solid green and blue lines in Figure 5) mainly differ at the peak: the benchmark scenario (i.e., green solid line) reaches a maximum LAI of 5.2, while the alternative scenario (i.e., blue solid line) attains 6.5. Overall, the PBIAS of the alternative scenario relative to the benchmark is 6.3%, while predicted data shows a PRMSE equal to 17%. The performance results of SAFY in simulating LAI dynamics support the integration of alternative weather data sources, such as reanalysis or satellite-derived datasets, with remotely sensed crop parameters. While not intended to replace ground-based observations, these alternative sources offer a valuable complement, especially in areas where the in situ data are sparse or unavailable. Their combined use can enhance the robustness and scalability of agro-hydrological modeling without compromising the reliability of the estimates.

3.5. Assessment of Net CWR and Yield

This section presents a comparative assessment of the performance of the alternative scenario, the ground-based weather observations, and the S2 LAI-driven benchmark scenario. The alternative scenario was based on AgERA5 + CM SAF weather data combined with S2 LAI. The net irrigation volume of water measured at the farm of interest (Table 2) matches the definition of the net CWR in this case study [35].

Following Equation (13), the net CWR equals 318.7 mm for the benchmark scenario and 318.6 mm for the alternative scenario. These two outcomes are surprisingly similar due to the overestimation of the ETc by the alternative scenario, which compensated for the underestimation of the precipitation. This closeness shows that the alternative scenario is reliably capable of producing CWR estimates that are comparable to those obtained from the benchmark scenario. Moreover, with respect to the onsite farm measurements, the overall PBIAS in determining irrigation needs is 8.4%.

With regard to fresh yield estimates, as computed via Equation (15), the benchmark scenario provides a prediction of 120.2 t ha⁻¹, closely matching the actual yield of 121 t ha⁻¹, whereas the alternative scenario slightly overestimates it, with a predicted value of 124.7 t ha⁻¹. The proposed methodology shows an overall PBIAS of about 3.0% in fresh yield predictions.

4. Discussion and Conclusions

The present study proposed a cutting-edge approach to estimate CWR and fresh yield of tomato crops in a Mediterranean agricultural context, by integrating Sentinel-2-derived LAI with reanalysis data from AgERA5 and satellite-based radiation data from CM SAF SARAH-3, within the framework of the SAFY crop growth model. To the best of our knowledge, this is the first study in the scientific literature that employs the two most up-to-date freely available gridded weather datasets, AgERA5 and CM SAF SARAH-3 weather datasets, for the estimation of CWR and yield. Moreover, it is the first time that the SAFY model was used by coupling weather reanalysis and remotely sensed data.

For a similar purpose of estimating CWR and yield, a recent study [35], which was conducted at the same farm located in the Campania Region, integrated ERA5-Land reanalysis and CM SAF SARAH-2.1 datasets with Sentinel-2-derived canopy cover estimates within the AquaCrop model. The result of the methodology proposed in that study showed an overestimation of CWR by approximately 5% and of yield by 4% with respect to onsite measurements. These findings are consistent with those of the present study, in which CWR and yield estimates by AgERA5 and CM SAF SARAH-3 within the SAFY-E framework differed from onsite measurements by about 8.4% and 3%, respectively. Although the estimates obtained with our proposed approach did not result in a significant improvement in CWR and yield estimation than previous studies, the rationale behind this research lies in the use of an alternative crop growth model to AquaCrop, namely, SAFY-E that explicitly relates biomass production and evapotranspiration rates to LAI, rather than to canopy cover. Indeed, LAI is a more comprehensive vegetation index than canopy cover, and its satellite-derived estimates allow for the representation of key biophysical processes throughout crop development stages, including the presence of senescent or necrotic tissues during the senescence phase [49].

The calibration of the SAFY model, while requiring a relatively small number of parameters, represents a critical step in ensuring reliable model outputs. Seven of the twelve model parameters were derived from a previous study in a climatically and agronomically similar region [36], and the remaining five were locally calibrated using S2 LAI data that were computed for several farms in the study region. Despite the parsimonious structure of SAFY, the model effectively captured LAI dynamics, as indicated by the low PRMSE values presented in the calibration phase (Section 3.3), that were found to be equal to 34% and 30%, respectively, for two groups of data that differ from each other in their transplantation day. These results are consistent with other applications of SAFY for tomatoes in a similar climate context [36] that showed PRMSE of about 37%. Then, the results for LAI dynamics in the model validation phase suggested the robustness of the calibrated SAFY model. The assimilation of S2 LAI improved model accuracy under both benchmark and alternative scenarios, i.e., the former driven by ground-based weather observations and the latter by the AgERA5 + CMSAF dataset, confirming the advantage of incorporating remote sensing data into crop growth models. Notably, the alternative scenario based on freely available gridded weather data (i.e., AgERA5 + CMSAF) and S2 LAI showed a good agreement with the benchmark scenario, with a PRMSE of 17% and a PBIAS of 6.3%, in terms of LAI.

When comparing the modeled fresh yield and net CWR values with ground-truth data from the monitored farm in 2021, both benchmark and alternative scenarios performed well. The benchmark scenario predicted a fresh yield that was remarkably close to the actual measured value. The alternative scenario, despite being based on remotely sensed and reanalysis data, produced a slightly higher yield estimate, leading to a PBIAS of about 3.0%. The accuracy of net CWR estimation was similarly encouraging, with the alternative scenario yielding a value almost identical to the benchmark, and a PBIAS of 8.4% compared to the observed irrigation volume. These performances validate the methodological assumption that high-efficiency drip irrigation and standard crop management allow the use of net CWR as a proxy for actual irrigation needs.

These findings underscore the growing potential of reanalysis and satellite datasets to complement in situ meteorological measurements in areas with sparse or incomplete monitoring networks, and they are in line with other recent studies that leverage the synergy between reanalysis datasets and satellite-derived vegetation indices for agricultural water management (e.g., [4,5,16,21,22,35]). For instance, the outcomes presented by [31,35] also demonstrated the utility of Sentinel-2 data for estimating evapotranspiration and yield in tomato crops under Mediterranean conditions.

Moreover, this study confirms previous findings about the limitations of reanalyzing precipitation data under convective weather patterns [5,21,56], as evidenced by the high PRMSE observed for rainfall in AgERA5. Nevertheless, the integration with CM SAF radiation products and the application of bias correction procedures significantly improved the reliability of the AgERA5 dataset.

A crucial implication of the findings of the proposed research is the demonstrated feasibility of applying this methodology in data-scarce environments. By complementing ground-based measurements with remotely sensed and freely available gridded datasets, the proposed approach offers a scalable and cost-effective solution for irrigation planning and water use efficiency assessment at the farm and regional levels. This is particularly relevant in the context of climate change, which is expected to exacerbate water scarcity in Southern Europe and other semi-arid regions. Indeed, climate-oriented studies require sufficiently long historical data series, which, in the case of CWR and yield estimation, can be reconstructed by implementing the proposed approach based on the use of consistent reanalysis-based meteorological data combined with Sentinel-2 imagery. The assimilation of satellite observations can help reduce uncertainties in crop model parameter estimation arising from spatial and temporal variability. Moreover, the use of reanalysis data ensures the global availability of complete and coherent weather datasets with adequate spatial resolution and, importantly, long temporal coverage extending several decades into the past.

Despite these promising results, several limitations and potential improvements should be acknowledged. First, while the SAFY model incorporates a direct insertion method for assimilating S2 LAI, more advanced data assimilation techniques (e.g., Ensemble Kalman Filter or variational approaches) could further improve model performance by better accounting for uncertainties in both model predictions and observational data [57,58,59]. Second, the assumption of negligible soil water storage changes, while consistent with what is reported in the literature and the specific situation that applies to the balance over the whole irrigation season, may not be held in all agro-environmental settings. Incorporating soil moisture data, either from in situ sensors or satellite sources, could help refine CWR estimates. Additionally, although the study focused on a single crop (processing tomato) and a single farm, the methodology is inherently transferable. Future studies could explore its applicability to other crop types and agro-climatic regions.

In conclusion, the integration of Sentinel-2 LAI with AgERA5 and CM SAF SARAH-3 data within the SAFY model framework proved effective in accurately estimating both crop water requirements and yield under Mediterranean conditions. The findings support the use of this method as a viable alternative to conventional observation-based systems, especially in areas where ground-based meteorological data are limited or unavailable. With further refinement and scaling, this approach can contribute to the development of decision-support tools for the sustainable management of irrigated agriculture and agricultural planning under current and future climate scenarios.