Estimating Evapotranspiration of Rainfed Winegrapes Combining Remote Sensing and the SIMDualKc Soil Water Balance Model

: Soil water balance (SWB) in woody crops is sometimes difficult to estimate with one-dimensional models because these crops do not completely cover the soil and usually have a deep root system, particularly when cropped under rainfed conditions in a Mediterranean climate. In this study, the actual crop evapotranspiration (ET c act ) is estimated with the soil water balance model SIMDualKc which uses the dual-K c approach (relating the fraction of soil cover with the crop coefficients) to improve the estimation of the water requirements of a rainfed vineyard, using data from a deep soil profile. The actual basal crop coefficient (K cb act ) obtained using the SIMDualKc model was compared with the K cb act estimated using fraction of ground cover and height (A&P approach), which is a simplified approach based on measurements of the fraction of ground cover and crop height. Spectral vegetation indices (VIs) derived from Landsat-5 satellite data were used to determine the fraction of ground cover (f c VI ) and thus the density coefficient (K d ). The SIMDualKc model was calibrated using available soil water (ASW) measurements down to a depth of 1.85 m, which significantly improved the conditions for using an SWB estimation model. The test of the model was performed using a different ASW dataset. A good agreement between simulated and field-measured ASW was observed for both data sets along the crop season, with RMSE < 12.0 mm and NRMSE < 13%. The calibrated K cb values were 0.15, 0.60, and 0.52 for the initial, mid-season, and end season, respectively. The ratio between ET c act and crop evapotranspiration (ET c ) was quite low between veraison and maturity (mid-season), corresponding to 36%, indicating that the rainfall was not sufficient to satisfy the vineyard’s water requirements. VIs used to compute f c VI were unable to fully track the plants’ conditions during water stress. However, ingestion of data from remote sensing (RS) showed promising results that could be used to support decision making in irrigation scheduling. Further studies on the use of the A&P approach using RS data are required.


Introduction
Estimating the evapotranspiration of orchards and vineyards using the soil water balance approach is often difficult due to the soil extent explored by the root system, Water 2024, 16, 2567.https://doi.org/10.3390/w16182567https://www.mdpi.com/journal/waterespecially under rainfed conditions [1][2][3].Under such conditions, the root system varies between 0.5 and 6 m, although it is suggested that a small fraction of roots can grow to greater depths [4][5][6][7], at which soil water content measurements are not normally surveyed.Additionally, the root system of these crops tends to explore the soil further into the interrow spacing.Grapevine root systems were studied across a wide range of climates and soil textures, showing that most active roots (about 80%) are located in the first 1.0 m of soil [8,9].Vineyards have long been rainfed [7,10,11] as the species is inherently adapted to tolerate dry periods, typical of many wine-growing regions [6].However, irrigation is nowadays commonly adopted because it allows improvement of the wine quantity and quality [11][12][13][14][15][16][17].Vineyards have mechanisms to control transpiration, the most relevant of which is the pronounced stomatal control [5,6,11,18,19].These plants also have a strategy to further explore the water reservoir in the soil by using a deep root system [5,6,13,[20][21][22].
Both mechanisms allow for efficient use of available water [5,6,11,[19][20][21][22], particularly in drier periods.Under rainfed conditions, the root system can be expected to develop further than in a comparable irrigated vineyard.There are few studies reporting a maximum rooting depths of vines greater than 6 m [23]; however, it has been suggested that a small fraction of roots can grow to a depth of 20 m in the absence of impermeable barriers [4][5][6][7].
The root system of the vine depends on the characteristics of the soils, the planting density, and the crop management used.Soil characteristics that have the greatest impact on root distribution include the soil bulk density, resistance to soil penetration, and texture [19].Soil water content is difficult to quantify due to the heterogeneity of the water distribution in the soil [3].However, it is possible to assess the vineyard water status by analysing the relationship between the actual crop evapotranspiration and its partitioning and the predawn leaf water potential (ψ p ) of grapevines.For instance, Malheiro et al. [24] reported a threshold of −0.3 MPa as a limit for irrigating vineyards cultivar (cv.)Moscatel Galego-Branco.For water stress conditions, Pellegrino et al. [25] also reported ψ p ranging from −0.1 MPa to −0.36 MPa as indicative of weak to moderate water stress for rainfed vineyards.In addition, Dinis et al. [18] quantified ψ p as varying from −0.3 MPa to −0.47 MPa for cv.Semillon and from −0.30 MPa to −1.07 MPa for cv.Muscat, with both vineyards in rainfed conditions.Carbonneau [26] defined the water stress limits as follows: no water deficit (0 MPa ≥ ψ p ≥ −0.2 MPa), mild to moderate water deficit (−0.2 MPa ≥ ψ p ≥ −0.4 MPa), moderate to severe water deficit (−0.4 MPa ≥ ψ p ≥ −0.6 MPa), severe to high water deficit (−0.6 MPa ≥ ψ p ≥ −0.8 MPa), and high water deficit (<−0.8MPa).
A common approach to estimating crop water requirements is the Food and Agriculture Organization of the United Nations (FAO) two-step approach which combines the climate conditions (reference crop evapotranspiration, ET o ) with the crop characteristics (crop coefficient, K c ), also named the K c -ET o approach.This approach was proposed in FAO56 [27] and has been widely adopted [28].The FAO56 K c -ET o approach can be applied with a single or a dual crop coefficient.In the first case, soil evaporation and crop transpiration are combined into a single K c value for each crop stage; for the latter, daily plant transpiration is based on the basal crop coefficient (K cb ), while daily soil evaporation is estimated using an evaporation coefficient (K e ).Thus, ET c is divided into crop transpiration (T c = K cb ET o ) and soil evaporation (E s = K e ET o ).
The standard tabulated values of K c and K cb allow the assessment of ET c under potential and well-watered conditions [27].The standard tabulated K c and K cb values for trees and vines were recently reviewed and updated by [29].However, under natural field conditions, the crop is often subject to biotic and abiotic stress due to water deficits caused by inadequate irrigation, improper management practices, soil quality and salinity, unsuitable crop varieties or rainfed conditions.Therefore, a water stress coefficient, K s , in the range between 0 and 1.0 is introduced as a multiplicative factor to estimate actual values of K c or K cb , i.e., K c act or K cb act [27,28,30,31].The actual crop evapotranspiration (ET c act ) is generally smaller than the potential value (ET c ) and can be defined as follows: Water 2024, 16, 2567 3 of 28 ET c act = (K s K cb + K e ) ET o = K c act ET o (1) The actual crop transpiration may be measured using the eddy covariance technique, e.g., [32][33][34], the Bowen ratio energy balance method, soil water balance, or a lysimeter, as reviewed by [35].The partitioning of evapotranspiration may be performed by combining soil evaporation measured in micro-lysimeters or mini-lysimeters [36] with actual crop transpiration estimations with sap flow methods [37][38][39].In addition, properly calibrated models allow assessing crop water requirements, and provide to adequate support for irrigation management, including under water deficit conditions.These models employ different functions and frequently do not use the FAO K c -ET o approach, e.g., the transient model HYDRUS-2D [40].Other examples have recently been reviewed [35].Models applying the dual-K c approach include SIMDualKc [41,42], which has been shown to be suitable for olive orchards [31,34,38,43] and other woody perennial crops, such as vineyards [44,45], peach trees [46], and almond, citrus, and pomegranate [43,47].
Alternatively to the models' usage, ref. [48] suggested an approach to obtaining the basal crop and crop coefficients (K cb , K c ) using a density coefficient (K d ), which is estimated with information of the fraction of the ground covered by the plants' canopy (f c ) and crop height (h) [31,48].In this approach, the estimation of K cb considers two other parameters: the multiplier on f c , which describes the influence of canopy density (M L ), and the resistance correction factor (F r ).M L characterizes the transparency of the canopy to solar radiation while F r is an empirical downward adjustment when vegetation exhibits tight stomatal control to transpiration.In the case of f c , the value may be measured using ground or remote sensing data [35,49,50].Application examples are provided by [36,39].A full review of the parameter values for M L and F r is provided by [28].
In recent decades, remote sensing (RS) data have been used to estimate crop evapotranspiration considering two main approaches: (i) satellite-based surface energy balance models (SEB) [32,[51][52][53][54], and (ii) spectral vegetation indices for estimation of basal crop coefficient (K cb ) based on the FAO56 method, K cb-VI [49,50,[55][56][57].The K cb-VI approach requires information for a smaller number of variables than the SEB models, being based on elementary principles.Nevertheless, in contrast to the SEB models, the K cb-VI approach ignores the effect of stomata closure related to the occurrence of water stress and assumes that this effect does not significantly affect the reduction in evapotranspiration compared to the effect of crop size [57].
The estimation of K cb based on spectral vegetation indices has already been performed with different approximations.An overview on this topic is given by [49].Two of the world's most widely used spectral indices for this approximation are the Normalized Difference Vegetation Index, NDVI [58], and the Soil Adjusted Vegetation Index, SAVI [59].The formulation of NDVI and SAVI combines red and near infrared (NIR) reflectance to provide an indirect measure of red-light absorption by chlorophyll (a and b) and reflectance of NIR by the mesophyll structure in leaves [49,60,61].Compared to NDVI, SAVI is less sensitive to the soil backscatter effect, which is an advantage in crops with discontinuous ground cover, such as vineyards [59,62].These spectral vegetation indices have also been used to determine the fraction of soil covered by the crop, f c .
Significant gaps exist in the determination of the soil water available for the evapotranspiration process due to the uncertainty in the volume of soil explored by the root system of vines.Consequently, this uncertainty also occurs when modelling the soil water balance (SWB), particularly in the case of one-dimensional models.To improve the soil water balance and actual crop ET estimates in a rainfed managed vineyard, the current study uses a combined approach of ground and remote sensing data ingested in the SWB model SIMDualKc.To support the everyday decision making, the A&P approach was also tested using the estimates of SIMDualKc model.Thus, a comparison of the K cb SIMDualKc with the K cb derived from the observed values of f c and h (K cb A&P ) [48] was included.The A&P approach is considered a useful approach to improve irrigation management and parameterize water balance models.The novelty of the current study lies in the precise determination of the soil water balance in a deep soil profile that can be explored by the roots, combined with a set of ground-truth data including ψ p measurements.The soil water content data allowed us to perform an adequate parameterization and calibration of a modelling tool.To the authors' knowledge, this is the first time that the A&P approach has been used to estimate rainfed vineyard evapotranspiration.

Materials and Methods
In the present study, the ground data set was collected in 1987 at a vineyard experimental site located in the Ribatejo region (Center Portugal).The remote sensing (RS) data characterizing the vineyard development was acquired by the Landsat 5 satellite (downloaded from the Earth Explorer portal; https://earthexplorer.usgs.gov/,accessed on 15 May 2023).The following subsections provide a detailed description of all data sets and modelling tool.

Study Area and Crop Characterization
The experiments were developed in a 2.13 ha vineyard plot of Escola Superior Agrária (School of Agriculture), located in Santarém, Ribatejo region (39 • 15 ′ 38.15 ′′ N, 8 • 42 ′ 37.7 ′′ W) (Figure 1).The sample collection area (SCA) is quite representative and corresponds to 50.7% (1.08 ha) of the total vineyard site.approach is considered a useful approach to improve irrigation management and parameterize water balance models.The novelty of the current study lies in the precise determination of the soil water balance in a deep soil profile that can be explored by the roots, combined with a set of ground-truth data including ψp measurements.The soil water content data allowed us to perform an adequate parameterization and calibration of a modelling tool.To the authors' knowledge, this is the first time that the A&P approach has been used to estimate rainfed vineyard evapotranspiration.

Materials and Methods
In the present study, the ground data set was collected in 1987 at a vineyard experimental site located in the Ribatejo region (Center Portugal).The remote sensing (RS) data characterizing the vineyard development was acquired by the Landsat 5 satellite (downloaded from the Earth Explorer portal; https://earthexplorer.usgs.gov/,accessed on 15 May 2023).The following subsections provide a detailed description of all data sets and modelling tool.

Study Area and Crop Characterization
The experiments were developed in a 2.13 ha vineyard plot of Escola Superior Agrária (School of Agriculture), located in Santarém, Ribatejo region (39°15′38.15″N, 8°42′37.7″W) (Figure 1).The sample collection area (SCA) is quite representative and corresponds to 50.7% (1.08 ha) of the total vineyard site.The data was collected in 1987 on a 20-year-old vineyard, cv.black Trincadeira, grafted on rootstock R110, planted at 3.0 m × 1.5 m, trained in a vertical shoot positioned trellis, pruned to the bead of 2 to 3 buds and a total load ranging between 6 to 10 buds, and with a high plant vigour.The vineyard was aligned, trellised, and oriented in the SSW-NNE Water 2024, 16, 2567 5 of 28 direction.The timing of the phenological stages was recorded according to the Bagiolini scale as follows [19]: (i) cotton bud (bud swelling) in the first week of March, (ii) green tip (bud opening) occurred ten days later, (iii) onset flowering occurred between April 10 and 15, (iv) end of flowering between May 20 and 25, (v) pea-berry stage normally occurred in the first week of July, and (vi) complete ripening took place in the last week of September.These stages were then converted to those proposed by [27] as follows: initial stage 5 March-9 April, development 10 April-19 May, mid-season stage 20 May-30 July, and late-season 31 July-25 September (Figure 2).Weed control in the inter-row was carried out with herbicides in April.
Water 2024, 16, x FOR PEER REVIEW 5 of 29 The data was collected in 1987 on a 20-year-old vineyard, cv.black Trincadeira, grafted on rootstock R110, planted at 3.0 m × 1.5 m, trained in a vertical shoot positioned trellis, pruned to the bead of 2 to 3 buds and a total load ranging between 6 to 10 buds, and with a high plant vigour.The vineyard was aligned, trellised, and oriented in the SSW-NNE direction.The timing of the phenological stages was recorded according to the Bagiolini scale as follows [19]: (i) cotton bud (bud swelling) in the first week of March, (ii) green tip (bud opening) occurred ten days later, (iii) onset flowering occurred between April 10 and 15, (iv) end of flowering between May 20 and 25, (v) pea-berry stage normally occurred in the first week of July, and (vi) complete ripening took place in the last week of September.These stages were then converted to those proposed by [27] as follows: initial stage 5 March-9 April, development 10 April-19 May, mid-season stage 20 May-30 July, and late-season 31 July-25 September (Figure 2).Weed control in the inter-row was carried out with herbicides in April.The vineyard predawn ψp (as previously mentioned in Section 1) and available soil water content relationship was analysed as an indicator of the vineyard water stress level and to better understand the soil-plant water relationships.The ψp measurements were carried out using a pressure chamber [63] on a total of nine dates, from June to September, on 7 to 10 leaves of different plants in each date.These measurements were considered to be representative of the vineyard.To minimize measurement errors, all ψp measurements were carried out close to the vines, with a time interval of around one minute between cutting the leaf and reaching the balance between the pressure in the chamber and the pressure in the xylem [19].

Climate Characterization
According to the Köppen-Geiger climate classification [64], the study area has a warm temperate climate (Csa), with dry and hot summers (Tair > 22 °C) and mild rainy winters, thus a typical Mediterranean climate.Average annual evapotranspiration ranges from 712 mm to 815 mm while average annual precipitation ranges from 674 mm to 844 mm, mostly concentrated in the winter months, considering an average of the years 1982-1987 [19].
Weather data were obtained from the Santarém weather station (39°15′ N, 8°42′ W, 73 m a. s. l.), located 1 km away from the experimental site.
Daily data collected included maximum and minimum temperature (Tmax and Tmin, °C), solar radiation (Rs, W m −2 ), and average relative humidity (RH, %).The station is under reference site conditions [27], which allows the estimation of the reference evapotranspiration (PM-ETo).Daily precipitation (mm) was also collected in the station.Based on [65], weather data were assessed in terms of quality and integrity.A brief characterization of the prevailing weather conditions in the experimental area is shown in Figure 3 for the period 1982-1987 (mean values) and for the study year (1987).The mean annual precipitation in the period 1982-1987 was 744.57  The vineyard predawn ψ p (as previously mentioned in Section 1) and available soil water content relationship was analysed as an indicator of the vineyard water stress level and to better understand the soil-plant water relationships.The ψ p measurements were carried out using a pressure chamber [63] on a total of nine dates, from June to September, on 7 to 10 leaves of different plants in each date.These measurements were considered to be representative of the vineyard.To minimize measurement errors, all ψ p measurements were carried out close to the vines, with a time interval of around one minute between cutting the leaf and reaching the balance between the pressure in the chamber and the pressure in the xylem [19].

Climate Characterization
According to the Köppen-Geiger climate classification [64], the study area has a warm temperate climate (Csa), with dry and hot summers (T air > 22 • C) and mild rainy winters, thus a typical Mediterranean climate.Average annual evapotranspiration ranges from 712 mm to 815 mm while average annual precipitation ranges from 674 mm to 844 mm, mostly concentrated in the winter months, considering an average of the years 1982-1987 [19].
Weather data were obtained from the Santarém weather station (39 • 15 ′ N, 8 • 42 ′ W, 73 m a. s. l.), located 1 km away from the experimental site.
Daily data collected included maximum and minimum temperature (T max and T min , • C), solar radiation (R s , W m −2 ), and average relative humidity (RH, %).The station is under reference site conditions [27], which allows the estimation of the reference evapotranspiration (PM-ET o ).Daily precipitation (mm) was also collected in the station.Based on [65], weather data were assessed in terms of quality and integrity.A brief characterization of the prevailing weather conditions in the experimental area is shown in Figure 3 for the period 1982-1987 (mean values) and for the study year (1987).The mean annual precipitation in the period 1982-1987 was 744.57(±37.1)mm, while in the year under study, 1987, it was 784 mm, which was quite close to the mean.The average reference crop evapotranspiration was 2.68 (±2.2) mm d −1 in 1982-1987 and was higher in 1987, reaching an average value of 3.71 mm d −1 .Thus, higher annual ET o values and similar P values were recorded in 1987 compared to the previous five-year average.Figure 3 clearly shows that most of the precipitation was concentrated in the months of November to February, when the vineyards were dormant.it was 784 mm, which was quite close to the mean.The average reference crop evapotranspiration was 2.68 (±2.2) mm d −1 in 1982-1987 and was higher in 1987, reaching an average value of 3.71 mm d −1 .Thus, higher annual ETo values and similar P values were recorded in 1987 compared to the previous five-year average.Figure 3 clearly shows that most of the precipitation was concentrated in the months of November to February, when the vineyards were dormant.

Soil Characterization and Soil Water Content Monitoring
Soil properties were assessed by collecting disturbed soil samples at different depths.The vineyard soil in the studied area is an Anthrosol [66] with a sandy loam texture down to a depth of 1.90 m, most of the sand being fine.Collection of undisturbed soil samples for determination of volumetric water content at field capacity was not possible due to the unstable soil surface layer and significant structural discontinuities.In addition, some soil layers exhibited very low saturated hydraulic conductivity (Ks < 0.5 cm d −1 ), which also made it difficult to determine soil moisture at field capacity.Thus, the volumetric soil water content at field capacity and at permanent wilting point were obtained using the pedotransfer functions determined for the Portuguese conditions [67] using the particle size and the soil bulk density.
A neutron probe (Humiterra, Laboratório Nacional de Engenharia e Tecnologia Industrial, Portugal) was used to monitor soil water content (SWC) at each 0.10 m, up to 1.85 m, in two locations.Before use, the probe was calibrated following the procedures of [68,69].As suggested by [68], special calibration of the probe was performed for the surface layers up to 0.15 m.Several transparent access tubes were placed surrounding the plants as shown in Figure 4.The measurements were carried out on seven dates every 16 days in the early morning from 23 April to 8 September 1987.

Soil Characterization and Soil Water Content Monitoring
Soil properties were assessed by collecting disturbed soil samples at different depths.The vineyard soil in the studied area is an Anthrosol [66] with a sandy loam texture down to a depth of 1.90 m, most of the sand being fine.Collection of undisturbed soil samples for determination of volumetric water content at field capacity was not possible due to the unstable soil surface layer and significant structural discontinuities.In addition, some soil layers exhibited very low saturated hydraulic conductivity (K s < 0.5 cm d −1 ), which also made it difficult to determine soil moisture at field capacity.Thus, the volumetric soil water content at field capacity and at permanent wilting point were obtained using the pedotransfer functions determined for the Portuguese conditions [67] using the particle size and the soil bulk density.
A neutron probe (Humiterra, Laboratório Nacional de Engenharia e Tecnologia Industrial, Portugal) was used to monitor soil water content (SWC) at each 0.10 m, up to 1.85 m, in two locations.Before use, the probe was calibrated following the procedures of [68,69].As suggested by [68], special calibration of the probe was performed for the surface layers up to 0.15 m.Several transparent access tubes were placed surrounding the plants as shown in Figure 4.The measurements were carried out on seven dates every 16 days in the early morning from 23 April to 8 September 1987.

Modelling Approach
We assessed the accuracy of a SWB model fed with ground truth data after proper calibration and a simplified approach that combines ground truth data with remote sensing data.

Modelling Approach
We assessed the accuracy of a SWB model fed with ground truth data after proper calibration and a simplified approach that combines ground truth data with remote sensing data.

SIMDualKc Modelling Tool
The SIMDualKc modelling tool was developed with the aim of simplifying the implementation and computation of water use and irrigation requirements using the dual crop coefficient approach.The tool can be applied to a wide variety of situations, including crops that do not fully cover the soil (e.g., orchards), intercropping systems, mulching impacts (plastic and organic), active ground cover, and soil and water salinity.
In SIMDualKc, which is a one-dimension soil water balance modelling tool, the daily estimation of crop water requirements is made using the soil water depletion in the rootzone as follows [27,41]: where D r represents depletion in the root zone (mm), P represents the rainfall amount (mm), RO refers to the surface runoff (mm), I represents the net irrigation (mm), CR describes the capillary rise (mm) obtained of the groundwater table (mm), ET c act is the actual crop evapotranspiration (mm), and DP is the is the root zone deep percolation (mm), all referring to days i or i − 1.
The actual ET c is partitioned into actual crop transpiration (T c act ) and soil evaporation (E s ) as follows: The stress coefficient (K s ) is calculated daily as a linear function of the root zone depletion D r (mm): where TAW represents the total available soil water (mm) and RAW is the readily available soil water (mm), with RAW = p TAW, and p is the soil water depletion fraction for conditions of no-stress [27,48].When the root zone depletion is higher than RAW, i.e., in situations where the water depleted fraction is larger than p, the stress coefficient is lower than one (K s < 1.0).The evaporation coefficient (K e ) will be the maximum immediately after rainfall or irrigation events occur and the wetted soil surface is being partially covered by plants canopy.This higher K e value is dependent on the K c value being maximum (i.e., K c max ), which signifies the upper threshold of evaporation and transpiration from any cropped surface and reflects the natural restrictions imposed by the available energy on the transpiration coefficient K cb on the same day, and thus on K c max − K cb [48,70].Nevertheless, it changes day-to-day as a function of the total water available for evaporation in the soil surface layer; thus, the estimative of K e is made by a dimensionless reduction factor, K r , as follows: where f ew is the wetted soil fraction exposed to direct solar radiation, which is calculated as f ew = min (1 − f c , f w ) according to the fractions of ground covered by plants' canopy (f c ) and wetted by irrigation (f w ).
The value of K r depends on the cumulative depth of water depleted from the topsoil and is calculated daily through the soil water balance considering the soil evaporation layer's thickness (Z e , m).Calculations are based on the assumption that the drying cycle happens in two stages, with the water in the topsoil and the energy available at the soil's surface limiting the first stage [36,48] and thus with K r reducing once the evaporated depleted water exceeds the readily evaporable water (REW).Thus, K r is computed as follows: where D e,i−1 is the amount of water evaporated from the evaporable soil layer at the end of day i − 1.
The adjusted K cb calculation already includes a water stress coefficient (K s ), that represents situations where water is a limiting factor.The soil evaporation coefficient (K e ), in turn, is calculated by separating this coefficient into two parts: the K ei relative to the fraction of soil wetted by irrigation and precipitation (f ewi ), and the K ep , which is based on the fraction of soil wetted only by precipitation (f ewp ).
Mandatory SIMDualKc input data include the following: (i) weather data required for calculation of the PM-ET o or computed elsewhere, namely precipitation and, in case of adjustment of K c /K cb to weather conditions, u 2 and RH min ; (ii) crop characteristics data, which include the dates of the diverse crop growth stages, the crop height, rooting depth, the depletion fraction for no stress, the basal crop coefficients, and the fraction of ground cover or the LAI for each defined stage; (iii) soil characteristics, such as the soil water holding characteristics (soil water at field capacity and wilting point) or the TAW, or, as in the case of the current study, the use of pedotransfer functions (PTF) used to derive the TAW for diverse soil layers; (iv) the surface layer characteristics: depth (m), total evaporable water (TEW, mm), and readily evaporable water (REW, mm); (v) irrigation schedules that include different options, such as rainfed.
Other model functions were used to improve the SWB estimates.Therefore, other input data used with SIMDualKc in the current study included the following: (i) the deep percolation or drainage fluxes (mm d −1 ) is calculated with a decay function over time describing the soil water storage (W) close to saturation in the period following events of intense rainfall or irrigation.The SIMDualKc model uses a decay function [71] for the estimation of the deep percolation as follows: where parameter a D is the soil water storage value comprised between the field capacity and the saturation, and b D < −0.0173 for soils draining quickly and b > −0.0173 for soils with slow drainage.
(ii) Capillary rise computed using the parametric equations developed by [71], the parameters of which (a 1 , b 1 , a 2 , b 2 , a 3 , b 3 , a 4 , and b 4 ) depend on the soil's physical and hydraulic characteristics and are subjected to the model's calibration process [41,71] (Table 1); and (iii) surface runoff, which is estimated with the curve number (CN, dimensionless) method [72].CN ranges from 0 to 100, meaning there is no runoff, and all rainfall becomes runoff, respectively.RO was estimated using the CN approach [51,72], in which CN value changes depending on the soil and vegetation type and the antecedent moisture in soil.The SIMDualKc model adjusts CN daily to represent the influences of adding or subtracting soil water content on soil infiltration properties by linking the CN value to soil water depletion in the surface layer.[41,71]).

Conditions Parameters
Capillary rise W c = a 1 .D w b1 (mm) a 1 = W FC , soil water storage to maximum root depth (Z r ) at field capacity (mm); a 1 = θ FC Z r .1000 W s = a 2 .D w b2 (mm) D w ≤ 3 m b 1 = −0.17 1000, i.e., storage above the average between those at field capacity and the wilting point (mm) b 2 = −0.27 Note(s): W a represents the actual root zone soil water storage (mm); W c represents the critical soil water storage (mm); W s is the steady soil water storage (mm); θ FC is soil water content at field capacity (non-dimensional); θ WP is the soil water content at the wilting point (non-dimensional); D w is the depth of groundwater (m); D wc is the critical depth of groundwater (m); ET m is the potential crop evapotranspiration rate (mm d −1 ), usually ET m = ET c (mm d −1 ); CR max is the potential capillary flux (mm d −1 ); CR is the actual capillary flux (mm d −1 ); k is the factor associating the evapotranspiration with transpiration (non-dimensional); LAI is leaf area index (non-dimensional); and t is the time after occurrence of irrigation or rainfall events that produced water storage over field capacity (days).
The description of the calibration procedure and testing of the SIMDualKc model followed in the current study is provided in Sections 2.4.3 and 2.4.4.Further details are given by [41,42,73,74].

Estimating K cb Values Using the A&P Approach and Remote Sensing Data
In the A&P approach [48], K cb A&P is computed with the equation below [41,48] where impacts of plant density and/or leaf area are taken into consideration as a function of a density coefficient (K d ): where K c min is the minimum value of K c for bare soil (in the absence of vegetation).K cb full is the K cb at maximum plant growth near full ground cover, K d is the density co-efficient.K d describes the increase in K cb with increasing vegetation density.(Equation ( 9)) thus allows adjusting the K cb to the vegetation and ground cover conditions [48,51].K d is computed as follows: (10) where M L (dimensionless) is a multiplier for f c relative to canopy density and shading, f c eff (dimensionless) corresponds to the fraction of ground effectively covered or shaded by plants at midday, and h is the crop height (m).
The parameter M L reflects the density and thickness of the canopy and sets an upper limit on the relative magnitude of transpiration per unit of ground area as represented by f c .K d has also been used in other studies to adjust K cb to actual density conditions for full cover crops [35] and in partial cover crops using both ground [75] or remote sensing data [49, 50,76].
The K cb full represents a ceiling limit on K cb mid for vegetation under no-water stress and with a full ground cover and LAI value higher than 3. Following [27], the K cb full is estimated as a function of mean plant height (h) and corrected for climate conditions as follows: where F r is a downward adjustment coefficient for stomatal control of transpiration and k h is a multiplicative factor of crop height, u 2 is the daily mean wind speed (m s −1 ) considered at 2 m above ground level through the growth period, RH min (%) is the daily mean of minimum relative humidity over the growth cycle, and h is the average plant height (m) for the mid-season stage.Before the climatic correction, a value of 1.20 is considered as a superior threshold for K cb full .The crop height influence is considered in the sum 1 + k h h, with k h = 0.1 for trees and vine crops, as recommended by [28,35].Taller crops and situations where the local climate is windier or drier than typical (standard) climatic conditions (RH min = 45% and u 2 = 2 m s −1 ) are expected to have higher total K cb full values.When vegetation shows greater stomatal adjustment transpiration, as is common in most annual crops, the F r parameter applies an empirical correction (F r ≤ 1.0).When crops show strong vegetative vigour and decline consequently by training and pruning, as well as when water availability is restricted, F r is high for trees and vines.As proposed by [27], F r , can be estimated as follows: r l r typ (12) where r l and r typ are, respectively, the average of leaf resistance and the typical leaf resistance (s m −1 ) for the considered plant, ∆ is the slope of the saturation vapor pressure vs. air temperature curve, kPa, and γ is the psychrometric constant, kPa • C −1 , both for the same period when K cb full is calculated.The earliest established version of that equation considered a fixed r typ = 100 s m −1 , a normal value for yearly crops; however, default F r values for trees and vines and several annual crops were recently revised and updated by [28].
Pereira et al. [35] provided examples of the K cb A&P approach's application to a variety of annual and perennial crops, as well as active soil cover in the interrow for wine vineyards.The K cb A&P technique does not require any calibration/test process when using the tabulated parameters [28,31].
Alternatively, in the A&P approach, the K d can be estimated under actual conditions using remote sensing data of the fraction of soil covered by vegetation (f c VI ).In the present study, we have assumed that f c eff is approximately equal to the f c VI derived from spectral vegetation indices computed with RS data.These data were derived from spectral vegetation indices obtained through satellite data, namely Landsat 5 images for the period under analysis.Five cloud-free Landsat-5 images covering the study area, relative to the path/row 204-033, were available and downloaded from Earth Explorer portal (https://earthexplorer.usgs.gov/,accessed on 15 May 2023) for the study period (dates 26 April 1987, 28 May 1987, 29 June 1987, 31 July 1987, and 17 September 1987).From each of these images, 12 pixels covering the sample collection area (SCA) within the studied vineyard under study were selected.The SCA is considered as representative of the vineyard field and includes the SWC monitoring system.
The SAVI was considered to calculate the f c VI , as it is less sensitive to soil background reflectance variability than other VIs [49,50].
where ρ red and ρ NIR are the reflectance at red and NIR spectral domains, and L is the soil conditioning factor, varying between 0 and 1.A value of L equal to 0.5 is considered for the most common environmental conditions and was found to minimize the effects of soil brightness variation and eliminate the need for calibration under different soil conditions [49, 50,77].The f c VI was computed as follows: where f c is the fraction of ground cover by vegetation and SAVI, SAVI max , and SAVI min correspond to the vegetation index for a specific date and pixel, vegetation index at maximum vegetation cover, and vegetation index at minimum vegetation cover (bare soil), respectively.The SAVI max and SAVI min values were obtained from the literature considering woody crops [49, 50,78].In the present study, the SAVI max and SAVI min values considered were 0.75 and 0.09, respectively.When calculating K d , it was assumed that the fraction of soil effectively covered at solar noon (f c eff ) was equal to the fraction of soil covered by vegetation (f c ).The M L factor, used to calculate K d was not changed and remained equal to 1.5 [48].

Parameterization, Calibration and Testing Procedures of SIMDualKc Model
The first step in the calibration procedure was to define the upper and lower boundary conditions.A value of 1.20 is assumed as an upper limit for K cb full before climate adjustment.As mentioned above, for different conditions from those standard, i.e., considering taller crops and local climate windier/drier or windier than RH min = 45% and u 2 = 2 m s −1 , higher K cb full values can be obtained.The lower boundary conditions are K cb ini equal to 0.15, which corresponds to bare soil conditions.
The observed parameters of weather data, dates of the crop growth stage, crop height (h), root depth (Z r ), and soil characteristics were input into the modelling tool.The weather data used were the daily maximum and minimum temperatures ( • C), T max and T min , respectively, the daily average wind speed, measured by an anemometer at a height of 6 m (km h −1 ), the daily average relative humidity (%), RH med , the daily number of sunshine hours (h), and the daily precipitation (mm), corresponding to the year of 1987.
The initial values for the non-observed parameters (K cb , depletion factor p, a D , b D ) were set using diverse sources of information.Based on the vineyard density, the training system, and the f c , the K cb value was taken from [28]; for the depletion factor, the soil evaporative layer (TEW, REW, evaporable layer-Z e ), and a D , the values were calculated according to the soil textural characteristics (sandy loam soil); and for b D , values were retrieved from [71].The capillary rise parameters (a 1 , a 2 , b 1 , b 2 , a 3 , b 3 , a 4 , and b 4 ) were initiated using the values proposed by [71] as well as the water table depth (WTD, m) retrieved from the national database (https://snirh.apambiente.pt/,accessed 30 September 2023).
The model calibration procedure followed that described by [73], and it consisted of progressively adjusting the values of the non-measured parameters, i.e., K cb , p, TEW, REW, Z e , a D , b D , CR parameters, and CN values, seeking to reduce the differences between the model-predicted and neutron-probe-observed values of available soil water (with ASW = (SWC − θ WP ) 1000 Z r ), i.e., ASW SIMDualKc and ASW field data, measured in 1987.Thus, the initial K cb values used in the simulation were those tabulated by [28] for vineyards.The p factor was considered as a constant value throughout the cycle, considering that the study was performed in a 20-year rainfed vineyard and that, during these stages, the activation of deeper roots is to be expected, increasing the plant's ability to cope with water scarcity, as discussed by [79].
Regarding the evaporable soil layer (Z e ), the initial values for TEW and REW were derived from the characteristics of the soil, i.e., field capacity and the permanent wilting point values, and the textural characteristics, for the selected thickness of the evaporative layer.
In the following procedures, the DP, CN, and CR parameter values were adjusted.The initial values for the deep percolation parameters a D and b D were 275 and −0.0173, respectively.The CN value was assumed to be equal to 68 [72], according to soil characteristics.The WTD varied from 4. The model was run until no further improvements were achieved, and the best values of the parameters (hereinafter referred to as calibrated parameters) were retained.Once the model was calibrated, the test consisted of running the model considering the calibrated parameters with a different dataset than the data set used in the calibration step (ASW 1D), i.e., it used the calibrated Kcb, p, TEW, REW, Ze, a D , b D , and CR parameters and CN values.In the present study, due to ASW data set limitations for a different year, the model test was performed using a measured ASW data set for a different location (2A location).The two ASW datasets used for calibration and testing of the SIMDualKc model contain 10 and 7 observations, respectively, according to the available neutron probe measurements.
Since the weeds in the vineyard under study were controlled by tillage and herbicide in the inter-row and row, respectively, neither mulching nor active ground cover were considered in the simulations.

Modelling Tool Statistical Accuracy Assessment
The accuracy of the calibration and test was assessed using a set of goodness-offit indicators described below.These indicators have been used in other SIMDualKc modelling performance evaluations, e.g., in studies related with irrigated and rainfed vineyards [44,45,47], to assess the impacts of salinity in ET [30,80], or an application to olive groves [31].
The calibration/test procedure was considered acceptable once the test results indicators' accuracy was judged comparable to those obtained for the calibration dataset.The selected goodness-of-fit indicators were also used by [73,81].To calculate these indicators, pairs of observed available soil water (ASW) and predicted (simulated) ASW values, respectively, O i and P i (i = 1, 2, . .., n) and whose means are Ō and P, were used as follows: (i) The regression coefficient (b 0 , dimensionless) of the linear regression is pushed to the origin between the observed and predicted values; the goal value is b 0 = 1.0, which implies that the projected values are statistically equivalent to the observed ones; (ii) The coefficient of determination (R 2 , dimensionless) of the ordinary least-squares regression between the observed and predicted values should be close to 1.0, indicating that the model explains the majority of the variance in the observed values; Water 2024, 16, 2567 13 of 28 (iii) Root mean square error (RMSE, mm), the desired value of which is zero, demonstrating a perfect match between observed and predicted values, must be much smaller than the mean of the observed values; (iv) The normalized RMSE (NRMSE, %), whose target value is zero, signifying a perfect match between observed and predicted ASW values, must be much smaller than the mean of the observed values; (v) The average absolute error (AAE, mm day −1 ) represents the average error related to the predicted and ought to be significantly less than the average of the observed values; (vi) The Nash-Sutcliffe model efficiency (EF, dimensionless) [82] measures the relative magnitude of the mean square error (MSE = RMSE 2 ) relative to the observed/measured data variance [82,83]; its target value of 1.0 denotes that MSE is negligible for observed values.

Performance of the SIMDualKc Model in Calculating Soil Water Content
The crop characterization in the SIMDualKc model was carried out by entering the dates of the vegetative cycle with an indication of root depth, plant height (h), and soil water depletion fraction (p).The characterization of the crop relative to the K cb values for the different phases of the cycle (initial, intermediate, and final), and soil characteristics (soil evaporation layer, runoff and deep percolation, capillary rise) are shown on Table 2.These initial values of K cb , h and p were from [28].The initial p value, proposed by FAO [27], was adjusted during calibration since this is a rainfed vineyard adapted to water stress.
Results in Table 2 show that, for most cases, the values of the parameters used for initializing the model are relatively close to those obtained after proper model calibration (the variation was 12.2% on average, with K cb end and p factors responding for the higher variation increasing by 23% and 25%, respectively).The depletion fraction p's calibrated values (Table 2) are greater than those suggested by [27,28], which relates to the fact that the vineyard was rainfed and, therefore, well-adapted to low water availability conditions.The calibrated p value is in the range of those reported for rainfed vineyard [44,45].A slightly lower p value was reported by [84] for irrigated cv.Loureiro vineyards.Differently, Campos et al. [55] reported a p value of 0.65 for a drip-irrigated vineyard.
The textural characteristics of the soil and the water-retention capacity of the soil evaporation layer were used to estimate the initial values for Z e , REW, and TEW calculations, as proposed in [27].In this way, the values of these calibrated soil evaporation parameters are the same as those indicated by [27] for sandy loam-textured soils.Similarly, the calibrated runoff parameter CN was kept unchanged from the initial value proposed by [51,72], considering the soil texture.One of the parameters associated with deep percolation, a D , was estimated from the water available in the soil at saturation and field capacity, and it was slightly changed from the initial values, decreasing by 3.5%.The b D parameter, estimated from the drainage characteristics of the soil [71], was left unchanged.Figure 5 shows the simulated and observed available soil water (ASW) dynamics throughout the season.Results in Figure 5 show that the model is able to adequately simulate the dynamics of the ASW observations.The differences between observations and simulations in the calibration set (Figure 5a) were lower in the intermediate and higher in the final stage of the crop.In other words, the ASW dynamics simulated with SIMDualKc agree well with the ASW observations.In addition, the results agree with the predawn leaf water potential (ψ p ) observations.The ψ p varied from −0.08 to −0.95 (±0.32)MPa and from −0.09 to −0.53 (±0.16)MPa for calibration and testing, respectively.The SIMDualKc model simulates the onset of water stress conditions (ASW < RAW) from DOY 136 onwards, while the ψ p observations are between −0.2 and −0.4 MPa, thus representing a slight water stress (Figure 6).The decrease in the ψ p , increase in the plant water stress, agrees well with the simulations of the ASW from then on, with the ASW being much lower than the RAW limit.The ψ p reached values close to −1.0 MPa in the second week of September, and the daily minimum ψ p varied between −1.4 MPa and −1.6 MPa [19], which agrees well with the intense soil water stress simulated with SIMDualKc.
Water 2024, 16, x FOR PEER REVIEW 15 of 29 between −0.2 and −0.4 MPa, thus representing a slight water stress (Figure 6).The decrease in the ψp, increase in the plant water stress, agrees well with the simulations of the ASW from then on, with the ASW being much lower than the RAW limit.The ψp reached values close to −1.0 MPa in the second week of September, and the daily minimum ψp varied between −1.4 MPa and −1.6 MPa [19], which agrees well with the intense soil water stress simulated with SIMDualKc.Rainfed vineyards show similar ψp dynamics during the June-August period in South Portugal (typical Mediterranean climatic conditions), i.e., the occurrence of slight to moderate water stress, reaching severe water stress (−1.56 MPa and −1.96 MPa) by September, as reported by [85].Differently, in a rainfed vineyard in Douro Wine Region, located in the North of Portugal, where climatic demand is lower during July-September, Malheiro et al. [24] reported ψp ranging from −0.3 to −0.5 MPa, indicating slight to moderate water stress.
In a study developed in rainfed vineyards cv.Chardonnay in Catalonia, Spain [86,87], low ψp values up to −1.36 MPa were reported.Similar findings were reported for Mediterranean climate conditions by [88,89].
Figure 5 shows a slight mismatch for the extremes of the period considered, suggesting a more abrupt progression over time of the measured values.However, the statistical indica- Rainfed vineyards show similar ψ p dynamics during the June-August period in South Portugal (typical Mediterranean climatic conditions), i.e., the occurrence of slight to moderate water stress, reaching severe water stress (−1.56 MPa and −1.96 MPa) by September, as reported by [85].Differently, in a rainfed vineyard in Douro Wine Region, located in the North of Portugal, where climatic demand is lower during July-September, Malheiro et al. [24] reported ψ p ranging from −0.3 to −0.5 MPa, indicating slight to moderate water stress.
In a study developed in rainfed vineyards cv.Chardonnay in Catalonia, Spain [86,87], low ψ p values up to −1.36 MPa were reported.Similar findings were reported for Mediterranean climate conditions by [88,89].
Figure 5 shows a slight mismatch for the extremes of the period considered, suggesting a more abrupt progression over time of the measured values.However, the statistical indicators showed a good performance of the model (Table 3).Both the calibration and the test comparing available soil water simulated by the SIMDualKc model and available soil water measured using a neutron probe have a good correlation, with a regression coefficient (b 0 ) of 0.97 (Table 3).The coefficient of determination (R 2 ) is equal to 1 in both cases, which indicates that the model can explain the variance of the data.Regarding the modelling efficiency (EF), the values also show a good result, with values equal to or higher than 0.97, which indicates that the residual variance due to modelling is comparable to the variance of the measured data, as depicted in [83].The values of root mean square error were quite similar in both the calibration and test, with RMSEs of 11.1 and 11.9 mm, respectively, while the mean absolute error (AAE, mm) was 9.5 to 10.2, respectively.Additionally, the NRMSE presents a good result, with values below 13%.For vineyards, there are only a few results in the literature regarding the calibration of the SIMDualKc model using soil water content data.The RMSE and NRMSE (11.5 mm and 12%, respectively) obtained in the present study are higher than those verified by [84] for a rainfed vineyard cv.Loureiro in Ponte de Lima, Northwest Portugal, by [44] working in a vineyard cv.Godello and cv.Mencía in Galicia, Spain, and also higher than those estimated by [45] for a vineyard cv.Albariño in Pontevedra, Spain.Likewise, in the present study, a small error (RMSE) was reported when [90] simulating water flow within the HYDRUS (2D/3D) model towards a two-year set of soil water content measurements from a rainfed vineyard cv.Aglianico.Similarly, da Silva et al. [91] found small values of RMSE comparing soil water content measured with TDR probes and estimated using the SWAP model for irrigated crops (passion fruit and pastures).On the contrary, Galleguillos et al. [92] found RMSE values higher than those reported in the present study when assessing soil moisture profiles with HYDRUS-1D model for several Mediterranean rainfed vineyards.Although the values of RMSE and NRMSE reported in the present study indicate errors of estimation, they represent less than 4.17% and 4.35% of the TAW for RMSE and NRMSE, respectively.Darouich et al. [47] also obtained RMSE and NRMSE lower than the values verified in the present study for a rainfed vineyard in Monferrato, northern Italy.In the reported studies [44,45,47,84], the soil depth was 1.20 m, 1.0 m, 0.60 m, and 0.80 m, respectively, lower than that considered in the present study (1.85 m).Nonetheless, given the very different edaphoclimatic characteristics in places where annual rainfall is higher, the root system is expected to explore more superficial layers, and the lower limit of the control volume in the modelling process can be located at a depth closer to the surface than in the current situation, unlike in places with lower rainfall and deeper soils.Moreover, in situations where the plants are under greater water stress, either due to more demanding environmental conditions or to the absence of irrigation (as in the present study), there will be a tendency for the root system to grow deeper, easily surpassing the common threshold (approx.1.0 m) as depicted by several authors [4][5][6][7]23], sometimes deeper than 2 m (for an irrigated vineyard under extremely arid conditions) [93] or even higher than 6 m, as reported by [7].

Crop Coefficients Dynamics over the Season
The daily values of precipitation, the potential basal crop coefficient (K cb ), the actual basal crop coefficient (K cb act ), the soil evaporation coefficient (K e ), and the actual crop coefficient (K c act = K cb act + K e ) calculated by SIMDualKc model are shown in Figure 7.For both calibration and test, the K cb act and the K cb values are coincident during most of the crop cycle, except for part of the mid-season (DOY 196), till harvesting, when rainfall events are not sufficient to avoid water stress (as seen in Figure 6), i.e., few rainfall events occurred during spring, winter, and autumn.The calibrated value of K cb ini is equal to the standard value proposed in [28] for vineyards (0.15).However, during the mid-season and late season, the calibrated values of K cb are quite different from standard values (K cb mid = 0.65 and K cb end = 0.40), being K cb mid = 0.60 and K cb end = 0.52 (as shown in Table 2).These differences are related to the rainfed conditions of the studied vineyard, which reflect its tolerance to water stress.The calibrated K cb values (K cb ini , K cb mid , and K cb end , respectively) in the present study are lower than those reported by [44] for vineyards cv.Godello (0.30, 0.80, and 0.60) and cv.Mencía (0.20, 0.75, and 0.60) in Galicia, Spain, probably related to the higher annual rainfall amount in that location.In the same way, the K cb calibrated here are lower than those obtained by [45] for a vineyard cv.Albariño under irrigation conditions, which can explain the differences in comparison to the values verified in the present study.The results of K cb obtained in [45] for the K cb mid (mean 0.57) with moderate stress are quite similar to the K cb mid values calibrated in the present study.Silva et al. [84] also reported calibrated K cb values in ranges of 0.09-0.13,0.21-0.25,and 0.27-0.22(for development, mid-season and late season) for a vineyard cv.Loureiro under rainfed treatment, which are lower than those calibrated in the present study.The difference can be related to higher amounts of precipitation in the location reported in [84].
study.The results of Kcb obtained in [45] for the Kcb mid (mean 0.57) with moderate stress are quite similar to the Kcb mid values calibrated in the present study.Silva et al. [84] also reported calibrated Kcb values in ranges of 0.09-0.13,0.21-0.25,and 0.27-0.22(for development, mid-season and late season) for a vineyard cv.Loureiro under rainfed treatment, which are lower than those calibrated in the present study.The difference can be related to higher amounts of precipitation in the location reported in [84].As verified for Kcb and Kcb act, the Kc act and Ke have a similar pattern, especially in the initial and final stages.The Kc act peaks occur mainly when the soil is wetted, after rainfall events, and the evapotranspiration process is dominated by soil evaporation, i.e., the transpiration amount is small in this period.Furthermore, in Figure 7, it is possible to find times (especially in the early growth phases) when the Ke values are very similar to the Kc act values, close to 1.2, as well as in the end season, with Kc act close to 1.0, and close to harvest, when the Kc act values are close to and higher than 1.2.This pattern is mainly related to the rainfall during these periods (Figure 7) as well as the absence of ground cover vegetation.Similar trends in Ke and Kc act values were observed by [44] for the cultivars cv.As verified for K cb and K cb act , the K c act and K e have a similar pattern, especially in the initial and final stages.The K c act peaks occur mainly when the soil is wetted, after rainfall events, and the evapotranspiration process is dominated by soil evaporation, i.e., the transpiration amount is small in this period.Furthermore, in Figure 7, it is possible to find times (especially in the early growth phases) when the K e values are very similar to the K c act values, close to 1.2, as well as in the end season, with K c act close to 1.0, and close to harvest, when the K c act values are close to and higher than 1.2.This pattern is mainly related to the rainfall during these periods (Figure 7) as well as the absence of ground cover vegetation.Similar trends in K e and K c act values were observed by [44] for the cultivars cv.Godello and Mencía in Galicia, NW Spain, and [84] for cv.Loureiro in Ponte de Lima, Portugal.
Numerous K e peaks on the soil evaporation curves (Figure 7) show how the vineyard responded to rainfall events at its distinctive growth stages.These K e peaks occur mostly at the initial start of rapid growth and at the beginning of mid-season periods.K e peaks respond to the total soil wetting that occurs from rain events (f w = 1).During almost all mid-season, maturity, and harvesting stages, K e peaks are small and not very frequent due to the dry soil conditions with the absence of rain.This pattern of K e response to rainfall was also reported by [44,45,84] for vineyards cv.Godello and cv Mencía, cv.Albariño, and cv.Loureiro, respectively, under a rainfed treatment in Spain and Portugal.

Estimation of the Fraction of Ground Cover from Vegetation Indices
The f c retrieved from SAVI (f c VI ; Equation ( 14)) was estimated for five dates, namely those with cloud-free images for the period under study (Table 4).The lowest f c VI value was estimated for the beginning of the growing season (DOY 116, f c = 0.174) and the highest f c VI was verified for the mid-season (DOY 148, f c = 0.286).The temporal evolution of SAVI is similar to the f c VI , with the lowest SAVI value estimated for the beginning of the growing season (start rapid growth) and the highest value observed in the mid-season.This tendency was observed for table grapes using NDVI [94], as well as for other crops and VIs, like maize, barley, and olive, using SAVI and NDVI [50].The f c VI obtained in the present study (ranging from 0.17 to 0.28, Table 4) are lower than those reported by [94] for a f c VI relationship of table grape vineyards cv.Perlette and Superior in the semi-arid region of Northwest Mexico.However, Er-Raki et al. [94] used NDVI for the computation of f c VI instead of NDVI.Additionally, the f c values of the present study are closer to the limit values presented in [27] for vines and other perennial crops.The authors reported f c values ranging from 0.25 to 0.45, with K cb mid values between 0.46 and 0.80 and K cb end values varying from 0.20 to 0.60.On the other hand, Valentín et al. [10] reported f c values ranging from 0.04 to 0.28 and from 0.06 to 0.33 for the 2017 and 2018 seasons, respectively, in a rainfed vineyard cv.Monastrell, in Albacete, Spain, with maximum values similar to those observed in the present study.Darouich et al. [47] reported f c values ranging from 0.15 to 0.28 for an Italian rainfed vineyard, which is similar compared to the f c values verified in the present study.It is important to consider the spatial resolution of the Landsat-5 images available at the time of the study, 30 m × 30 m, which means that no more than 12 pixels per image from the SCA can be used to estimate the f c for the vineyard studied.

Comparison between K cb Obtained with SIMDualKc Model and Predicted with the A&P Approach
The K cb A&P values obtained through f c derived from remote sensing (f c VI ), applying Equation (9) [48], were compared with the K cb obtained through the SIMDualKc model to verify the accuracy of using the A&P approach combined with RS data.The five K cb values obtained by SIMDualKc for each day where K cb A&P was estimated using the f c VI were compared.
Table 5 shows that the K cb A&P values are close to the values obtained by the calibrated SIMDualKc (K cb SIMDualKc_1D ), especially for 26 May and 29 June 1987.For these dates, the plants were not under water stress (shown in Figure 6) and both the SIMDualKc model and A&P approach were able to precisely estimate the K cb values.On the contrary, the K cb A&P values for the final stages (after 31 July) are greater than those for K cb SIMDualKc .It is noteworthy that vegetation indices (VI) detect crop stress when a reduction in chlorophyll green cover or changes in canopy geometry occurs and thus do not immediately detect the slight water stress conditions in plants when the effect is only noticeable in the transpiration rates and predawn water potential (Figure 6).During the two first weeks of August, the water stress increase was moderate, and after the third week onwards, it was severe (Figure 6), which can explain the higher deviation between K cb SIMDualKc and K cb A&P values that occurred on September 17 (Table 5).For these stress conditions, it is necessary to add ancillary modelling approaches based on soil water balance, as also reported by [50,95], or based on a thermal signal, as demonstrated by [96], or even using a combined K cb-VI approach with soil water balance for assessing actual K c , as demonstrated in [49,50].
Regarding the test process, the K cb A&P and K cb SIMDualKc values are very similar and the deviation between them is low, except for the value corresponding to the late-season stage, following the same pattern observed in the calibration (Table 5).As shown in Table 5, the deviation between K cb A&P and K cb SIMDualKc values starts when plants suffer slight water stress (confirmed by Figure 6), and the highest difference between K cb A&P and Water 2024, 16, 2567 19 of 28 K cb SIMDualKc_2A occurs for the last crop stage, when the plant water stress is moderate, as also observed for calibration (K cb SIMDualKc_1D ).The modelling efficiency was low for the test (poor results with values between 0.03 and 0.38) and it presented a lower coefficient of determination (R 2 ) than model calibration.However, the low number of Landsat-5 images available for the study period somehow affects the results of the quality of fit indicators.Nevertheless, the difference between the K cb A&P and the K cb SIMDualKc is small for most of dates, mainly when the plants are not under water stress.Conversely, when moderate (or severe) water stress starts, (after 31 July 1987), the difference between the K cb A&P and the K cb SIMDualKc values is greater (especially for 31 July 1987 and17 September 1987).
It is also worth mentioning that while the results obtained with SIMDualKc refer to specific positions in the plot, namely the measurement position considered for the model calibration (1D) and the position considered for the test (2A), the results for the A&P approach use the f c VI values from SAVI derived from satellite images.The Landsat-5 satellite images available in the study period have a pixel size of 30 m × 30 m, thus representing an area on the ground where the variability of soil conditions is higher than the variability of the soil water content measurement positions.
The SIMDualKc model and the A&P approach were not able to explain the entire variance of the data due to the small number of observations of the f c VI data.This small number of available satellite images was highlighted as a limitation in a study by [55].Moreover, reduced efficacy in the A&P approach as a result of insufficient f c and h field observations was also reported by [31].The current availability of a large number of satellite missions with improved spatial and temporal resolutions (e.g., Landsat 8, Landsat 9, and Sentinel-2) can help overcome this data availability limitation.

Water Balance and Respective Components
Figure 8 summarizes the various soil water balance components for the studied year that were estimated using the SIMDualKc model.The ET c act values of the current study are comparable to those reported by [85] for a nearby vineyard.For calibration (1D), regarding the runoff process (RO), it occurred only for two periods: in the initial crop stage (3.6 mm), and at the late season (with 7.7 mm).The capillary rise (CR) contribution to soil water balance for the calibration process was estimated as a total of 25.2 mm from development till the late-season stage, with 52% of the total CR occurring in the mid-season.For test (2A), the CR contribution was 15.8 mm from the mid-season up to the late-season stage.The difference in CR between the two positions (1D and 2A) can be explained by the variability of the soil in the vineyard area, which is composed, as described by [19], of calcareous and non-calcareous materials in the form of complexes, such as fine sandstones, clays, and argillites with a texture variation from loamy to clayey.Besides that, in this area, there is a variation in the slope of the terrain (approximately 2.5%), and position 1D (used for to calibrate the model) is located in a higher landscape position than position 2A (used for testing the model).Naturally, it is expected that greater accumulation of water in the soil will occur in lower topographical positions, associated with the soil's water retention capacity, as demonstrated in Figure 5 (available soil water) and Figure 6 (predawn leaf water potential).Furthermore, Pacheco [19] mentioned that this is an area intensely marked by crops and with frequent annual ploughing up to 0.20-0.30m, sometimes reaching 0.65-0.80m.Thus, the natural soil horizons are mixed to a greater or lesser extent.Therefore, taking this into account and as the soil is an Anthrosol, it is understandable to have this variation in CR, as verified in the present study.Even so, it is worth mentioning that there was no significant difference in vine yield in the year under study between the two positions evaluated, with 5.22 kg plant −1 in 1D and 3.80 kg plant −1 in 2A, as described in [19].
stones, clays, and argillites with a texture variation from loamy to clayey.Besides that, in this area, there is a variation in the slope of the terrain (approximately 2.5%), and position 1D (used for to calibrate the model) is located in a higher landscape position than position 2A (used for testing the model).Naturally, it is expected that greater accumulation of water in the soil will occur in lower topographical positions, associated with the soil's water retention capacity, as demonstrated in Figure 5 (available soil water) and Figure 6 (predawn leaf water potential).Furthermore, Pacheco [19] mentioned that this is an area intensely marked by crops and with frequent annual ploughing up to 0.20-0.30m, sometimes reaching 0.65-0.80m.Thus, the natural soil horizons are mixed to a greater or lesser extent.Therefore, taking this into account and as the soil is an Anthrosol, it is understandable to have this variation in CR, as verified in the present study.Even so, it is worth mentioning that there was no significant difference in vine yield in the year under study between the two positions evaluated, with 5.22 kg plant −1 in 1D and 3.80 kg plant −1 in 2A, as described in [19].Variability in precipitation and its distribution across the different stages of crop growth were verified for the study year (1987), which had less precipitation and was drier than the previous five years' average (1982)(1983)(1984)(1985)(1986)(1987) (as depicted in Figure 3).The runoff (RO, mm) represents 5% of precipitation, and capillary rise (CR, mm) represents 7% (position 1D) and 11% (position 2A), respectively.These percentages show that rainfall was primarily utilized for crop evapotranspiration.The highest quantities of RO and CR were verified at the maturity and end-season crop phases, when crop evapotranspiration was lowest (Table 6).Table 6.Average values ± standard deviation of actual evapotranspiration (ET c act , mm) and its partition into soil evaporation (E s , mm) and actual transpiration (T c act , mm), soil evaporation to actual evapotranspiration ratio (E s /ET c act , %), crop transpiration to actual evapotranspiration ratio (T c act /ET c act , %), and actual evapotranspiration to maximum (potential) evapotranspiration ratio (ET c act /ET c , %) for the crop growing periods of the rainfed vineyard under study.The soil water balance values (average values for calibration and test) estimated with the SIMDualKc model are summarized in Table 6.The actual evapotranspiration (ET c act ) ranges from 68 mm to 55 mm from the initiation stage to late season, respectively.The higher value is observed in the mid-season (143 mm), which represents 40% of the total in the crop cycle.Most of the ET c act (85%) occurs between the beginning and mid-season stages, with higher precipitation in March and April having a significant effect on this.A similar pattern occurs for the actual transpiration (T c act ), with 82% occurring from initiation to mid-season stages.Since the vineyard was not irrigated, the contribution from precipitation and the capacity of the soil to store water (∆ ASW, Figure 8), and to contribute to ET c act (including capillary rise), are higher during mid-season, indicating that the water stored in the soil (especially in the deeper layers) played an important role in the actual crop evapotranspiration for the studied area.The daily actual transpiration (T c act ) and soil evaporation (E s ) for the year of study estimated with the SIMDualKc model are presented in Supplementary Figure S1 (Annex I).

Initial
By analysing the consumptive of water (Table 6), it can be observed that in the ET c act partitioning, the soil evaporation (E s ) was the main component of the evapotranspiration process, particularly during the initial and development crop phases.E s values were 84% and 52% of the total ET c act in the aforementioned stages.This variation is related to higher precipitation on these periods, which kept the soil wet.On the other hand, E s contribution to ET c act was smaller than T c act at the mid-season and late-season stages, with values ranging from about 4% to 24% of ET c act .During these stages, the transpiration becomes more important and is the main consumptive water use, representing 97% and 75% of ET c act .Once again, these values are explained by the influence of precipitation, soil water storage, and capillary rise, and therefore the rainfed condition of the vineyard.In general, it was found that E s and T c act values represents 36% and 64% of ET c act during the entire crop season.Similar results for evapotranspiration partition occurring during the mid-season, and, though less important, during the late season, were observed by [10] and by [47] for rainfed vineyards.Valentín et al. [10] studied vineyards under two watering regimes that are frequently applied in the Mediterranean region for this crop (rainfed and deficit irrigation) and [47] evaluated a rainfed Italian vineyard, also in a Mediterranean condition.The differences between these studies and the present study can be explained by different amounts of rain and soil water storage capacity of the respective locations.
Results regarding the ET c act /ET c ratio (Table 6) show that ET c act was smaller by 17% relative to the potential ET c in the studied year.During the mid-season, that ratio ET c act /ET c was small, and ET c act was smaller by 13% compared to the potential ET c .These reductions are probably low in non-irrigated scenarios with low rainfall, as analysed above, which did not affect yields (as reported by [19]) when comparing calibration and test positions.

Conclusions
In the present study, soil water balance modelling using SIMDualKc was evaluated in a rainfed vineyard in Santarém, Portugal, using soil water content field data as a reference.These data were collected at a depth (1.85 m) greater than that commonly used for modelling, therefore allowing us to better represent the soil volume explored by the roots.Additionally, the actual crop coefficient (K cb act ) obtained in SIMDualKc model (K cb SIMDualKc ) was compared with K cb estimated using the A&P approach [48] (K cb A&P ), where f c was estimated from spectral vegetation indices derived from Landsat 5 images to further estimate K d .
For the specific characteristics of this study area, namely the soil, the climate, and the studied vineyard cultural practices (spacing, crop height, inter-row management), the calibration and test of the SIMDualKc model were successfully performed, proving that it is possible to calibrate the model considering a soil profile depth greater than those that are normally used for vineyard ET modelling with soil water content.
Previous studies that adopted a similar calibration procedure of SIMDualKc with soil water content values were carried out in areas with higher annual rainfall and milder temperatures than those recorded in the region of Santarém.Although these studies provided good results for the application of SIMDualKc model, this was performed for less deep soil profiles (up to 1.0 m).
For the study year (1987), a good fit was achieved between the soil water content values measured in the field with the neutron probe and the values simulated with the SIMDualKc model, both for the calibration and the test performed.
Furthermore, the comparison between K cb SIMDualKc and the K cb A&P showed a small difference for most values throughout the different crop stages.However, the reduced number of satellite images with which to estimate f c VI and derive K d in the A&P approach was a limitation in obtaining a good fit between the K cb act simulated by the SIMDualKc model and the K cb act estimated by the A&P approach.Nevertheless, nowadays, increasingly available satellite missions can potentially contribute to better approximating the soil water balance modelling to the real conditions of vegetation development.
We can suggest that the present study allowed us to improve the knowledge about the application of the SIMDualKc model in vineyards, exploring the application of the model for conditions of increased root depth, as expected in rainfed conditions under Mediterranean influence, and thus potentially contributing to better water management.
The current study presented some challenges.It was conducted on a single season basis because soil water monitoring was discontinued, and the vineyard was replaced and converted to an irrigated vineyard a few years after.Further data collection could therefore not be carried out.This can be viewed as a limitation as validation of the model with an independent data set was not possible.The monitoring was carried out in 1987, which can be seen as a further constraint.However, this data set, which is not widely available, could be used with a modelling tool and a new approach that enabled robust results from the validation and testing of these tools, which could be considered a strength of the study.
Since the ET of rainfed vineyards depends on the climatic demand conditions (ET o ), as well as on the amount and distribution of precipitation, while considering the effects of increasing temperatures and decreasing precipitation, gaps exist for future research on modelling crop water requirements under climate variability and change scenarios, in particular in Mediterranean climate conditions, in order to use water more efficiently in agriculture.The modelling approaches used in the present study can form the basis for this type of study.
Moreover, model fitting results (namely modelling efficiency and variance explained by the model) were very good, indicating an enhanced accuracy of the model when using increased depth for calibration field data of vineyards.

Figure 1 .
Figure 1.Study area location in Santarém, Portugal.(Vineyard approximate boundaries in black and sample collection area (SCA) in red).1D (▲) and 2A (▄) are the locations of soil water content measurements used for calibrating and testing the SIMDualKc model, respectively.SAVI is the Soil Adjusted Vegetation Index.

Figure 1 .
Figure 1.Study area location in Santarém, Portugal.(Vineyard approximate boundaries in black and sample collection area (SCA) in red).1D (▲) and 2A ( ▄ ) are the locations of soil water content measurements used for calibrating and testing the SIMDualKc model, respectively.SAVI is the Soil Adjusted Vegetation Index.

Figure 2 .
Figure 2. The annual cycle of the vine and the crop growth stages.The crop growth stages are delimited according to the FAO segmented curve [27].

Figure 3 .
Figure 3. Average monthly reference evapotranspiration (ETo) and precipitation (P) for the period 1982-1987 and for the study year (1987) in Santarém, Portugal.

Figure 3 .
Figure 3. Average monthly reference evapotranspiration (ET o ) and precipitation (P) for the period 1982-1987 and for the study year (1987) in Santarém, Portugal.

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Figure 4 .
Figure 4. Schematic partial top view (a) of the experimental layout and the access tubes (AT, blue circles) (b) locations at the experimental field, Santarém, Portugal.

Figure 4 .
Figure 4. Schematic partial top view (a) of the experimental layout and the access tubes (AT, blue circles) (b) locations at the experimental field, Santarém, Portugal.
2 m to 4.61 m during the crop season.The measured values of WTD were taken from a piezometric station nearby the experimental plot which belongs to Portugal's National Water Resources Information System (https://snirh.apambiente.pt/,accessed 30 September 2023).The values of the parameters a 1 , a 2 , b 1 , b 2 , a 3 , b 3 , a 4 , and b 4 that vary according to soil texture were based on those proposed by [71] for loamy sandy soils.The maximum root depth was based upon measurements taken in open soil profiles in the studied vineyard; thus, Z r max = 1.85 m.

Figure 5 .Figure 5 .
Figure 5. Available soil water dynamics for the calibration (a) and test (b) of the SIMDualKc model.Dots represent observations while the curve represents simulations of the available soil water (ASW).TAW represents the total available water, and RAW denotes the rapidly available water.

Figure 5 .
Figure 5. Available soil water dynamics for the calibration (a) and test (b) of the SIMDualKc model.Dots represent observations while the curve represents simulations of the available soil water (ASW).TAW represents the total available water, and RAW denotes the rapidly available water.

Figure 6 .
Figure 6.Severity of water stress in a rainfed vineyard, according to the predawn leaf water potential (ψp) limits proposed by[26], grown in Santarém, Central Portugal.

Figure 6 .
Figure 6.Severity of water stress in a rainfed vineyard, according to the predawn leaf water potential (ψ p ) limits proposed by[26], grown in Santarém, Central Portugal.

Figure 7 .
Figure 7. Standard and actual basal crop coefficients (Kcb, Kcb act), soil evaporation coefficient (Ke), and actual crop coefficient (Kc act = Kcb act + Ke) and precipitation (P) computed by the SIMDualKc model in a rainfed vineyard in Santarém, Portugal.

Figure 7 .
Figure 7. Standard and actual basal crop coefficients (K cb , K cb act ), soil evaporation coefficient (K e ), and actual crop coefficient (K c act = K cb act + K e ) and precipitation (P) computed by the SIMDualKc model in a rainfed vineyard in Santarém, Portugal.

Table 1 .
Summary of the equations used by the SIMDualKc model to compute capillary rise (from

Table 2 .
Initial and calibrated parameter values of the SIMDualKc model.

Table 3 .
Statistical indicators obtained for the comparison between soil water content simulated by the SIMDualKc model and soil water content measured using a neutron probe for the calibration and the test positions.
Note(s): b 0 and R 2 are the coefficients regression and determination; RMSE is the root mean square error; NRMSE is the normalized RMSE; AAE is the average absolute error; and EF is the model efficiency.

Table 4 .
Soil Adjusted Vegetation Index (SAVI) and the fraction of ground cover derived from SAVI (f c VI ) for a rainfed vineyard in Santarém, Portugal.

Table 5 .
K cb estimated by the SIMDualKc model for calibration (K cb SIMDualKc_1D ) and for test (K cb SIMDualKc_2A ), K cb from A&P approach (K cb A&P ), and the deviation between K cb SIMDualKc and K cb A&P for a rainfed vineyard in Santarém, Portugal.
R s Solar or shortwave radiation [MJ m −2 day −1 ] TAW Total available soil water of the root zone [mm] TEW Total evaporable water from the soil surface layer [mm] T c Crop transpiration [mm d −1 ] T c act Actual crop transpiration [mm d −1 ] Depth of the surface soil layer from where soil evaporation occurs [m] Z r Rooting depth or root length [m] θ FC Soil water content at field capacity [m 3 m −3 ] θ WP Soil water content at the permanent wilting point [m 3 m −3 ] ψ p Predawn leaf water potential [MPa]