Introduction

In a world demanding immediate actions for solving the water crisis (Naddaf 2023), implementing irrigation scheduling (IS) technologies could significantly contribute to efficient water use in agriculture (Zinkernagel et al. 2020). When farmers schedule irrigation, they are unaware that the water volume used to produce a kilogram of food would meet household water consumption per capita for several months (Mekonnen and Hoekstra 2020; Bo et al. 2021). This situation indicates a clear disparity between the level of water used by agriculture and that used by others (Flörke et al. 2018; Wang et al. 2023). The core of the most commonly used IS methods has remained invariable over time; using these methods requires acquiring specialized equipment, handling large volumes of climate data, measuring soil properties, or managing software (Gu et al. 2020). Innumerable farmers worldwide lack technical knowledge, economic, or access-to-data capabilities to perform any of these IS methods for their crops (Yohannes et al. 2019; Berthold et al. 2021).

All these limitations are also evident for Hass avocado growers in Colombia. Beyond the economic benefits propelled by the rising global demand for Hass avocados, the volume of water required for their production in Colombia has grown exponentially. In 2018, Colombian Hass avocado production represented an estimated total water footprint of approximately 300 Mm3 (Sommaruga and Eldridge 2020); and in 2016, exported virtual water trade was 31 Mm3 (Caro et al. 2021). Although rainfall is the main source of water for the crop (Erazo-Mesa et al. 2021), supplementary water from irrigation is needed to reach optimal fruit development (Grajales 2017). Moreover, Diaz et al. (2021) identified a gap between incipient avocado growers' water management knowledge and the newest irrigation technologies. (Díaz et al. 2021), and regional environmental agencies have reported an increase in requests for crop irrigation water concessions (CVC 2021).

One way to track IS parameters, bypassing some limitations of traditional IS methods, is through remote-sensing (RS) technologies (Tolomio and Casa 2020). RS technologies, scaled down to easy-to-use, cheap or free-access, and wide-coverage tools, have been demonstrated to be powerful tools for irrigators (Erazo-Mesa et al. 2022a). Synthetic-aperture radar (SAR) images have shown promising results for estimating the surface soil water content (SSWC), the water content in the first 5–10 cm of the soil depth (Li et al. 2021), at local and regional scales (Peng et al. 2021). SAR images have been used to estimate the occurrence of irrigation events, detect and map irrigated areas, and quantify applied volumes of water at a regional scale by employing SAR satellite projects for soil moisture and ocean salinity (SMOS), soil moisture active passive (SMAP), and advanced microwave scanning radiometer 2 (AMSR2) (Jalilvand et al. 2019; Dari et al. 2021) and at a plot scale using the Sentinel-1 (S1) project (Bousbih et al. 2018; Le Page et al. 2020; Ouaadi et al. 2020). Bousbih et al. (2018) and Han et al. (2020) estimated the SSWC using the water cloud model (WCM) for nonorchard crops, obtaining root-mean-square error (RMSE) values lower than 6.4 and 3.16% (Vol), respectively.

Among the current challenges of using SAR images to schedule irrigation are the satellite revisit time, which is on average 4 days in countries at the equator, and the lack of correspondence between the effective root depth of some crops (for Hass avocados is 60 cm) and the superficial estimation of SSWC (Peng et al. 2021). To counterbalance the first limitation, some RS-based IS applications forecast irrigation parameters (Montgomery et al. 2015; Brinkhoff et al. 2019). Regarding the second limitation, some studies have modeled the soil water content at the root zone from SSWC for wheat (Babaeian et al. 2021) and Hass avocados (Erazo-Mesa et al. 2022b).

Hass avocado growers could take advantage of SAR images, because SSWC dynamics are directly related to the superficial distribution of tree roots (Lahav and Whiley 2002), a thin layer of litter on the soil surface near the trunk in some cultures which retains moisture (Bernal-Estrada et al. 2020), coarse soils and irrigation systems (Salgado and Cautín 2008), and dense canopy during the productivity period (Bernal and Díaz 2020). This research aims to develop an irrigation scheduling web application for Hass avocado orchards located in Valle del Cauca (Colombia) based on S1 images.

Theoretical background

The development and successful implementation of IS-SAR required a robust theoretical foundation associated with the SSWC, WCM, Artificial Neural Networks (ANNs), and irrigation scheduling concepts. A comprehensive theoretical background is essential for multiple reasons. First, it underpins our understanding of the underlying principles and mechanisms governing soil water dynamics, which is fundamental to precise irrigation management. Second, a solid theoretical foundation allows for the informed selection and integration of the Water Cloud and ANN models, ensuring the accuracy and reliability of our approach. Third, it enables the development of effective irrigation scheduling strategies that optimize water resource utilization while minimizing environmental impacts.

Soil surface water content (SSWC)

Precise measurements of available water in the root zone are required for irrigation scheduling of crops. However, accounting for accurate estimations of soil water content in space and time at plot, farm, and regional scales is challenging. Microwave measurements from SAR satellites have demonstrated being sensitive to backscattering properties of the soil surface by which these can detect soil water content changes from topsoil (Karthikeyan et al. 2017). The radar sensor's soil cover type and wavelength mainly determine the depth at which the soil water content can be estimated (Babaeian et al. 2019). According to Babaeian et al. (2019), the theoretical penetration of the C-band signal, used here through the Sentinel-1 project, reaches 1.5 cm for agricultural soils. However, some studies have compared soil water content measurements in a range of 0–12 cm of soil depth with a backscattering coefficient from Sentinel-1 obtaining reasonable correlations (Bousbih et al. 2018; Han et al. 2020; Ouaadi et al. 2020).

We define SSWC as the water content in the first 10 cm of the soil depth (Li et al. 2021). Erazo-Mesa et al. (2022b) studied the influence of soil water content (\(\theta\)) at several depth ranges on the soil water balance at depths of 0–60 cm (\({\theta }_{0-60f}\)) for three Hass avocado orchard plots in Valle del Cauca (Colombia) and determined that the 5–10 cm range depth correlated better with the soil water balance, which is named here as \({\theta }_{5-10f}\).

Water cloud model (WCM)

WCM describes how the microwave signal backscatters on vegetation–soil–water systems, representing the vegetation canopy as a cloud with identical droplets randomly distributed within the canopy. Initially introduced by Attema and Ulaby (1978) and with some variants from the original (Ouaadi et al. 2020), this semiempirical model splits the total backscattering coefficient \({\sigma }_{pp}^{o}\) from SAR images to a determined polarization (\(pp\)) (for this study VV and VH) and radar signal incidence angle \(\alpha\) into the microwave signal backscattered by vegetation \({\sigma }_{pp-veg}^{o}\), soil \({\sigma }_{pp-soil}^{o}\), and the soil-vegetation interphase \({\sigma }_{pp-soil/veg}^{o}\) (usually neglected) (Eq. 1)

$${\sigma }_{pp}^{o}={\sigma }_{pp-veg}^{o}+{\sigma }_{pp-soil/veg}^{o}+{{\tau }^{2}\sigma }_{pp-soil}^{o}.$$
(1)

Canopy structure, leaf size and distribution, and vegetation water content influence the \({\sigma }_{pp-veg}^{o}\) strength, and their effects are indiscriminately introduced in the WCM by parameters \(A\) and \(B\) (Eq. 2 and 4) (Prévot et al. 1993). Parameter \(V\) is usually computed from the leaf area index (LAI) using the function \(V={L}^{E}\), where \(E\) is a parameter to find in the model calibration, and \(L\) is LAI (Han et al. 2020). Due to the heterogeneity of vegetation–soil–water systems, the impact of the surface soil backscattered signal is adjusted by a two-way vegetation attenuation effect and added to the WCM through the \({\tau }^{2}\) value. \({\sigma }_{pp-soil}^{o}\) depends on surface roughness (inferred from parameters \(C\) and \(D\) in Eq. 3) and surface soil water content, called \(Mv\) originally in the WCM but customized for this study as \({\theta }_{5-10S}\) (Eq. 3). The contribution of \({\theta }_{5-10S}\) in the signal backscattered by soil can be linearly (Han et al. 2020) or exponentially (Bousbih et al. 2018) expressed (Eq. 3)

$${\sigma }_{pp-veg}^{o}=A V \mathrm{cos}(\alpha )(1-{\tau }^{2})$$
(2)

and,

$${\sigma }_{pp-soil}^{o}=C{10}^{D\cdot ({\theta }_{5-10s})}$$
(3)

and,

$${\tau }^{2}={e}^{-2BVsec(\alpha )}.$$
(4)

Artificial neural network (ANN)

An ANN is a bioinspired algorithm that operates by emulating how the neural system in the human brain builds reasoned decisions from previous knowledge and new information perceived by senses (Samek et al. 2019). From Widrow's Adaline to deep or convolutional neural networks, ANN fundamentals are nearly the same: a structured net of processing units (neurons) is sorted in layers, where connections among neurons are strengthened through training (Montesinos et al. 2022). ANNs have been used as an alternative to retrieve SSWC from SAR images with better agreement than semiempirical backscattering models (Bousbih et al. 2018; Mirsoleimani et al. 2019). A perceptron multilayer consists of a supervised ANN with m layers, n neurons by layer, and an algorithm that back-propagates the error.

Irrigation scheduling

Irrigation scheduling consists of apply the right amount of water in the proper moment to avoid that crop plants suffer water stress. Using the premise of maintaining the soil water in a crop within the desired limits (Eisenhauer et al. 2021), in this case the allowable depletion limit and field capacity, when the IS-SAR user computed the irrigation requirement can act in three ways (Fig. 1): (1) When \(\theta\) is between field capacity \({\theta }_{f}\) and the irrigation triggering limit (i.e., available water was not depleted), supplemental irrigation can be performed; (2) when \(\theta\) is situated left \({\theta }_{MB}\), exceeding the irrigation triggering limit, imminent irrigation must be applied; and 3) when \(\theta\) is right of \({\theta }_{f}\), soil accounts with excess water and irrigation are not needed (Fig. 1). The amount of water (water depth in millimeters) to be applied in actions 1 and 2 will be quantified by \(({\theta }_{f}-\theta )\bullet 600\), where \({\theta }_{f}\) and \(\theta\) are expressed in fractional units and 600 corresponds to the crop root effective maximum depth (in millimeters) (Fig. 1).

Fig. 1
figure 1

Irrigation actions according to the water content of a cultivated soil found by users in IS-SAR

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Materials and methods

Influence area of IS-SAR and plots’ characteristics

IS-SAR was implemented for Hass avocado growers located in the current and potential production area (PPA) in the department of Valle del Cauca (Colombia) (Fig. 2a). PPA has an extension in Valle del Cauca of 330,279 ha and is characterized by a mountain landscape in a range of altitudes from 1500 to 2500 m.a.s.l and slopes that exceed 25%. The mean temperature and annual rainfall range from 18 to 24 °C and 1000–2000 mm in PPA, respectively, and soils were formed from volcanic ashes of igneous and metamorphic rocks at altitudes above 1800 m.a.s.l. and sedimentary, igneous, and metamorphic rocks below 1800 m.a.s.l. (CVC and IGAC 2017). Approximately 400 growers distributed in 5216 ha in the north and center of Valle del Cauca manage Hass avocado orchards from 1 to 430 ha, predominating small farms (Díaz et al. 2021; MADR 2021).

Fig. 2
figure 2

Location of Colombia in South America (a), location of Valle del Cauca in Colombia (b), and location of the influence area of IS-SAR in Valle del Cauca (a)

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Our study is focused on a detailed pixel-level analysis of the S1 imagery (spatial resolution 100 m2). It is expected that the retrieved spectral response of S1 images results of a mixture of the avocado canopy, sparse pastures, and bare soil in 100 m2, in which are 2 to 4 avocado trees (49 m2 to 24.5 m2, respectively) given a tree density in the study plots. The low tree density is an advantage for modeling the surface soil water content for Hass avocado crops, compared with high-density crops where the contribution of soil to the backscattering coefficient close to harvest significantly decreases. Sentinel 2 imagery was also evaluated to calculate NDVI time-series data to be used as a proxy to derive LAI as input parameter for \(V\) (Eq. 2).

In the influence area of IS-SAR (Fig. 2a), the commercial 2-ha plots in Laurentina, Poncena, and Olival orchards were selected, which were cropped with Hass avocado at densities of 408, 238, and 204 trees ha−1, respectively (Fig. 2c, d, e). The canopy area and trunk diameter varied according to the age of trees. The average values measured for canopy area were 6.28 ± 3.30, 9.70 ± 3.35, and 1.43 ± 0.69 m2 for Laurentina (3.5 years), Poncena (5 years), and Olival plots (2.5 years), respectively, and average trunk diameters measured for Laurentina, Poncena, and Olival plots were 0.47 ± 0.08, 0.34 ± 0.11, and 0.52 ± 0.12 m, respectively.

The soil properties measured in the laboratory for the three plots determined that these mostly have a sandy loam texture, with a sand content higher than 57% and a content clay content varying from 9 to 23%, and an average total available water of 0.08 cm3 cm−3. Three monitoring trees were selected for each plot, where soil matric potential at 15, 45, and 75 cm of depth was measured from 15 August 2020 to 15 August 2021 (Fig. 2c, d, and e) using granular matrix sensors. Moreover, climate data were recorded in this period using portable weather stations installed in the center of each plot.

Regarding irrigation, a drip system was implemented for the Laurentina plot; Olival plot accounted for micro-sprinklers; and Poncena’s grower irrigated the trees one at a time with a hose. Approximately one fertigation events a week were implemented in Laurentina, totaling 44 in the study period (1245 mm). Conversely, irrigation was scheduled based on a visual manifestation of water deficit in trees in the Olival and Poncena plots. In Olival, no irrigation was needed during the study period, because rainfall met the water requirements of the crop, while in Poncena, the crops were irrigated five times (153 mm). The amount, date, and time of each irrigation event for Laurentina and Poncena were recorded. Annual precipitation of 1372, 1782, and 1275 mm for Laurentina, Olival, and Poncena plot were recorded, respectively.

Methodological framework

This study can be described in four major steps (Fig. 3). First, \({\theta }_{5-10f}\), \({\sigma }_{pp}^{o}\), and \(\alpha\) were merged by date to calibrate the WCM and ANN models. Second, the best model that retrieved \({\theta }_{5-10S}\) using S1 images was selected, and the best-adjusted linear regression parameters to predict soil water content \(\theta\) at 0–60 cm (\({\theta }_{0-60f}\)) from \({\theta }_{5-10S}\) were found. Third, \(\theta\) at field capacity (\({\theta }_{f}\)) and permanent wilting point (\({\theta }_{pwp}\)) were spatially modeled, and finally, IS-SAR was designed, evaluated, and uploaded online to Hass growers (Fig. 3). Each of these steps comprises other steps, which are shown in Fig. 3’s flowchart and described in detail later. All these procedures described in the following sections and the graphical outputs (package ggplot2) were coded in R scripts.

Fig. 3
figure 3

The four steps outlined in the methodological framework used in this study

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Step 1: Calibrating the WCM and ANN models

Soil volumetric water content time-series and irrigation practice description

\({\theta }_{5-10f}\) And \({\theta }_{0-60f}\) time-series were obtained from the Erazo-Mesa’s et al. (2022b) study who modeled the vertical water dynamics in the soil profile up to 90 cm at nine Hass avocado trees in the Laurentina, Olival, and Poncena plots (Fig. 2). Soil matric potential, climate, soil properties, and crop parameter data were monitored, the first two hourly, at the trees from 15 August 2020 to 15 August 2021 as inputs to calibrate the Richards equation, van Genuchten, and Mualem pore distribution models (Mualem 1976; van Genuchten 1980; Hillel 2014) through Hydrus-1D software (Simunek et al. 2012). Further details for the field equipment, Hydrus-1D modeling, and procedures to select the surface depth range for \(\theta\) can be found in Erazo-Mesa et al. (2022b).

Processing of Sentinel-1 images

A collection of 152 Sentinel-1 C-band images at the Level-1 GRD was processed on Google Earth Engine (GEE) using the framework routine developed by Mullissa et al. (2021). With a spatial resolution of 10 m, VV and VH polarizations, and ascending–descending orbits, this collection was delimited by the geographic quadrant 76.869–75.990 W and 3.295–4.478 N and filtered from 15 August 2020 to 15 August 2021. The 152 S1 images were composed of 48 Sentinel 1A (S1A) and 106 Sentinel 1B (S1B) images from orbits 142 and 48 and acquired at 15:51 UTC and 04:21 UTC, respectively. The revisiting time was 12 and 7 days between S1A and S1B images, respectively, and averaged 4 days among consecutive S1 images.

The procedures executed by Mullissa’s et al. (2021) framework routine included additional border noise correction, a multitemporal speckle filter, and radiometric terrain normalization using the NASA SRTM 30-m DEM, according to the incidence angle. Then, the \({\sigma }_{pp}^{o}\) in VV and VH polarizations (in dB units), \(\alpha\) (in degrees units), and acquisition date (in decimal format) were extracted from the images' pixels intersected with tree monitoring coordinates.

S1 images and \({\uptheta }_{5-10\mathrm{f}}\) integration

The time-series product of merging by date \({\theta }_{5-10f}\), \({\sigma }_{pp}^{o}\), and \(\alpha\) was split into calibration (15 August 2020–15 February 2021) and validation (16 February 2021–15 August 2021) datasets. The calibration dataset, with 384 records, was used to calibrate the WCM and train the ANN, and the validation dataset, with 306 records, was used to select the best model.

Inversion, NSGA-II implementation, and parameter optimization of WMC

WCM calibration consists of finding the values of parameters \(A\), \(B\), \(C\), \(D\), and \(V\) that minimize the difference between \({\theta }_{5-10S}\) and \({\theta }_{5-10f}\). Although the normalized vegetation index (NDVI) at the tree monitoring coordinates was computed from Sentinel-2 images to calculate the LAI, the scarce free-cloud images in the study area impeded consolidating an NDVI time-series similar to that obtained from S1 images. Thus, parameter \(V\) was optimized as the other WCM parameters.

In this study, the WCM was calibrated using the optimization genetic algorithm NSGA-II (Deb et al. 2002), according to Kumar et al.’s (2012) suggestions. First, \({\theta }_{5-10S}\) was computed using \({\sigma }_{pp}^{o}\) and \(\alpha\) from the calibration dataset and synthetic parameters \(A\), \(B\), \(C\), \(D\), and \(L\), provided by NSGA-II. The computed \({\theta }_{5-10S}\) was compared iteratively (100 generations and a population size of 500) with \({\theta }_{5-10f}\) through a three-objective optimization function (Eq. 5–7). In Eq. 5–7, \({f}_{1}\) is the RMSE function, \({f}_{2}\) is one minus the coefficient of determination \(r\) \((1-r\)), \({f}_{3}\) is a function that computes the number of undefined/infinite \({\theta }_{5-10S}\) outputted values \(m\) (ideally zero), \(({x}_{i},{y}_{i})\) represents the paired values (\({\theta }_{5-10S}, {\theta }_{5-10f})\) for a time \(i\), and \(n\) is the number of calibration dataset pairs

$${f}_{1}(x,y)=\sqrt{\frac{1}{n}{\sum }_{i=1}^{n}{({x}_{i}-{y}_{i})}^{2}}$$
(5)
$${f}_{2}\left(x,y\right)=1-\frac{{\sum }_{i=1}^{n}({x}_{i}-\overline{x })({y}_{i}-\overline{y })}{\sqrt{{\sum }_{i=1}^{n}{({x}_{i}-\overline{x })}^{2}{({y}_{i}-\overline{y })}^{2}}}$$
(6)
$${f}_{3}\left(x,y\right)=m.$$
(7)

Since no restriction in the sign and magnitude of \(A\), \(B\), \(C\), \(D\), and \(V\) were reported in the forecited studies, they were set to vary between − 100 and + 100 in NSGA-II. The best combination of \(A\), \(B\), \(C\), \(D\), and \(V\) was selected based on the crowding distance. NSGA-II implementation and validation were coded in an R script, wrapping the R function nsga2R (Tsou 2013) into a set of R functions to achieve the procedure previously described.

ANN architecture and training

To train the ANNs, 25 multilayer perceptron networks were configured, building two hidden layers and adding 1 to 5 neurons for each layer. These architectures were trained 200 times, for a total of 5000. The input variables for each architecture corresponded to \({\sigma }_{pp}^{o}\), \(\alpha\), and tree monitoring coordinates, and the output variable corresponded to \({\theta }_{5-10f}\). All these variables were scaled between 0 and 1. The calibration dataset was split into 60, 70, and 75% of the data for training and the remaining percentage was used to select the best architecture, which accounted for the lowest RMSE (Eq. 5) and the highest \(r\) (right side of Eq. 6). ANN implementation was conducted using the function neuralnet from the neuralnet R package (Fritsch et al. 2019).

Step 2: Selecting the best model

\({\theta }_{5-10S}\) Was computed using the validation dataset and the calibrated the WCM and trained ANN models and was added to the validation dataset. Then, RMSE (Eq. 5) and \(r\) (right side of Eq. 6) were computed. Two selection criteria were considered to select the best model: the lowest RMSE and highest \(r\) and the simplicity by either coding its mathematical formulation or importing its dependent libraries to the IS-SAR project.

Step 3: Interpolating soil water content at field capacity and permanent wilting point

\({\theta }_{f}\) And permanent wilting point \({\theta }_{pwp}\) at a depth of 30 cm, and geographic coordinates were extracted from a soil survey study that described 300 georeferenced soil profiles in the study area (Fig. 1) (CVC and IGAC 2017). A geostatistical analysis was implemented to obtain the \({\theta }_{f}\) and \({\theta }_{pwp}\) maps. This analysis consisted of exploring these data to identify outliers, selecting the theoretical semivariogram, interpolating using ordinary kriging, and validating the interpolation (Oliver and Webster 2015). In addition to RMSE and \(r\), mean error (ME), mean absolute error (MAE), and the comparison between the average of the observed (\({\overline{x} }_{obs}\)) and predicted-by-interpolation values (\({\overline{x} }_{pred}\)) were used to validate the \({\theta }_{f}\) and \({\theta }_{pwp}\) interpolations. The resulting maps were computed with a pixel size of 500 × 500 m.

Step 4: Implementing IS-SAR

Web application design

IS-SAR is an interactive web map application based on Sentinel-1 images that contains navigating, locating, zooming in–out, and plotting controls. This application has a module displaying one of the three irrigation actions described in the section "Irrigation scheduling", according to the current soil water content in the target plotted by the user. IS-SAR was designed using Django (Python) and JavaScript web frameworks and GEE API repositories (back-end). HTML, CSS, and JavaScript were used to design the front end. IS-SAR is hosted on the GitHub contribute project https://github.com/Viinky-Kevs/IS-SAR-APP.

Once users draw the target plot in IS-SAR, the application functions call the framework routine developed by Mullissa et al. (2021) to obtain \({\sigma }_{VH}^{o}\) and \(\alpha\) from the most recent S1 image and compute \({\theta }_{5-10s}\) for the target plot area using the best model selected. Then, \({\theta }_{0-60}\) is retrieved from \({\theta }_{5-10s}\) using the calibrated linear model. IS-SAR obtains the \({\theta }_{f}\) and \({\theta }_{pwp}\) values from the closest \({\theta }_{f}\) and \({\theta }_{pwp}\) map pixels to the user plot centroid and compares them with the \({\theta }_{0-60}\) average in the user-drawn plot to select the irrigation action and compute the amount of water required to apply the irrigation.

Based on the 27 available S1 images from 14 August to 9 December 2021, the consistency of IS-SAR for irrigation scheduling in the study area was evaluated simulating the IS-SAR user executions for Laurentina, Olival, and Poncena plots. For each plot, simulations consisted of creating an account, loading to IS-SAR its boundary in shapefile format (done once), calculating the irrigation actions and the irrigation water depth (to actions 1 and 2), and recording these data into a database.

Results

WCM and ANN calibration and the best model selection

The WCM and ANN were successfully calibrated using the entire monitoring tree dataset and split by tree to retrieve \({\theta }_{5-10s}\) from \({\sigma }_{pp}^{o}\), \(\alpha\), and the tree coordinates (for ANN). In WCM calibration, the best solutions accounted for an NSGA-II convergence, \(m=0\), and infinitive crowding distance. After calibrating the WCM using the backscattering coefficient at VV and VH polarizations, \({\sigma }_{VH}^{o}\) was selected to retrieve \({\theta }_{5-10s}\), because the RMSE was lowest and \(r\) was highest for the nine monitoring trees. The resulting values for the WCM parameters \(A\), \(B\), \(C\), \(D\), and \(V\) varied from − 99.99 to 98.90. When comparing these among trees and plots, no recognizable pattern in the magnitude and sign of these parameters was found. Regarding ANN training, the error threshold and the maximum number of cycles were set to 0.02 (in 0–1 scaled units) and 1000, respectively. Therefore, the ANN training finished in a reasonable time (1 h), with an acceptable prediction error, and converged a high percentage of the tested ANN. The ANN architecture with the lowest RMSE and highest \(r\) in the training stage for \({\sigma }_{VH}^{o}\) was 5:5 (5 neurons for the two hidden layers).

The evaluated Hass avocado plots' soil water content at depths of 5–10 cm changed considerably over time (Fig. 4). \({\theta }_{5-10f}\) varied from 0.11 m3 m−3, a value close to \({\theta }_{pwp}\) for monitoring tree O3 (Fig. 4f), to 0.49 m3 m−3, a value close to saturation for monitoring tree P2 (Fig. 4h). These changes were mainly produced by fallen rain and applied irrigation (Fig. 4c, f, and i), evapotranspiration, and sandy soils, which poorly retained moisture. \({\theta }_{5-10f}\) averaged 56%, 97%, and 73% of the time above \({\theta }_{f}\) for Laurentina, Olival, and Poncena trees, respectively. These percentages suggest that fallen rain was frequent and abundant for the Olival plot and that irrigation was not needed, while irrigation was needed for the Laurentina and Poncena plots.

Fig. 4
figure 4

Surface soil water content retrieved from the Water Cloud Model (WCM), Artificial Neural Networks (ANN), and their comparison with that simulated by Hydrus-1D for the calibration and validation periods at monitoring trees of Laurentina (a–c), Olival (d–f), and Poncena (g–i)

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\({\theta }_{5-10S}\) varied in the monitoring trees at a rate from 0.02 to 0.04 m3 m−3 between consecutive estimations (Fig. 4). Due to the low frequency of the data, the \({\theta }_{5-10s}\) time-series presented a nonnatural behavior in its changes, hindering the identification of sudden increases and later decreases in moisture after inputs of water, as observed in the \({\theta }_{5-10f}\) time-series (Fig. 4). The WCM and ANN models were consistent with the \({\theta }_{5-10s}\) estimation in the calibration and validation periods, with an average absolute difference between models of 0.02, 0.03, and 0.03 m3 m−3 for the Laurentina, Olival, and Poncena monitoring trees, respectively (Fig. 4), and a maximum difference of 0.05 m3 m−3 for the monitoring tree O3 (Fig. 4f). An increasing error in the \({\theta }_{5-10s}\) time-series was observed in the monitoring trees P2 and P3 for the validation period (Fig. 4h, i, respectively), coinciding with a high \({\theta }_{5-10f}\), a consequence of the frequent rainfalls in this period.

The error and agreement between \({\theta }_{5-10f}\) and \({\theta }_{5-10S}\), calculated for the WCM and ANN models in the calibration and validation periods, are shown in Table 1. The WCM estimated \({\theta }_{5-10S}\) with a maximum RMSE of 0.04 m3 m−3 and 0.05 m3 m−3 per-tree calibration and validation, respectively, representing 17% (tree O1) and 15% (tree P2) of the average \({\theta }_{5-10f}\). The \(r\) value broadly varied for the WCM among trees with a maximum of 0.33 for calibration and reported a value of 0.01 for five trees for validation. The ANN model slightly improved the WCM performance, obtaining maximum RMSEs of 0.03 m3 m−3 and 0.07 m3 m−3 for calibration and validation per tree, respectively, which represent 18% (tree O3) and 30% (tree O1) of the average \({\theta }_{5-10f}\). The \(r\) for ANN was consistently higher than that for WCM for per-tree calibration with a value higher than 0.40, but this decreased for validation, obtaining a maximum value of 0.44. Regarding the performance per plot, the RMSE average for the two models was lower in Laurentina for calibration and validation, compared with the RMSE average of the other plots (Table 1).

Table 1 Root-mean-square error (RMSE) and Pearson correlation coefficient (\(r\)) for the calibration and validation of the water cloud model (WCM) and artificial neural network (ANN) for the nine monitoring trees in the study area
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Differences of 0.02 and 0.01 were calculated by comparing the RMSE of ANN and the WCM for calibration and validation, respectively, suggesting a better performance of ANN when all-trees data were used. Moreover, the \(r\) value for the ANN exceeded 0.37 and 0.27, which were obtained by the WCM for validation and calibration, respectively. Although the trained ANN model performed consistently better than the WCM, the WCM was selected to retrieve \({\theta }_{5-10s}\) from S1 images due to its simplicity in tracking the surface soil water content for the IS-SAR web application. The calibration and validation of the WCM and ANN models for all trees resulted in a higher RMSE and higher \(r\) values than those obtained per tree. However, all-tree optimized WCM parameters integrally represent the \({\theta }_{5-10S}\) dynamics in the study area.

From surface soil water content to soil water content at depths of 0–60 cm

The linear regression model implemented to obtain \({\theta }_{0-60}\) from \({\theta }_{5-10S}\) resulted in Eq. 8, with an RMSE of 0.05 m3 m−3, \(r\) value of 0.51, and \(P<0.05\)

$${\theta }_{0-60}={0.637\theta }_{5-10S}+0.090.$$
(8)

Soil water content at field capacity and permanent wilting point maps

\({\theta }_{f}\) And \({\theta }_{pwp}\) maps were obtained with a spatial resolution of 500 × 500 m by applying the geostatistical steps described in Sect.  2.5 (Fig. 5). In the exploratory analysis, 45 outliers were removed for both variables, and after testing several transformation functions without improving the interpolation performance, \({\theta }_{f}\) and \({\theta }_{pwp}\) data were processed without transformation. The semivariogram analysis resulted in selecting the Spherical and Mattern models for \({\theta }_{f}\) and \({\theta }_{pwp}\), respectively, with the parameters shown in Table 2. The found nugget values indicate a high variability among samples separated at very short distances. The \({\theta }_{f}\) and \({\theta }_{pwp}\) semivariogram ranges of 22 and 6 km imply that spatially distributed points of \({\theta }_{f}\) are autocorrelated at a greater distance than \({\theta }_{pwp}\). The difference between the averaged observed (\({\overline{x} }_{obs}\)) and interpolated (\({\overline{x} }_{pred}\)) values for \({\theta }_{f}\) and \({\theta }_{pwp}\) was 0.01 and 0.01, respectively (Table 2).

Fig. 5
figure 5

Soil water content at the field capacity (a), permanent wilting point (b), and total available water (c) interpolated at the study area

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Table 2 Semivariogram model and cross-validation parameters in the geostatistical analysis for the field capacity and permanent wilting point in the study area
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In the resulting interpolated maps, \({\theta }_{f}\) varied from 0.17 to 0.37 m3 m−3 with an average value of 0.28 m3 m−3, \({\theta }_{pwp}\) varied from 0.10 to 0.29 m3 m−3 with an average value of 0.17 m3 m−3, and the total available water (i.e., \({\theta }_{f}-{\theta }_{pwp}\)) varied from 0.03 to 0.24 m3 m−3 (Fig. 5). The lowest \({\theta }_{f}\) values were in the northwest and southwest of the study area, where Laurentina and Olival's monitoring trees were located (Fig. 5a). The location of the highest and lowest \({\theta }_{pwp}\) values coincided with that of \({\theta }_{f}\). The zone with a low total available water is delimited by the range 0.030–0.094 and is distributed in 20.2% of the study area, where the monitoring trees are located (Fig. 5).

IS-SAR web application

IS-SAR is a web application for Hass avocado growers in the Valle del Cauca (Colombia) that need scheduled irrigation in their orchards. This application, accessible from http://www.is-sar.com, accounts for the calibrated WCM, two layers of \({\theta }_{f}\) and \({\theta }_{pwp}\) at a spatial resolution of 500 × 500 m, and a linear regression model to transform \({\theta }_{5-10S}\) into \(\theta\) to retrieve the soil water content in the target plot at the crop effective root depth of 0–60 cm using the most recent S1 image. To access the main IS-SAR page (Fig. 6b), users must create an account and log in (Fig. 6a). Then, users must locate their plot and draw it using the drawing polygon tool. IS-SAR computes \(\theta\), determine the irrigation action according to the \(\theta\) position in the total available water and recommend the user the action to take and the water depth to apply (Fig. 6c).

Fig. 6
figure 6

Login page (a) and main application page (b) of the IS-SAR web application and simulation of irrigation scheduling for plot "L2": soil water spatial variability (c) and the amount of water to be applied for the selected irrigation action (d)

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To evaluate IS-SAR, 27 simulations were conducted in the Laurentina, Olival, and Poncena plots on dates coinciding with the S1 revisit time (Fig. 7). In the simulation period, in the Laurentina plot, 397 mm of irrigation was applied, plus 553 mm of rainfall kept the soil water close to field capacity and below the irrigation triggering limit. IS-SAR recommended applying supplementary irrigation (action 1) of 12 mm on average for the Laurentina plot, which is equivalent to applying, on average, one drip irrigation of 39 L tree−1 for 1.2 h (dripper flow of 4 L h−1) (Fig. 7a).

Fig. 7
figure 7

Irrigation water depth to be applied in IS-SAR simulation actions on dates coinciding with the S1 revisiting time for the Laurentina (a), Olival (b), and Poncena (c) plots

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Although no irrigation was applied in the Olival plot and the rainfall of 464 mm was smaller than that in Laurentina, this plot did not reach the irrigation triggering limit (Fig. 7b). In the case of applying irrigation when IS-SAR indicated the need for it, each Olival plot's tree should have received 91 L for 2.8 h. A water shortage at the supply source meant that irrigation was not applied in the Poncena plot for the simulation period. Then, the rainfall of 504 mm was not enough to keep the soil water content at field capacity, increasing to 107 L tree−1 over 3.4 h for each simulated irrigation event (Fig. 7c).

Discussion

Sentinel-1 and its implications in irrigation scheduling

Considering the irrigation frequency in the Laurentina plot in the maximum crop water demand (approximately one fertigation event per week) and other Hass avocado orchards with similar irrigation system, climate and soil conditions (Grajales 2017), the S1 revisiting time of 7 days (Fig. 4) is suitable to track the soil water content and schedule and irrigate Hass avocado crops in Colombia, avoiding water stress. Similar IS-SAR satellite-based applications also account for week-based irrigation scheduling (Montgomery et al. 2015). Access to IS-SAR on the same days as the S1 revisit time, i.e., based on the S1 revisiting time calendar, could benefit avocado growers (Hill and Allen 1996; Fessehazion et al. 2014).

Water cloud model and artificial neural networks

LAI is an essential parameter for calibrating the WCM, because it relates to the backscattered signal from vegetation (Prévot et al. 1993). In the absence of LAI field data, the ten images resulting from filtering by cloudy percentage (< 60%) of the Sentinel 2 (S2) GEE collection for the study period were insufficient to build a robust NDVI time-series and compute the LAI of the monitoring trees. Therefore, our model is limited, because only S1 images were used to calibrate the water cloud and artificial neural network models. This variant for the WCM calibration differs from recent studies that used S1 and S2 images for calibrating the WCM (Bousbih et al. 2018; Ouaadi et al. 2020). In addition, the RMSE of 6% (vol) found for the WCM calibration and validation for sandy soils in this study, which have a reduced range of total available water, could increase the uncertainty of water depth computed in IS-SAR.

Despite not having LAI data in the WCM calibration, the RMSE and \(r\) values found after comparing the WCM and ANN model with the surface soil water content modeled by Hydrus-1D for sandy soils were similar to those reported by Bousbih et al. (2018) and Ouaadi et al. (2020). However, when a robust LAI model is integrated into the WCM, as Han et al. (2020) reported, the RMSE and \(r\) values decrease and increase, respectively. Thus, LAI field data are required to improve the WCM calibration, reduce the error, and increase the agreement with the field SSWC data. In the same line with that found here, similar studies in sparce density tree crops have shown how the vegetation influences the soil moisture retrieved by SAR images. Chiraz et al. (2022) and Courault et al. (2022) found that the correlation of soil moisture with S1 measures under the canopy are lower compared with this when is measured on the row space among trees and Shashikant et al. (2021) found a strong correlation of vegetation descriptors with the WCM.

In WCM calibration, the accuracy of SSWC retrieved from the backscattering coefficient with VH and VV polarizations depends on specific characteristics of the calibration sites, vegetation characteristics, and the inclusion of additional parameters such as soil texture and roughness. Although Bousbih et al. (2017) and Hajj et al. (2017) reported that \({\sigma }_{VV}^{o}\) was more sensitive to vegetation cover, Baghdadi et al. (2017), in the same line as that found here for sandy soils, found that \({\sigma }_{VH}^{o}\) was more precise than \({\sigma }_{VV}^{o}\). Compared with the WCM, the ANN model retrieved SSWC with a lower RMSE and a higher \(r\) value with the calibration and validation datasets. The addition of the monitoring tree coordinates (in decimal degree units) as input variables in the ANN training phase improved the performance of the model. Similar results were found by adding a priori rainfall and soil moisture condition information (El Hajj et al. 2017; Bousbih et al. 2018).

IS-SAR web application

IS-SAR is a novel web application to track the water content in soils cropped with Hass avocado and schedule irrigation at the plot level. No antecedents were found in irrigation scheduling web applications based on SAR images. Similar scheduling irrigation web applications use optical images (Montgomery et al. 2015; Calera et al. 2017) but cannot be used in Valle del Cauca due to its cloudy conditions throughout the year. IS-SAR, available for Hass avocado growers in the Valle del Cauca on http://www.is-sar.com, could be extended to be used in other Colombian regions using additional calibration points. Once implemented, the potential impacts of IS-SAR in Hass avocado orchards include improved irrigation scheduling, reduction in the applied irrigation water volumes, and a good match between water supply and crop water demand, all of which increase the use of digital agriculture practices (Erazo-Mesa et al. 2022a).

In 10 of the 12 months in which the WCM was calibrated and in the 5 months in which IS-SAR was evaluated, the ENSO climate phenomenon La Niña increased rainfalls and decreased the crop irrigation water demand in the study area. In the context of scarce rainfall and an increase in Hass avocado irrigation demand caused by El Niño, the S1 revisiting time of 7 days would result in a long irrigation schedule. Although the WCM was calibrated using field data from nine monitoring trees, which provided a proper generalization of the soil water content dynamics in the study area, it is recommended to check with a soil moisture probe or similar device the correspondence between the in-field soil water content and the outputted values by IS-SAR. Notably, the more precise the \({\theta }_{f}\) and \({\theta }_{pwp}\) maps are, the more accurate the IS-SAR irrigation estimation. Moreover, IS-SAR depends on the correct and continuous operation of S1 satellites.

The results of IS-SAR simulations shown in Fig. 7 coincided with the soil water dynamics, applied irrigation, and climate recorded and observed in the field from 15 August 2021 to 9 December 2021 for the Laurentina, Olival, and Poncena plots. Notably, the high amount of rainfall caused by La Niña and irrigation (for Laurentina) implied that the water irrigation depth did not accumulate, decreasing to critical soil water content values. Although the available water content at the three plots was similar, averaging 0.10 m3 m−3, the high field capacity and permanent wilting points in the Poncena plot soil retrieved from the corresponding maps caused this plot to exceed the irrigation triggering limit in all IS-SAR queries.

Conclusions

We developed a near-real-time irrigation information tool—IS-SAR—to assist Hass avocado growers in designing better irrigation tasks and understanding water crop consumption. The IS-SAR implementation allows us to conclude that the Sentinel-1 revisiting time of 7 days is appropriate to schedule Hass avocado irrigation in the current climate and soils of Valle del Cauca (Colombia). The ANN model performed better than the WCM in estimating SSWC due to its flexibility in adding a priori information. In permanently cloudy conditions, such as those presented in the Andean mountains of Valle del Cauca, LAI field data are required to improve the agreement with the field SSWC data. Under extreme wet conditions such as La Niña, further testing and evaluation of IS-SAR are needed. We are posing IS-SAR as a regional application to farmers who need to schedule irrigation for orchard and nonorchard crops.