Introduction

The soil ecosystem is one of the world’s most complex and diverse. Furthermore, they provide 98.8% of humanity’s food as well as carbon storage, climate regulation, and mitigation of climate change (Nguyen et al. 2021b). However, the intensification of agricultural production, various anthropogenic pressures, and climate change were contributing to soil degradation. The primary forms of this degradation are erosion, loss of organic carbon, pollution, sealing, compaction, salinization, waterlogging, acidification, nutrient imbalance, and loss of biodiversity (Khormali et al. 2009). Among these threats, soil salinity is a significant problem affecting agricultural development worldwide. Salinization is the accumulation of salts in the soil under the influence of salt water supply, the aridity of the climate, or particular hydrological conditions (Naimi et al. 2021; Wang et al. 2020a; Wu et al. 2018). It is estimated that 10 to 30% of the irrigated areas of the world are affected by salinity or alkalinity, i.e., approximately 76 million hectares of irrigated land, of which 69% of affected land is located in Asia, 19% in Africa, and 5% in Europe (Wicke et al. 2011). Salinization affects about 1.5 million hectares of cultivated land annually (Gorji et al. 2017), causing a decrease of about 10% in global food production (Wu et al. 2018). Therefore, assessing the distribution of soil salinity in space is necessary to support decision-makers in building appropriate agriculture development strategies to address food security issues in countries.

The increase in the level of salinity in recent years had negative impacts on the problem of food security in the world. Therefore, various studies have been conducted in the last decades to assess and quantify soil salinity. These methods have been divided into directive (the traditional) and indirect (Nguyen et al. 2021b; Wang et al. 2019a; Wu et al. 2018).

The traditional method is mainly based on measuring the laboratory’s electrical conductivity of soil samples (Gorji et al. 2015). Although these methods have been proven effective in assessing and quantifying soil salinity over the past decades, several studies have pointed out that this method needs to be revised and suitable for monitoring the evolution of these phenomena. In particular, this method is complicated to monitor regularly over a large area because it requires many samples to sufficiently evaluate soil salinity characteristics due to their fast spatial modification over short distances (Mulder et al. 2011). Although there has been an increase in the number of the type of proximal sensors including soil-visible and near-infrared (Vis-NIR) and electromagnetic induction (EMI) (Corwin 2021; Hu et al. 2019; Peng et al. 2022), however, these instruments monitor soil salinity in a small area (Vermeulen and Van Niekerk 2017). This requires several sensors to monitor large areas at the required spatial resolutions effectively.

To limit these gaps, in the last years, remote sensing has received attention from researchers as a promising method to monitor soil salinity in a wide area. At different scales and resolutions, remote sensing images are advantageous for earth observation. Currently, remote sensing data is crucial to evaluating and mapping soil salinity both globally and regionally (Taghizadeh-Mehrjardi et al. 2016). Currently, radar and optical data have recently become available. Nevertheless, visual remote sensing products depend on solar radiation and, therefore, are limited to monitoring soil salinity in the presence of cloud cover and rely on solar radiation. Radar sensors provide images with high spatial and temporal resolution. These images offer alternative perspectives to improve the ability to monitor soil salinity. In addition, radar sensors can obtain information regardless of weather conditions (clouds, rain, etc.) and time conditions (day-night). However, one of the significant challenges when using remote sensing imagery is its inability to effectively monitor subsurface processes that do not directly influence the spectral responses of topsoil. Additionally, this method uses radar backscatter coefficients to monitor soil salinity, so in many cases, it is mistaken for soil moisture.

Studies of soil salinity have used geostatistical techniques such as kinging, universal kriging, and regression kriging, especially in interpolating soil salinity from soil sample analysis (Hengl et al. 2007; Li et al. 2015; Shahabi et al. 2017; Tajgardan et al. 2010). Due to their unbiased estimates of the weights surrounding sampling points, these methods have proven to be effective. The potential relationship between remote sensing data and soil characteristics has been investigated using a variety of regression methods, such as multivariate linear regression (Lesch et al. 1995a, b; Vermeulen and Van Niekerk 2017). However, the successful use of this method must satisfy certain assumptions such as the standard normal distribution and the linear relationship. Therefore, this method can lead to significant errors. In the natural environment, soil characteristics are not normally distributed, limiting regression models’ quantification capacity. Moreover, the relationships between environmental factors and soil salinity are never linear. Therefore, these methods have been recommended to be replaced by more powerful methods to accurately interpolate soil salinity. Recent research has demonstrated that machine learning-based remote sensing is a useful technique for monitoring soil salinity, including random forest (Fathizad et al. 2020; Wang et al. 2021a), Xgboost (Nguyen et al. 2021b), support vector machine (Jiang et al. 2019), decision tree (Rao et al. 2006; Taghizadeh-Mehrjardi et al. 2014), and artificial neural network (Dai et al. 2011; Jiang et al. 2019). These methods find the linear and non-linear between independent and dependent variables based on the inherent relationships of the data. Therefore, machine learning can effectively solve complex linear patterns of soil salinity phenomena, even in data-limited regions. They also tend to have fewer user-defined parameters, allow estimates of independent variables’ importance and can deal with noisy data. However, the issues of overfitting and underfitting are still considered significant challenges when using machine learning. Also, the extrapolation problem, i.e., the model cannot predict the soil salinity if the data is out of range of the training data which needs to be solved to support the decision-makers. Several studies have pointed out that these problems can be solved when integrating appropriate optimization algorithms with individual models (Nguyen 2022a; Tran and Kim 2022). Optimization algorithms can be divided into three main groups: evolutionary based as genetic algorithm (Calixto et al. 2010), swarm based as particle swarm optimization (Jiang and Xue 2022), artificial bee colony (Li et al. 2019), gray wolf optimizer (Cui et al. 2022; Zhou et al. 2022), and physics based as Henry gas solubility optimization (Ding et al. 2021), atom search optimization (Hua et al. 2022). These algorithms were successful in improving the predictive ability of individual models. However, there is no universal conclusion for the best models for soil salinity monitoring. Moreover, according to the non-free-lunch, no general models can solve the problem of soil salinity in all regions (Nguyen 2022a). Therefore, developing new models is essential in practice and in science.

This study aims to develop novel models by integrating the Xgboost (XGB) with optimization algorithms, namely, sparrow search algorithm (SSA), bird swarm algorithm (BSA), moth search algorithm (MSA), Harris hawks optimization (HHO), gray wolf optimizer (GWO), and particle swarm optimization (PSO) in Ben Tre province where often affected by soil salinity problem. The performances of these models are compared with reference models like random forest and CatBoost. The novelty of this study is that the first time the XGB model is integrated with SSA, BSA, MSE, HHO, GWO, and PSO algorithms to estimate soil salinity in the Ben Tre province of Vietnam where the salinity problem is increasingly serious in the context of climate change and sea level rise. The initial hypothesis in this study is that the four optimization algorithms will successfully improve the performance of the XGB model and its accuracy of the hybris models (XGB-SSA, XGB-BSA, XGB-MSA, and XGB-HHO) will outperform the reference models, namely, XGB-GWO and XGB-PSO. This approach can also adapt to the different regions while improving the performance of the prediction models. The results of this study provide the first reference points for the discussion of the soil salinity monitoring method. The finding of this study can help decision-makers to build appropriate strategies to develop agriculture.

Material and methods

Study area

Ben Tre province is one of the 13 provinces of the Vietnamese Mekong Delta, covered by a natural surface of 2359.8 km2. As of 2021, the province’s population is estimated to be around 1.34 million people. The average altitude of the Ben Tre province varies from 1 to 3 m above sea level. The study area is positioned in the tropical monsoon climate, with two main seasons: the rainy season from May to November and the dry season from December to April of the following year. The annual, on average is about 1500 mm, with about 93% of the precipitation concentrated in the rainy season. The drainage network of Ben Tre province is very dense, with four major rivers: My Tho, Ba Lai, Ham Luong, and Co Chien rivers. These rivers are all part of the Mekong system. The tides in Ben Tre province are mixed diurnal and semi-diurnal tides, that is, there are two troughs and two peaks in 1 day.

Ben Tre province has rich soil resources, with many types of soils such as sandy soils, alluvial soils, and alkaline soils. This is considered one of the favorable conditions for the agricultural development of the province. The study area is regarded as the giant breadbasket in the Mekong Delta. However, in recent years, the study area has been severely affected by saline intrusion, affecting agricultural development and food security. According to Vietnam’s Ministry of Natural Resources and Environment, over the next 30 years, the average total rainfall in the Mekong Delta in general and Ben Tre province in particular will decrease by 10–20%. The sea level will rise about 33 cm in 2050 and 1 m in 2100. This has a severe effect on the salinity situation of the study area. Therefore, soil salinity assessment plays a vital role in supporting decision-makers to build appropriate strategies for the development of agriculture (Fig. 1).

Fig. 1
figure 1

Location of the Ben Tre province in Vietnam

Full size image

Data used

Soil sample collection and preparation

A field survey was established to gather soil samples over the Ben Tre province, in which 150 soil samples were collected from 0 to 30 cm depths under the land surface to identify the electric conductivity (EC) value. Various soil-sampling strategies were proposed to enhance the quality of measurement such as zigzag, grid, or transect (Nosrati and Collins 2019). However, these methods were often used in small areas, which were not required high cost (TILSE 2022). In this research, the position of soil samples was randomly selected over the entire study area in different soil types to reflect the adequacy of data. The samples were collected according to the Vietnamese Guidance on Sampling Techniques (TCVN 7538-2:2005, ISO 10381-2:2002) and analyzed in the laboratory environment. Besides, the four plus one method was applied for each soil sample to ensure data stability. It means that four subsamples were acquired around one main sample. After taking soil samples, a testing method was used to quantify the EC value by measuring the electrical resistance of one soil and five water (1:5) suspensions (Sándor et al. 2020). The final EC value will be averaged of measured results from the primary and subsamples. In this study, soil samples were accumulated from 2016 to 2021 periods. In addition, all soil samples were collected under dry weather condition without cloud cover at the location of soil samples to combine with satellite imagery data for estimating the process of models.

Soil salinity geodatabase

After collecting the soil sample data, the soil salinity geodatabase was established before training the model. We ordered the Sentinel 2A remote sensing data from January 2020 to June 2021 by using the Google Earth Engine platform (https://earthengine.google.com/). The data was pre-processed (noise removal, radiometric correction, geometric precision correction, cloud removal, and image stitching processes) before extracting 28 indices including BI, GDVI, Int1, Int2, MSI, NDDI, NDI, NDII, NDVI, NDWI, NMDI, RVI, S1, S2, S3, S5, S6, SI, SI1, SI2, SI3, SI4, VSDI, SMMI, CRSI1, EVI1, MSAVI, and SAVI1. These indices are very significant in monitoring the salinized soil by detecting the changes of minerals in the soil via spectral properties (Kılıc et al. 2022). BI (brightness index) works as a representation for observing the changes in soil organic matter, sands, and salinity areas over time (Yahiaoui et al. 2015). The vegetation indices including NDVI, GDVI, RVI, EVI1, SAVI1, and MSAVI allow to identifying of soil-induced influences on the land vegetation based on the moisture differences, roughness variations, shadows, or organic matter differences (Guo et al. 2019; Wei et al. 2021; Zhu et al. 2021). NDWI helps to discriminate waterlogged areas from soil and vegetation areas (Nguyen et al. 2021b). The group of salinity indices including CRSI1, NDSI, SI, SI1, SI2, SI3, and SI4 shows the correlation between soil reflectance at various spectral bands and the salinity parameters, which were used in a lot of previous salinity monitoring studies (Gorji et al. 2020; Halder et al. 2022). On the other hand, Int1, Int2, MSI, NDDI, NDI, NDII, VSDI, and SMMI also allow for the recognition of soil properties, which directly relate to the ability of soil to salinize. Besides, 3 indices including DEM, D2S (distance to sea), and D2R (distance to river) were also obtained and calculated to import into the soil geodatabase. It is related to the process of saltwater intrusion into the soil. The D2S and D2R indices used the Euclid distance algorithm. Every index in the soil geodatabase used the same projection system.

Machine learning approach

Prediction of soil salinity in Ben Tre province was divided into four main steps: (i) data collection and preparation, (ii) construction of soil salinity model; (iii) model validation; and (iv) analysis of the soil salinity map (Fig. 2).

Fig. 2
figure 2

The methodology used for the soil salinity prediction

Full size image

(i) Data collection and preparation: the data in this study were separated into two groups: 150 soil salinity samples collected from several field missions from 2016 to 2021 and 43 independent variables calculated from the Sentinel 2A image from 2021. To increase consistency and reduce data redundancy, 43 independent variables were normalized over the range from 0 to 1 by applying min-max normalization according to Eq. 1.

$${X}_{\textrm{Normalized}=\frac{\left({x}_i-\min \right)}{\left(\max -\min \right)}}$$
(1)

Normalization generates new values that maintain the same general distribution and ratios as the source data while applying the same scale to the values of the different numeric columns used in the model. Several normalization techniques, namely, min-max, Z-score, logistic, and logNormal, were used in this. However, the models were more accurate with the min-max normalization technique.

Finally, 70% of the total soil samples will be used as training samples, while 30% of the remaining will be used for testing and validating the models.

(ii) Model construction: the selection of appropriate independent variables plays an important role in deciding the accuracy of the models because data redundancy can increase model calculation times and reduce the accuracy of regression models. Initially, 43 independent variables were chosen from topography, salinity index, vegetation index, and spectral index. The random forest technique combined with the trial-and-error method was used to select the important variables. In the end, 28 selected independent variables combined with 150 soil salinity samples were used to build nine models (XGB, XGB-SSA, XGB-BSA, XGB-MSA, XGB-HHO, XGB-GOA, XGB-PSO, RF, and CatBoost). Among these data, 70% were used to train the proposed models, while 30% to evaluate the models.

In this study, XGB models were coded using the Python platform with the TensorFlow library. The default parameters of the XGB model were used, except for the parameters n_estimator = 500, learning_rate = 0.3, subsample = 1, and colsample_bytree = 1. The XGB models were integrated with six self-coded optimization algorithms. The parameters for these models are the same (problem_size = 3, batch_size = 25, epoch = 500, pop_size = 50, “fit_func”: fun_avr2), except for the following specific parameters:

For SSA : “lb”: [0] * problem_size, “ub”: [1] * problem_size, ST = 0.8, PD = 0.2, SD = 0.1.

For BSA : “lb”: [0] * problem_size, “ub”: [1] * problem_size, ff = 10, pff = 0.8, c_couples = (1.5, 1.5), a_couples = (1.0, 1.0), fl = 0.5.

For HHO : “lb”: [0] * problem_size, “ub”: [1] * problem_size, n_best = 5, partition = 0.5, max_step_size = 1.0.

For GOA : “lb”: [0] * problem_size, “ub”: [1] * problem_size, c_minmax = (0.00004, 1).

For PSO : “lb”: [0] * problem_size, “ub”: [1] * problem_size, c1 = 2.05, c2 = 2.05, w_min = 0.4, w_max = 0.9.

The values of “ub” and “ib” are the upper and lower bounds of the parameters, which affect the speed of convergence of the models. Usually, these values range from −2 to 2. In this study, trial and error was performed, and the results showed that the values “ib” = 0 and “ub” = 0 give the best results to the model. The “ST,” “PD,” and “SD” parameters correspond respectively to the safety threshold, the number of producers (in percentage), and the number of sparrows that perceive the danger. The parameters “ff,” “pff,” “c_couples,” “a_couples,” and “fl” correspond to the frequency of light, the probability of seeking food, the coefficient of cognitive acceleration, the coefficient of social acceleration, the indirect and direct effect on the alertness behaviors of birds, and the tracking coefficient. The parameters “n_best,” “partition,” and “max_step_size” correspond respectively to the number of best butterflies to keep from one generation to the next, to the proportion of the first partition, and to the maximum step size used in the Levy technique flight. The parameters “c1” and “c2” correspond respectively to the local coefficient and the global coefficient, while “w_min” and “w_max” correspond respectively to the minimum and maximum weight of the bird.

(iii) In this study, several statistical indices, namely, RMSE, MAE, and R2 were applied to assess the accuracy of soil salinity models.

(iv) After evaluating the proposed models, these models were utilized to generate the soil salinity map in Ben Tre province. This map was created by computing the EC value of each pixel.

Xgboost

Extreme gradient boosting regression (XGR) is a variant of the gradient boosting approach that is primarily used to solve complex regression and classification problems (Sahin 2020). This algorithm was developed based on the boosting framework proposed by Freund and Schapire (1996). XGR is open source and is supported by an end-to-end tree enhancement system that can be extended. XGR generates a new model that can predict the residuals of the previous model, and the results are generated by summing them. This algorithm uses gradient descent to reduce the loss when adding new models. XGR can work well with multi-dimensional data; it is considered one of the important advantages when solving big data problems. The XGR model was used in a variety of studies to estimate susceptibility to natural disasters (Pradhan and Kim 2020; Sahin 2020). The use of the XGBoost model in the previously mentioned research works results in very high accuracy of the final results. XGR strength is that it can reduce processing time by obtaining the optimal number of boosting iterations in a single run (Costache et al. 2022). Furthermore, it is well known that the XGR can improve modeling accuracy by reducing overfitting (Samat et al. 2020), another factor in the decision to use this model for this research.

Sparrow search algorithm (SSA)

SSA is one of the herd optimization algorithms, proposed by Xue and Shen (2020). The foraging and food-holding behaviors of sparrows inspire SSO. The SSA works in 3 main stages (Ouyang et al. 2021; Xue and Shen 2020): the discovery phase, the monitoring phase, and the investigation phase. During the discovery phase, the sparrows discover food and orient the other sparrows in the group. Therefore, about 20% of the sparrows in the flock perform this phase. Meanwhile, the tracking phase is where the sparrow searches for food around its location during the discovery mission. During the survey, sparrows were randomly selected from the flock. They are responsible for sending signals to the swarm to a safe place when predators enter. SSA has the ability for rapid convergence, and it has been successfully applied in several fields. Most details of SSA are present in the study by Xue and Shen (2020). This study used SSA to optimize XGR model parameters including problem size, batch_size, epoch, and pop_size.

Bird swarm algorithm (BSA)

Meng et al. first suggested the BSA (Meng et al. 2016), which was primarily motivated by two behaviors of birds: social behavior and social interaction. It is a new global optimization algorithm inspired by the simulation of birds’ foraging, vigilance, and flight behavior, with few adjustable parameters, high convergence accuracy, and strong robustness (Varol Altay and Alatas 2020). The BSA works based on five main principles (Meng et al. 2016):

Principle 1: simulates the alert and foraging behavior of birds. These are considered arbitrary decisions.

Principle 2: during foraging, birds interact with each other and update previous best practices for food and social information.

Principle 3: is the process of vigilance. Birds with high food intake move to the center of the flock. This process is influenced by competition within the flock because all birds want to move to the middle of the community.

Principle 4: Birds with the most significant food reserves become productive birds, while birds with low food reserves become birds of prey. Birds with intermediate food reserves will be selected as productive or abundant birds.

Principle 5: the productive birds are still actively foraging.

The parameters in this situation are the cognitive and social acceleration coefficients. The rules are then altered for three different fuzzy systems, employing them in ascending and descending order and in experiments with trapezoidal and Gaussian membership functions to determine which of these two types produces superior results.

This study used BSA to optimize XGR model parameters including problem_size, batch_size, epoch, and pop_size.

Moth search algorithm (MSA)

The MSA is a bio-inspired metaheuristic developed by Wang (2018). The algorithm simulates phototaxis and Levy butterfly flights (Abd Elaziz et al. 2019). MSA is based on two flight characteristics of moths: levy flight, which is considered an exploitative process, and vertical flight, which is considered exploratory. The entire moth population is separated into two parts: subpopulation 1 and subpopulation 2. This division is based on the physical condition of the moths; however, females are often in the population. Subpopulation 1 and subpopulation 2 will be used to update its position using the Levy and vertical flight transitions (Feng and Wang 2022).

(i) Levy flight: stage 1 individuals will fly around the best individual in the Levy flight, and the positions of the individuals are constantly updated.

(ii) The flight straightly: for each individual in subpopulation 2, they tend to fly towards the light source.

In this study, MSA was used to optimize XGR model parameters including problem_size, batch_size, epoch, and pop_size.

Harris hawks optimization (HHO)

HHO is a meta-heuristic optimization algorithm, proposed by Heidari et al. (2019). This algorithm simulates the hunting behavior of the Harris hawk. Harris hawks hunt by using surprise attacks, and they can execute various hunting strategies. The HHO algorithm works on two main processes: exploration and exploitation. During exploration, Harris’s hawk uses his polar eyes to track and detect prey. However, in many cases, hawks cannot catch prey easily. Thus, hawks can wait and observe their target for several hours. In HHO, the Harris hawk is considered the candidate solution and the best candidate solution in the loop is considered the intended prey.

The exploration process is transferred to the exploitation process based on the escape energy of the prey. The energy of the prey is reduced considerably when fleeing. In the exploitation process, a hawk with a surprise pounce attacked the prey identified during the exploration phase. In reality, however, prey tends to get out of dangerous situations. Therefore, different chasing strategies of Harris hawks are employed to encircle prey. Hawks often implement hard and soft siege strategies in practice. That is, Harris hawks will surround their prey gently from all directions or firmly, depending on the prey’s energy. More details about the HHO algorithm are described in (Heidari et al. 2019). HHO was successful in several different fields like energy (Houssein et al. 2020) and natural hazard prediction (Tikhamarine et al. 2020).

In this study, HHO was used to optimize XGR model parameters including problem_size, batch_size, epoch, and pop_size.

Grasshopper optimization algorithm (GOA)

GOA is a meta-heuristic, which was developed by Saremi et al. (2017). The foraging behavior of grasshoppers inspires the GOA (Meraihi et al. 2021). Grasshoppers often feed in swarms and are based on two main phases: the exploration phase and the exploitation phase. During the crawling process, they move over a wide range and move flick, while grasshoppers focus on the local searching during the crawling process. These steps aim to reduce operational weaknesses (local optimization) or increase convergence speed (Lv and Peng 2021; Nguyen et al. 2021a). For each move change, the grasshopper connects and interacts with other grasshoppers in the swarm to update the current position, best position, and factors affecting the next move (Moayedi et al. 2021).

In this study, GOA was used to optimize XGR model parameters including problem_size, batch_size, epoch, and pop_size.

Particle swarm optimization (PSO)

PSO is a metaheuristic, that was proposed by Kennedy and Eberhart (1995). PSO is inspired by the movement to optimize food pathways for flocks of birds and fish (Kennedy and Eberhart 1995). In the PSO algorithm, birds and fish are considered as the elements that always find the best solution to solve the problems (optimization of the foraging path) called particles. These problems are solved in an n-dimensional space, and n represents different algorithm parameters (Band et al. 2020). To optimize foraging pathways, PSO optimizes the position and velocity of each particle. The position and velocity of each particle change after each iteration; they are continuously updated and are represented by an objective function and a direction vector (Bui et al. 2020; Nguyen et al. 2021a). After each loop, the position and velocity of each particle are plotted and calculated according to the following formula:

\({x}_i^t=\left({x}_{i1}^t,{x}_{i2}^t\dots {x}_{in}^t\right)\) and \({v}_i^t=\left({v}_{i1}^t,{v}_{i2}^t\dots {v}_{in}^t\right)\) is the position and velocity of particle i at time t. Therefore, the position and velocity of particle i at t + 1 are

$${v}_i^{t+1}=w\times {v}_i^t+{c}_1\times {r}_1\times \left({p}_i^t-{x}_i^t\right)+{c}_2\times {r}_2\times \left({g}_i^t-{x}_i^t\right)\textrm{with}-{v}_{\textrm{max}}\le {v}_i^{t+1}\le {v}_{\textrm{max}}{x}_i^{t+1}=\left({x}_i^t+{v}_i^{t+1}\right)$$

where xti is the i-th position of the particle, pti is the optimal position found, gti is the best position of the particle, r1 and r2 are the random constants, with values ranging from 0 to 1, w is the weight d inertia, and c1 and c2 are the social coefficients.

In this study, PSO was used to optimize XGR model parameters including problem_size, batch_size, epoch, and pop_size.

Random forest

RF is considered one of the popular algorithms and is first proposed by Breiman (2001). This algorithm combines between bagging ensemble and random subspace, which bases decision tree prediction to solve classification and regression problems (Quiroz et al. 2018). RF combines all the submodels to obtain results with higher prediction than the individual models. Each submodel was evaluated using majority voting to determine the best model (Nguyen 2022a; Tajik et al. 2020; Zeraatpisheh et al. 2019). RF function to be based on four main steps: (i) resamples from the original dataset using Bootstrap; (ii) the use of subsets to construct the decision tree in the forest; (iii) obtaining the final results by combining the prediction results of all the decision trees; and (iv) select the best result using the majority vote (Chen et al. 2020a). One of the important advantages of RF is that it can solve missing data problems by using the average value of neighboring samples. RF model accuracy can be influenced by the number of decision trees (Ntree) and candidate characteristics in subsets (mtry) (Horning 2010). In this study, several values of Ntree were tried like 100, 200, and 500. The accuracy of RF is higher with Ntree = 500.

CatBoost

CatBoost is considered one of the power machine learning algorithms, first proposed by Dorogush et al. (2018). This algorithm uses the permutation technique to predict classification and regression problems. In the training process, the dataset was randomly permuted and labeled to avoid overfitting and underfitting issues. CatBoost works based on three main steps: (i) dividing the dataset into subsets randomly; (ii) labeling for subsets and converting them to integers; and (iii) encoding the features (Hai Ly et al. 2022). CatBoost implements symmetric trees, which reduce prediction time. It takes advantage of random permutations to have a random parameter. CatBoost handles classification features using concepts such as ordered boosting and response coding (Saber et al. 2021).

Performance assessment

Assessing the model’s accuracy is critical for establishing the soil salinity model. Several statistical indices were applied to assess the precision of the proposed models, RMSE, MAE, and R2.

RMSE is considered a popular index to compute the standard deviation between observation values and prediction values. While MAE calculates the average error between the prediction and observation value. The value of RMSE and MAE varies from 0 to 1. The closer the RMSE and MAE value is to 1, the more accurate the model (Eldeiry and Garcia 2008; Hu et al. 2019; Yan et al. 2007). They are calculated by the following equation:

$$\textrm{RMSE}=\sqrt{\frac{1}{n}}\sum_{i=1}^n{\left({Y}_i-{Y}_j\right)}^2$$
$$\textrm{MAE}=\frac{1}{n}\sum_{i=1}^n\mid {Y}_i-{Y}_j\mid$$

Yi is the prediction value at sample i and Yj is the observation value at sample j. N is the number of samples.

R 2 is an index to quantify the relationships between independent and dependent variables in the regression model. It presents the fitness of the data and identifies the percentages of the fit results in the regression model. For example, the R2 value of 50% shows that 50% of the data is fit in the model. The higher the R2 value, the better the fit of the data in the model (Scudiero et al. 2014).

Results

Data pre-processing and exploitation

The selection of factors plays an indispensable role in the process of building a soil salinity model. Because data redundancy confuses the predictive model, which reduces model performance, the importance of 43 independent variables was assessed using the random forest (RF) technique. The results show that Int2 (0.34), BI (0.33), SAVI (0.32), NDVI (0.31), and Band 8 (0.3) are the most important variables on soil salinity in Ben Tre province, followed by MSAVI ( 0.29), RVI (0.27), NDI (0.26), distance to sea (0.25), GDVI (0.25), SI2 (0.25), SRSI (0.244), NMDI (0.24), NDII (0.23), Band 9 (0.23), SMMI (0.22), Band 1 (0.21), Band 7 (0.21), NDWI (0.21), S6 (0.2), Band 6 (0.2), Band 4 (0.19), S3 (0.19), Band 5 (0.18), SI3 (0.16), and Int1 (0.16). Two factors SI4 (0) and SI1 (0.05) are a minor influence on soil salinity. Moreover, in this study, the trial-and-error method was used to select the independent variables. Based on Figure 3, 20, 21, 22…40 independent variables were tried to use as model input data, and the models are more precise with 28 first independent variables. The 15 variable remainders were eliminated for the soil salinity models.

Fig. 3
figure 3

The importance of the variable conditioning

Full size image

In general, indices related to soil, vegetation, and brightness rates extracted from remote sensing data significantly affect the proposed models. The reasons associated with the nature of the study area, vegetation, and soil characteristics are the essential environmental variables for the rate of soil salinity. At the same time, the indices related to drought and the distance to the river had a minor influence on soil salinity in the Ben Tre province of Vietnam because the salinity characteristics of the soil are different from the drought characteristics in the study area. In addition, during the dry season, the canal/rift system in the study area does not have enough fresh water upstream, combined with solid tidal propagation leading to increased saline intrusion on the land. This is why the distance to the river is less important than the distance to the variable in the salt intrusion problem in Ben Tre province.

Model performance comparison

Figure 4 shows the R2 value for validation data for nine proposed models (XGR, XGR-SSA, XGR-MSA, XGR-BSA, XGR-HHO, XGR-GOA, XGR-PSO, RF, and CatBoost). It was found that all of the proposed models fit well to predict soil salinity. The proposed algorithms improve the precision of the XGR model and surpass the performance of the reference models, namely, RF and CatBoost. Among the proposed models, the XGR-HHO model is better than the other models with an R2 value of 0.932, followed by XGR-GOA (R2 = 0.931), XGR-MSA (R2 = 0.928), XGR-BSA (R2 = 0.926), XGR-SSA (R2 = 0.917), XGR-PSO (R2 = 0.916), XGR (R2 = 0.867), CatBoost (R2 = 078), and RF (R2 = 0.75), respectively.

Fig. 4
figure 4

R2 value for the validation dataset

Full size image

Besides the R2 index, several indices like RMSE and MAE were utilized to assess the precision of the proposed models. Table 1 shows the value of RMSE and MAE for the proposed studies. The results show that the XGR-HHO model outperformed the other models with the value of RMSE and MAE of 0.051 and 0.042, followed by XGR-GOA (RMSE = 0.055, MAE = 0.049), XGR-MSA (RMSE = 0.06, MAE = 0.047), XGR-BSA (RMSE = 0.062, MAE = 0.05), XGR-SSA (RMSE = 0.07, MAE = 0.06), XGR-PSO (RMSE = 0.08, MAE = 0.08), XGR (RMSE = 0.1, MAE = 0.09), CatBoost (RMSE = 0.12, MAE = 0.1), and RF (RMSE = 0.19, MAE = 0.19), respectively.

Table 1 Model performance and comparison
Full size table

In general, six optimization algorithms (SSA, MSA, BSA, HHO, PSO, and GOA) in this study improved the performance of individual XGR models, and the performance of hybrid models outperformed individual models (RF and CatBoost). Because hybrid models can eliminate the weak points of individual models and from that can improve the performance of individual models.

Soil salinity mapping

After validating the proposed models, these models were used to build the soil salinity map in the Ben Tre province. These maps were generated by feeding the models of all the study areas with conditioning factor values. Figure 5 shows the soil salinity maps produced by XGR, XGR-SSA, XGR-MSA, XGR-HHO, XGR-BSA, XGR-GOA, and XGR-PSO. In the field mission in 2021, it can be seen that the western part of the study area is mainly agricultural land and low salinity. However, the closer you get to the sea, the more the salinity phenomenon increases. This zone is primarily aquaculture and partly rice growing. By comparing the results mentioned above with the results of the forecasting models, although there are slight differences between the models, all the models follow a trend that the western regions have a low degree of severity, while the eastern regions are more saline. Among the proposed models, three models XGB-HHO, BSA, and RF have lower salinity values in the east than the remaining models.

Fig. 5
figure 5figure 5

Soil salinity in Ben Tre province of Vietnam produced by XGR-SSA, XGR-MSA, XGR-BSA, XGR-HHO, XGR-GOA, XGR-PSO, RF, and CatBoost

Full size image

Soil salinity in the study area varies over time and space and can be affected by factors such as drought, sea level rise, and endogenous salinization. During the dry season, especially in March and April, when rainfall in the research area decreases, the amount of fresh water from rivers flowing into the soil decreases. This phenomenon causes an increase in seawater intrusion and salinity levels in coastal areas, making them generally more saline than other areas in Ben Tre province. Additionally, in the context of climate change and sea level rise, the canal/ditch system does not receive enough fresh water from upstream, causing strong tidal surges that lead to saltwater intrusion and accumulation. Ben Tre province is considered one of the few provinces in the Mekong Delta region that is less affected by soil salinity, except for areas where aquaculture is practiced (i.e., coastal areas).

Discussion

The region most affected by soil salinity is the Mekong Delta in general and Ben Tre in particular. This natural disaster causes significant damage to the country’s economy. For example, in 2020, the Mekong Delta in Vietnam was affected by a major drought which caused soil salinization. During this natural event, salt water penetrated about 110 km inland, surpassing the 2015–2016 record by about 10 km. It was also discovered that seawater was infiltrating the Mekong River Delta from November 2019, which is 2–4 months earlier than in previous years. In February 2020, around 40,000 coastal households lacked fresh water and 20,000 ha of fruit trees as well as 6500 ha of vegetables in Ben Tre were damaged.

The construction of a dam upstream of the Mekong River in recent decades has led to water scarcity downstream, resulting in relative lowering of the riverbed downstream as a result of mining of the riverbed and a rise in sea level. Consequently, the sea level penetrated more and more rapidly into the ground as a result. All this has led to soil salinization in the Mekong Delta. This has been substantiated by previous studies. Hui et al. (2022) pointed out that the change in the hydrological regime is an important factor influencing soil quality and farmers’ decision-making. Therefore, developing a state-of-the-art method based on machine learning and remote sensing to monitor soil salinity is very important to help decision-makers plan agricultural development. Remote sensing uses spectral information reflected from objects on the earth to detect helpful information related to soil salinity. Soils with different salinity levels have different spectral characteristics, which are important bases for the surveillance of soil salinity utilizing remote sensing (Aldabaa et al. 2015; Allbed and Kumar 2013). Generally, the areas covered by a white salt crust have a high EC value. However, in several cases, in each band of the Sentinel 2 image, the spectral reflectance value of the soil sample does not increase when the EC value increases. Consequently, it is difficult to map soil salinity directly using multispectral bands and the spectral index (Wang et al. 2021b; Wang et al. 2020b). According to various studies, salinity indices and vegetation indices were applied to monitor and estimate the soil salinity value (Allbed and Kumar 2013). Due to differences in geographical location, topography, and vegetation type, the value of EC under vegetation cover is very different, from low EC value to high EC value. However, in several studies, vegetation areas are considered non-saline or slightly saline areas (Fernandez-Buces et al. 2006; Metternicht and Zinck 2003). Sentinel 2 data with a 10 m resolution can solve these problems. This study did not cover the vegetated area when modeling soil salinity, but we collected additional samples from the vegetated areas to monitor and estimate soil salinity using spectral indices (Taghadosi et al. 2019; Wang et al. 2020a).

The quantification of variable importance is an important task in building a soil salinity model. Because data redundancy can increase calculation times and sometimes decrease the accuracy of predictive models (Bui et al. 2020; Nguyen 2022b; Nguyen et al. 2021b). In this study, 43 independent variables were selected to build soil salinity models. The RF technique combined with the trial-and-error method was used to determine the appropriate independent variables for the soil salinity model. The results show that the spectral indices, namely, Int2 (0.34), BI (0.33), SAVI (0.32), NDSI (0.32), NDVI (0.31), and Band 8 (0.3) play important roles in monitoring soil salinity. Because this study uses Sentinel 2A images with a 10 m spatial resolution, they contain few mixed pixels, so areas with high spectral reflectance have high EC. In addition, the salinity index and geographical location also play a key role in assessing soil salinity. Due to the characteristics of ecology, hydrology, climate, and human activity that determine the movement and accumulation of salt, therefore, soil salinity varies considerably depending on geographical location (Ge et al. 2022; Wang et al. 2019b; Wang et al. 2021b). In addition, the study area has low relief (< 2 m), often affected by sea level rise. Areas close to the sea have higher EC values than those areas far from the sea (Loc et al. 2021; Tho et al. 2008). Besides using the RF technique to determine the important variables, this study also uses the trial-and-error method to filter out the factors not useful for the soil salinity model. It should be noted that this study applies a data-driven approach to monitor soil salinity. Therefore, besides the dependence on the characteristics of ecology, hydrology, climate, or human activities, the statistical relationships between the independent variables and the value of EC are considered as one of the important elements that determined the importance of variables (Nguyen 2022b).

The results justified the initial assumption in the introduction that the accuracy of hybrid models has surpassed the individual models. In addition to landslides, floods, groundwater salinization, and soil salinization, these results are consistent with results from many different studies using machine learning. Hybrid models can improve the ability of individual model prediction by eliminating weak classifications. In this study, six optimization algorithms, namely, SSA, MSA, BSA, HHO, GOA, and PSO successfully improve the prediction ability of the XGR model. Among these proposed models, the XGR-HHO model was better than the other models because HHO has advantages in terms of ease of implementation and high flexibility. Also, HHO can globally search at different stages (Alabool et al. 2021). The XGR-GOA model was ranked second because the GPA has a fast optimal solution-finding speed with high accuracy and, in particular, GOA is easy to combine with unique algorithms (Wang and Li 2019). Model XGR-MSA was ranked third because, in addition to its flexibility and ease of use, the MSA also has fast convergence speed and high convergence accuracy (Han et al. 2020). The XGR-BSA model was ranked fourth because the BSA has a simple design and is easy to implement. Moreover, this algorithm can solve optimization problems in a short time with high accuracy thanks to its capability to balance the process of exploration and exploitation. The accuracy of the XGR-SSA model was ranked fifth in predicting the value of EC. However, despite this algorithm’s success in improving the XGR model’s performance, the XGR-HHO, XGR-GWO, XGR-MSE, and XGR-BSA models’ performance was superior. This is due to this algorithm’s randomness and local optimization difficulty. The XGR-PSO model was ranked sixth since although PSO has the advantage in convergence speed, one of the important disadvantages of PSO is the problem of local optimization.

Several studies have also used machine learning to monitor soil salinity. Wang et al. (2021b) used SVM, RF, and ANN with Sentinel 2 data to construct the soil salinity map. The results indicated that the SVM model was better than the other models with the R2 value of 0.88. The accuracy of these models is less than in our study. Ge et al. (2022) applied bagging, classification and regression tree, RF, and gradient boosting regression tree (GBRT) with Sentinel 2 data to predict soil salinity in the Ebinur Lake region of China. The results reported that these models had the best accuracy with the R2 value of 0.88. These models were less efficient than in our study. Nguyen et al. (2021b) integrated GOA with DNN, SVR, XGR, and GPR combined with Landsat 8 data to predict soil salinity in the Vietnamese Mekong Delta. The results reported that the XGR-GOA model had surpassed the other models with the R2 value of 0.86. The performance of this model works less well than in our current study with the value of R2 of 0.99. Wei et al. (2022) integrated the particle swarm optimization (PSO) with support vector machine regression (SVR) and back-propagation neural network (BPNN) models to predict soil salinity in Keriya Oasis of China using the PALSAR-2 data and Landsat 8 data. The results indicated that the best accuracy of these models was with the R2 value of 0.88. So, these models perform worse than the models in our study with the R2 value of 0.99. Therefore, the results of our research can be used as an alternative solution to support decision-makers in the development of agriculture to ensure food security in the region.

The main contribution of this study is the development of new and less expensive methods to monitor soil salinity. Although this study successfully constructed a technique to monitor soil salinity, however, it also presents general limitations related to the uses of the data. The reliability of the generated soil salinity map is partially dependent on the collection scheme and the number of in situ samples. In this study, 150 samples were obtained in 2016–2020 so the map obtained cannot capture and express the dynamics of salinization processes through time. In addition, shallow groundwater depth at every pixel, which is hardly acquired, was not included as an input variable. So, all of these can increase the uncertainties of the results.

Conclusion

Soil salinization is the most dangerous environmental hazard, significantly affecting the country’s food security. Therefore, this study aims to develop a low-cost method to monitor soil salinity in the Ben Tre province of Vietnam, where often affected by soil salinity. The results of this study can support decision-makers in sustainable agricultural development to ensure food security in the country.

In Ben Tre province of Vietnam, factors related to soil characteristics, vegetation, and brightness rates are the most important variables in soil salinity.

The integration of optimization algorithms (HHO, SSA, MSA, BSA, GWO, and PSO) on the XGR model can significantly improve the precision of the XGR model and the performance of the hybrid models has surpassed reference models such as CatBoost and RF. The new models can be used to monitor soil salinity in any region, especially in the data-limited area.

The soil in the study area tends to be highly saline in the eastern regions, while the western regions tend to be slightly salty. The findings in this study can be important tools for building effective soil salinity management strategies in any area of the world. The methods proposed in this study can be developed to assess other natural hazards, such as flooding and groundwater salinization.

The soil salinity in the Mekong Delta and the study area in particular is strongly influenced by sea level rise and climate change. Therefore, in future research, studies on evaluating the effects of these problems on soil salinity are necessary to build appropriate agricultural development strategies to ensure food security.