Characterizing physical and hydraulic properties of soils in Al-Ahsa, Kingdom of Saudi Arabia.

Al-Ahsa Oasis is one of the oldest and biggest agricultural regions in Saudi Arabia. Thirty-six soil samples representing most of the soil type in the region were collected and analysed in a laboratory for physical properties including particle size (sand%, silt%, clay%), saturation θs , and bulk density ρ. The soil-water characteristic curve (SWCC) was measured using the filter paper method. Intensive statistical analysis included correlation, stepwise multiple linear regression analysis (SWR), mean square error (MSE), and F-test were used to evaluate the potential PTFs. Silt (silt%) and bulk density (ρ) were achieved a high accuracy in prediction of (ρ) and saturation (θs ) respectively. Both field capacity (FC) and wilting point (WP) were correlated significantly with θs with a very high prediction compatibility and MSE 0.004 and 0.001 respectively. Using tow levels of prediction demonstrated high correctness in predicting SWCC with correlation coefficient 0.986 and 0.952 with a low MSE equal to 0.0007 and 0.0028 respectively. The result of this study shown the high feasibility of developing a model for the prediction of SWCC using easily readable PTFs.

Introduction

Al-Ahsa is one of the oldest agricultural settlements in the region from 4000BCE Nowadays, Al-Ahsa is considered the largest agricultural area dominated by date palms with more than three million trees (Al-Wusaibai et al., 2012). Al-Ahsa soil is dominated by sandy and sandy loam soil with a very low percentage of clay and organic matter (Al-Barrak and Al-Badawi, 1988, Bashour et al., 1983), a high level of calcium carbonate (CaCo3) (Bashour et al., 1983, Chapman, 1974), and has the size of sand and silt particles (Al-Hawas, 1989).

Soil hydraulic properties are fundamentally involved in hydrological quantification, agriculture resource management, geo-environment, pollute transportation, geotechnical for construction and road engineering, and water resource construction, i.e., dam and irrigation and drainage projects (Fredlund et al., 2012, Hillel, 2003; Zapata, 1999).

The soil water characteristic curve (SWCC) contributes to analyzing and determining the water dynamics in unsaturated porous media. SWCC can be defined as a graph of non-linear functions describing the amount of water retained (θ) in soil under equilibrium at a given matric potential (ψ) under unsaturation conditions (Childs, 1940, Lu, 2020; Tuller and Or, 2004). For further detailed and comprehensive definitions, refer to (Fredlund and Xing, 1994).

SWCC is considered the first step in the assessment and the solo dominant variable governing changes in the behavior of saturated and unsaturated soils (Fredlund and Fredlund, 2020, Fredlund and Houston, 2009). Ergo measuring or estimating SWCC value accuracy is a determinative step in unsaturated soil physics and mechanics. Establishing a good and reliable estimation necessitates a good and reliable local soil database to be established with accurate and comprehensive measurements of the effective soil’s physical, chemical, and hydraulic properties (Fredlund and Fredlund, 2020, Fredlund and Houston, 2009; Madi et al., 2018; Nemes and Rawls, 2006; Wösten et al., 1999). Many studies and research were conducted over the past decades to evaluate and appraise the accuracy and suitability of SWCC’s laboratory measurement methods for various types of soil and under a wide range of soil suction (Agus and Schanz, 2007, Fondjo et al., 2020; Pan et al., 2010; Tripathy et al., 2014). The filter paper method first appeared as early as Gardner, (1937). The continued development and enhancement improved the performance and results of this method (Al-khafaf and Hanks, 1974, Bulut, 1996, Elgabu, 2013;Leong and Rahardjo, 2002; Elgabu (2013) reported a comprehensive table listing filter paper features in terms of brand and grade, suction range, suction equation, and equilibrium time. The filter paper method's correctness and meticulousness are confirmed as factual by many publications and authors (Al-khafaf and Hanks, 1974, Bulut and Leong, 2008, Fondjo et al., 2020; Tripathy et al., 2014).

Two methods generate the best fitting line for SWCC, mathematically, i.e., Brooks & Corey (1964), van Genuchten, 1980, and Fredlund and Xing, 1994 and statistically, i.e., Borg (1982), Rawls and Brakensiek, 1982, Rawls et al., 1991, and Gharagheer (2009). The most well-received mathematical equations are based on parametric equations with two to four parameters. Haghverdi et al. (2020), Sillers et al., 2001, and Khlosi et al. (2008) had performed an adequate examination for measuring the validity and simplicity of using those equations for different soil types. Results always heavily depend on the accuracy of calculating or adapting the model’s parameter by utilizing pedotransfer functions (Du, 2020, Khlosi et al., 2008; Madi et al., 2018; Rawls et al., 1991; Wösten et al., 1999). Statistical models are also reliant on the soil pedotransfere functions as mostly generated from stepwise regression analysis for the available soil data, which consequently determine the accuracy and sensitivity of the final model (Ghanbarian-Alavijeh and Liaghat, 2009; Mohawesh, 2013; Rawls and Brakensiek, 1982; Ren et al., 2020; Saxton and Rawls, 2006). The effect of soil physical properties on both types of models is obvious and prominent. The shape, position, and slope of SWCC are changed as affected by the physical, morphological, and chemical properties (Rawls et al., 1991). Clay and silt content attribute a proportional correlative effect on SWCC by extending the curve range and reducing the steepness. Silt and clay content increases the moisture content for SWCC in general (Bahmani and Palangi, 2016; Rawls et al., 1991; Saxton and Rawls, 2006). That reflects positively on water content at field capacity pF 2.52 (33 kPa) and wilting point pF 4.18 (1500 kPa) in all soil types (Givi et al., 2004; Qiao et al., 2019).

Throughout the evaluation of pedotransfer functions (PTFs), bulk density ρ always shows a negative effect on SWCC, includes field capacity FC and wilting point WP, as reported by many researchers (Bahmani and Palangi, 2016, Chaudhari et al., 2013, Contreras and Bonilla, 2018, Du, 2020). Bulk density ρ relates positively with sand content. On the other hand, silt and clay reduce the bulk density ρ (Chaudhari et al., 2013, Contreras and Bonilla, 2018, Du, 2020). The effect of CaCO3 on the bulk density ρ is contradictory and depends on the size of the CaCO3 fraction. If the dominant size is within the sand particles range, CaCO3 behaves as sand with increasing soil bulk density (Habel, 2013, Habel et al., 2015). On the other hand, if it is sized within silt or clay particles, bulk density ρ will be reduced inversely (Chaudhari et al., 2013, Chen et al., 2020, Jensen et al., 2005; Mahdi, 2008; Mahdi and Naji, 2015. Saturation θs, Field capacity, and wilting point are all part of the SWCC, which means that they behave according to the same factors affecting SWCC position or shape. For all soil groups θs, field capacity FC, and wilting point WP have an inverse relationship with sand and bulk density ρ and a positive relationship with silt, clay, CaCO3 (Bahmani and Palangi, 2016, Du, 2020, Givi et al., 2004; Mohawesh, 2013; Rawls et al., 1991; Santra et al., 2018).

Due to the absence of a soil hydraulic properties database for Al-Ahsa soils, the purpose of this paper firstly, to establish a base of soil water hydraulic properties database includes laboratory measurements for the soil water characteristic curve (SWCC), particles size distribution, and main physical properties i.e., bulk density, saturation, and CaCO3. Secondly, to develop a simple PTFs equations can predict the main soil properties from a limited available soil data. Thirdly, to develop an easy approach with acceptable accuracy to predict the SWCC.

Material and methods

Study area

The study was conducted in Al-Ahsa region which is referred to as the largest and oldest agricultural and settlement area in the Arabian Peninsula. It is located about 70 km west of the Arabian Gulf between the latitudes of 25˚ 21′ and 25˚ 37′ N and the longitudes of 49˚ 33′ and 49˚ 46′ E (Fig. 1). It takes L-shaped toward north and east with total area of 320 km2. According to Almadini et al., 2019 Al-Ahsa oasis consists of two major parts, the old and new oases. The total area of the old oasis is about 20,000 ha, of which 8200 ha are under irrigated cultivation being divide into 25,000 farms (Almadini et al., 2021). Al-Ahsa represents a typical extreme arid ecosystem, with a very low precipitation less than 73 mm per annual.

Fig. 1

Al-Ahsa general areal image shows geographical position and samples location. (image source: Esri, 2021, DigitalGlobe, GeoEye, Earthstar Geographics, CNES/Airbus DS, USDA, USGS, Aerogrid, IGN, and the GISUser Community).

Soil sampling and laboratory analysis

Forty-one samples were randomly collected from 41 locations in Al-Ahsa region. The locations of the soil samples in the field were determined using a handheld global positioning system (GPS) device with an accuracy of less than 5 m. Disturbed samples to depths of about 30 cm were collected using a soil auger with diameter of 10 cm. Samples were air-dried, ground, thoroughly mixed and passed through a 2 mm sieve and kept for physical and hydraulic measurements. Soil particle size (sand%, silt%, and clay%), bulk density ρ, and saturation percentage θ were measured in the laboratory according to the standard methods of SSSA (Soil Science Society of America) (Reynolds et al., 2002). Calcium carbonate CaCO3 was measured using calcimeter method described by Loeppert and Suarez, (2018).

Soil water characteristic curve (SWCC)

SWCC was measured using the filter paper method described in ASTM-D-5298 (ASTM-D5298-16, 2016) and (Al-khafaf and Hanks, 1974, Bulut and Leong, 2008; Scanlon et al., 2002). Bulut and Leong (2008) reported, filter paper technique as an indirect method for suction measurement has been heavily investigated and validated with an adequate acceptable level of accuracy results as compared with direct methods (Bulut, 1996, Bulut et al., 2001, Elgabu, 2013; Tripathy et al., 2014). Filter paper (Whatman No. 42) was sandwiched between two protection filter papers placed between two identical halves of soil specimen. Soil packed well to ensure perfect contact between soil and filter paper. Cane closed and sealed to prevent any loss in moisture. For each selected moisture content, the soil was packed in moisture cane equal to the bulk density. Canes were kept in an incubator for seven days to ensure equilibrium with a constant temperature of 25˚C. At the end of seven days, the filter paper was removed from the soil and immediately weighed with a 0.0001 g electronic balance to determine the wet weight. The filter paper was oven-dried at 105 °C for 24 h and weighed again to determine the water content of filter paper. Metric suction ψ was determined by matching filter paper moisture content with the calibration curves established by Al-Khafaf & Hanks, (1974) and ASTM-D5298-16, 2016. Field capacity FC and wilting point WP moisture content values were extrapolated from the suction vs moisture curve at pF value of 2.52 and 4.18 respectively.

SWCC fitting equation

Soil water characteristic curve (SWCC) was plotted and fitted using the “S” shaped equation. A parametric logistic regression equation with four parameters (PL4) was used for fitting the laboratory measured values of SWCC. The general form of PL4 equation presented in equation (1 and 2) as describe by (Davis et al., 2002; Deming, 2015)where a, b, c, and d are statistical fitting parameters a is the maximum value on y axis or estimated θ at zero pF which equals θs, b is slope factor at c point, c is the inflection point, and d is minimum value on y axis or the θ at infinite pF.

Developing the pedotransfer functions (PTFs)

First, the soil samples were randomly split into 36 samples as training set (used to generate the statistical model) and 5 samples as validation set (used to validate the model’s accuracy). Second, a stepwise multiple linear regression (SWR) model was generated using a backward elimination procedure subsisted at 95% significance level (Guan et al., 2013; Wang and Chen, 2018). Subset effects were selected according to mean square error (MSE), correlation coefficient (R), and F test significancy of explanatory variables information criterions. All explanatory variables that F test failed to be significant at 95% confidence level (p < 0.05) were eliminated from the PTFs. The SWR was used to generate a PTFs for the following below variables and parameters as of the following:

Bulk density (ρ): by using the variables of soil particles and CaCO.

Saturation (θ): by using the variables of soil particles size, CaCO, and ρ.

Field capacity (FC) and wilting point (WP): by utilizing the variables of soil particles size, CaCO%, θ.

SWCC fitting parameters (a, b, c, and d) by adapting the variables of soil particles size, CaCO, θ, FC, and WP.

Predict the complete SWCC using fitting parameters (a, b, c, and d) were generated by engaging two different levels of PTFs. Level one (L1) direct method used laboratory measured predictors from (iv), level tow (L2) indirect method used predictors were generated from (ii and iii).

The general form of the multiple linear regression equation is shown in equation (3) (Vereecken and Herbst).where is y and x were the response and predictor variables, β is the intercept, and β, β,…, β are the slopes of each predictor variable, and n is number of samples (observations). This test was preformed using Xlstat software (Addinsoft, 2021).

Pedotransfer function (PTFs) validation

Validation tests were performed over the validation set (5 samples) to determine the accuracy and the realism of the generated PTFs models (ρ, θ, FC, WP, and SWCC). PTFSs prediction accuracy is defined as how close a predicted value is to the physically measured value, this can be achieved through measuring the mean square error (MSE) and correlation coefficient (R).

Statistical analysis

Pearson correlation coefficient was used to investigate the relationships between soil physical and hydraulic variables and SWCC statistical fitting parameters in equation (2). The significance of the relationships were classified into four levels: no correlation when |R| < 0.28, weak correlation when 0.28 ≤|R|< 0.33, moderate correlation when 0.33 ≤|R|< 0.43, and strong correlation when 0.43 ≤ |R|≤ 1.0 (Addinsoft, 2021). The basic form of correlation coefficient is shown in equation (4) .where the x and y are the measured variables and and are predicted variables.

Mean square error (MSE), to measure the mean of the square of the difference between actual measured and predicted values to assess the suitability of the relationship and PTFs model. The general form of MSE equation:

Results

Soil physical and hydraulic properties

based on the content of sand, silt, and clay samples under this study scattered between loamy (L), loamy sand (LS), sandy (S), sandy loam (SL), silty (Si), silty loam (SiL), and as depicted in (Fig. 2) and listed in (Table 1). The maximum value of sand% was 95.38% for soil 3 (S), and the lowest value was 12.00% for soil 17 (Si), with an overall mean (52.480%), and standard deviation (24.880%). Silt content silt% ranged from 1.55% in soil 3 (S) to the maximum value was 86.00% in soil 17 (Si) with overall mean (43.513%) and standard deviation (25.5%). Clay content clay% varied from 1% in soil 31 (S) to a maximum value 19% in soil 32 (SL), with an overall mean (5.193%) and standard deviation (4.276%). The only correlation between soil texture components was reported between sand content sand% and silt content silt% with a high negative correlation (-0.986) as shown in (Table 2).

Fig. 2

Texture classes of the soil samples of Al-Ahsa (clay (≤2 μm), silt (2–50 μm), sand (50–2000 μm)) according to USDA classification (Klute, 1986).

Table 1

Soil physical property values sand%, silt%, clay%, bulk density ρ (g cm−3), and CaCO, saturation (θs), field capacity (FC), wilting poiny (WP), and soil type.

Sample No.	Sand	Silt	Clay	CaCO3	ρ	θs	FC(1)	WP(2)	Texture(3)
	%	%	%	%	(g cm-3)	(cm3 cm−3)	(cm3 cm−3)	(cm3 cm−3)
Trainig set
1	61.2	32.51	6.29	1.60	1.55	0.240	0.031	0.024	SL
2	79.5	16.41	4.09	1.25	1.55	0.233	0.125	0.058	LS
3	95.4	1.60	3.01	1.25	1.38	0.313	0.155	0.090	S
4	91.5	4.30	4.20	10.00	1.66	0.198	0.043	0.030	S
5	92.3	1.70	6.00	5.00	1.57	0.265	0.140	0.070	S
6	59.8	36.12	4.08	8.30	1.69	0.261	0.077	0.048	SL
7	82.5	11.00	6.50	23.75	1.42	0.358	0.243	0.132	LS
8	52.0	40.72	7.28	20.41	1.21	0.365	0.320	0.206	L
9	48.0	47.80	4.20	30.00	1.43	0.344	0.276	0.173	SL
10	48.5	40.50	11.00	33.75	1.24	0.348	0.289	0.163	L
11	55.0	40.74	4.26	40.80	1.41	0.415	0.210	0.100	SL
12	35.0	55.98	9.02	41.66	1.47	0.250	0.048	0.032	SiL
13	25.0	65.00	10.00	27.40	1.11	0.488	0.228	0.135	SiL
14	29.0	67.00	4.00	64.38	1.11	0.499	0.227	0.149	SiL
15	27.0	69.00	4.00	63.01	1.00	0.500	0.227	0.149	SiL
16	30.0	66.00	4.00	50.68	1.03	0.515	0.229	0.126	SiL
17	12.0	86.00	2.00	68.49	1.06	0.477	0.224	0.126	Si
18	16.0	82.00	2.00	42.47	1.01	0.505	0.326	0.131	Si
19	25.0	73.00	2.00	71.23	1.30	0.442	0.366	0.163	SiL
20	62.0	33.00	5.00	12.66	1.25	0.387	0.192	0.154	SL
21	52.0	46.00	2.00	6.33	1.37	0.335	0.161	0.026	SL
22	45.0	36.00	19.00	13.97	1.35	0.384	0.167	0.113	L
23	33.0	61.00	6.00	12.33	1.14	0.501	0.310	0.171	SiL
24	18.0	80.50	1.50	54.25	1.02	0.510	0.267	0.144	Si
25	25.0	73.50	1.50	43.56	1.07	0.481	0.302	0.162	SiL
26	61.0	29.00	10.00	6.85	1.25	0.437	0.149	0.116	SL
27	42.0	56.00	2.00	44.52	1.19	0.428	0.253	0.144	SiL
28	52.0	38.00	10.00	34.52	1.09	0.534	0.244	0.134	L
29	20.0	77.00	3.00	47.95	0.96	0.566	0.266	0.157	SiL
30	41.0	57.00	2.00	37.67	1.00	0.510	0.223	0.143	SiL
31	90.0	9.00	1.00	4.11	1.51	0.347	0.123	0.062	S
32	77.0	4.00	19.00	7.67	1.49	0.350	0.143	0.084	SL
33	76.0	20.00	4.00	6.71	1.39	0.354	0.167	0.100	LS
34	28.0	66.00	6.00	49.32	1.08	0.518	0.245	0.131	SiL
35	79.00	19.50	1.50	10.00	1.27	0.349	0.135	0.113	LS
36	74.0	24.50	1.50	15.34	1.52	0.319	0.181	0.119	LS
Validation set
37	24.00	74.00	2.00	52.00	1.06	0.42	0.193	0.106	SiL
38	40.00	48.00	12.00	39.00	1.25	0.48	0.170	0.120	L
39	71.00	27.50	1.50	35.00	1.18	0.45	0.149	0.085	SL
40	83.00	15.00	2.00	6.00	1.43	0.276	0.058	0.004	LS
41	94.0	3.50	2.50	8.99	1.49	0.320	0.086	0.009	S
Statistics
Maximum	95.380	86.000	19.000	71.233	1.690	0.566	0.366	0.206
Minimum	12.000	1.550	1.000	1.250	0.960	0.198	0.031	0.004
Mean	52.480	42.304	5.193	28.151	1.282	0.397	0.197	0.115
SD(4)	24.880	25.336	4.276	20.903	0.202	0.097	0.080	0.045

1) FC at soil potential (PF = 2.52).

2) WP at soil potential (PF = 4.18).

3) L: loamy; LS: Loamy sand; S: sandy; Si: silty; SiL: silty loam; SL: sandy loam.

4) Standard deviation.

Table 2

Correlation coefficient between soil physical properties sand%, silt%, clay%, and bulk density (ρ) against saturation (θs), field capacity (FC), and wilting point (WP).

	Silt	Clay	CaCO3	ρ	θs	FC	WP
	%	%	%	(g cm−3)	(cm3 cm−3)	(cm3 cm−3)	(cm3 cm−3)
Sand %	−0.985***	−0.096NS	−0.812***	0.774***	−0.748***	−0.567***	−0.476***
Silt %		−0.264NS	0.829***	−0.776***	0.743***	0.570***	0.466***
Clay %			−0.247NS	0.152NS	−0.106NS	−0.125NS	−0.028NS
CaCO3%				−0.683***	0.682***	0.576***	0.451***
ρ (g cm−3)					−0.929***	−0.661***	−0.653***
θs (cm3 cm−3)						0.700***	0.657***
FC (cm3 cm−3)							0.904***

*Significant at p < .05, **significant at p < .01, ***significant at p < .001, NS no significant.

generally precipitated in dry region soils. As Table 1 shows the content of CaCO ranged between 1.250%, soils 2 and 3, and 71.233%, soil 19. Overall mean is equal to 28.151% with standard deviation 20.903%. Silty loam (SiL) soils represented the highest content of CaCO while sandy soils (S) shown a lowest content among all samples. Table 2 shows the correlation between CaCO and other soil properties, a high significant negative correlation of CaCO with sand% (-0.829). In contrast, CaCO showed a high significant positive correlation with silt% (0.829), while no correlation with clay%.

depends on soil compaction and the arrangement of the particles in the soil body. Table 1 shows that value of ρ, which varied from 0.96 g cm−3, soil 29, to 1.69 g cm−3, soil 6, with mean (1.282 g cm−3) and standard deviation (0.202 g cm−3). Table 2 demonstrates the matrix correlation coefficients between ρ and other soil properties, ρ showed a significant positive correlation coefficients with sand% equal to 0.774, on the other hand a high significant negative correlation with silt% and CaCO with values of (-0.776) and (-0.683) respectively. Stepwise multiple linear regression (SWR) offered a significant F test at p greater than 0.05 for silt% only as shown in Table 3. SWR final equation written as:

Fig. 3 shows the goodness of eq. (6) for predicting ρ. This equation achieved a high significant correlation (0.775) and low MSE (0.0180) for training set as well as validation set (0.897) with MSE (0.015) (Table 3).

Fig. 3

Measured and predicted ρ using equation (6).

Table 3

Correlation coefficient (R), mean square error (MSE), and F test for physical and hydraulic properties prediction equations.

Equation No.	Set	R	MSE	F test	p(1)
6	Training	−0.776	0.018	51.475	2.68 × 10−8
	Validation	−0.897	0.015
7	Training	−0.929	0.001	213.975	3.11 × 10−16
	Validation	−0.768	0.004
8	Training	0.699	0.004	32.586	2.06 × 10−6
	Validation	0.849	0.007
9	Training	0.657	0.001	25.831	1.34 × 10−5
	Validation	0.893	0.004

1) significance level at 95% confidence.

represents the maximum soil capacity of moisture, in this study θ values were ranged from 0.198 cm3 cm−3, for soil 4 (S), to 0.566 cm3 cm−3, for soil 29 (SiL), with mean (0.397 cm3 cm−3) and standard deviation (0.097 cm3 cm−3). Table 2 shows the relationship between θ and other soil properties, ρ, and sand% were showed a very high inverse effect with correlation coefficients (-0.929) and (-0.748), respectively. Oppositely, silt% and CaCO were demonstrated a positive relation with highly significant correlations (0.743) and (0.682) respectively. SWR analysis resulted a significant F test only with ρ as shown in Table 3. Equation was generated using ρ:

Equation (7) performed a very high accuracy with a correlation coefficient equal to 0.929 and MSE 0.001 for training set. Validation set also showed high correlation (0.768) with very less MSE (0.004) as shown in (Fig. 4). The closeness to the identity line indicates the high accuracy level of the generated equation.

Fig. 4

Measured and predicted θ using equation (7).

is the moisture content at suction equal to pF 2.52. As shown in Table 1 the lowest value of FC (0.031 cm3.cm−3) for soil 1 (SL) soil and highest (0.366 cm3.cm−3) for soil 19 (SL), mean (0.197 cm3 cm−3), and standard deviation (0.08 cm3 cm−3). Table 2 shows a high correlation coefficient of FC with silt%, CaCO, and θ equal to 0.570, 0.576, and 0.700 respectively. On the other hand, negative correlation with sand% and ρ (-0.567) and (-0.661) respectively. SWR analysis showed a significant F test only with θ (Table 3), whereas the generated equation is:

Equations (8) achieved high correlation for training set (0.699), with low MSE equal (0.004), also validation set exhibited good correlation (0.849) with MSE (0.007) (Table 3). Fig. 5 shows the good matching between measured and estimated FC using equation (8) for both training and validation sets.

Fig. 5

Measured and predicted FC using equation (8).

, the lowest moisture can be extracted by plant at soil suction pF equal to 4.18, tables 1 demonstrated the that lowest value of WP (0.004 cm3.cm−3) for soil 40 loamy sand soil (LS), on the other hand the maximum value (0.206 cm3.cm−3) for soil 8 loamy soil (L), mean (0.115 cm3.cm−3), and standard deviation (0.045 cm3.cm−3). The effect of silt%, CaCO was highly significant with positive correlation coefficient (0.466), (0.451), (0.657), and (0.904) respectively. Sand% and ρ were shown high significant negative correlation (-0.476) and (-0.653), with WP respectively. SWR analysis only offered a F test significant with θ (Table 3) and generated equation (9):

Equation (9) preformed a high correlation coefficient 0.657 and high accurate MSE 0.001 for training set and correlation (0.893) with MSE (0.004) for validation set. Fig. 6 elucidates the high matching between measured and estimated WP for both training and validation sets.

Fig. 6

Measured and predicted WP using equation (9).

Statistical fitting parameters relationships

The results of the filter paper method were plotted in a graph, θ as y-axis and soil suction in a pF value as x-axis, as shown in Fig. 7 for sample No. 13.

Fig. 7

Soil water characteristic curve, sample No. 13, using filter paper method with the best-fitting line using equation (2), correlation coefficient R equal to 0.99.

The best-fitting line was established for all 41 samples using equation (2). All statistical fitting parameters (a, b, c, and d) were listed in (Table 4), with correlation coefficient values (0.990) for all samples. Table 5 shows the correlation coefficient between the fitting parameters in eq. (2) and soil physical and hydraulic properties.

Table 4

Statistical parameters for soil water characteristic curve using filter paper method and applying equation (2).

Sample No.	a	b	c	d	R(1)
Trainig sets
1	0.240	7.7888	1.6542	0.0238	0.99
2	0.233	2.5973	2.5856	0.0074	0.99
3	0.313	5.6409	2.1905	0.0843	0.99
4	0.198	4.4742	2.1311	0.0232	0.99
5	0.265	4.5355	2.3089	0.0603	0.99
6	0.261	6.8939	1.9394	0.0477	0.99
7	0.358	4.1617	2.7698	0.0907	0.99
8	0.365	6.0070	3.6472	0.1294	0.99
9	0.344	11.9495	2.7276	0.1609	0.99
10	0.348	8.6334	2.8958	0.1304	0.99
11	0.415	5.5676	2.4731	0.0553	0.99
12	0.250	4.1800	1.5679	0.0264	0.99
13	0.486	3.5740	2.0400	0.1080	0.99
14	0.506	1.4540	2.0350	0.0240	0.99
15	0.506	1.4540	2.0350	0.0400	0.99
16	0.518	2.2770	2.0540	0.0400	0.99
17	0.477	2.6050	2.0960	0.0600	0.99
18	0.508	3.6450	2.8750	0.0300	0.99
19	0.422	4.7050	3.7770	0.0020	0.99
20	0.381	6.1000	1.9610	0.1520	0.99
21	0.334	2.7439	1.76	0.0855	0.99
22	0.378	4.4360	1.9190	0.1050	0.99
23	0.504	2.2840	3.1080	0.0010	0.99
24	0.518	2.1770	2.5080	0.0220	0.99
25	0.487	3.0987	2.6302	0.0621	0.99
26	0.437	3.3390	1.4140	0.1070	0.99
27	0.431	4.4190	2.3610	0.1210	0.99
28	0.540	3.2050	2.0470	0.0930	0.99
29	0.569	1.8040	2.2370	0.0240	0.99
30	0.513	3.3110	1.8700	0.1170	0.99
31	0.346	2.3630	1.8190	0.0210	0.99
32	0.340	3.5133	2.1543	0.0958	0.99
33	0.343	3.8850	2.0920	0.0830	0.99
34	0.515	3.4530	2.1420	0.0930	0.99
35	0.350	2.88	1.2668	0.1053	0.99
36	0.318	2.6000	3.7800	0.4800	0.99
Validation sets
37	0.412	5.4353	2.1644	0.0984	0.99
38	0.476	2.8126	1.4951	0.1001	0.99
39	0.444	2.7637	1.6614	0.057	0.99
40	0.267	7.3667	2.0249	0.0123	0.99
41	0.301	3.4347	2.0780	0.0371	0.99

1) Correlation coefficient

Table 5

Correlation coefficient (R) for fitting parameters in equation (2) (a, b, c, and d) and soil physical and hydraulic properties, sand%, silt%, clay%, and bulk density (ρ) against saturation (θ), field capacity (FC), and wilting point (WP).

	a	b	c	d
Sand %	−0.748***	0.280*	−0.131NS	0.145NS
Silt %	0.747***	−0.315*	−0.151NS	−0.196NS
Clay %	−0.118NS	0.246NS	−0.148NS	0.330**
CaCO3%	0.680***	−0.311*	0.208NS	−0.191NS
ρ (g cm−3)	−0.934***	0.446***	−0.028NS	−0.090NS
θs (cm3 cm−3)	0.999***	−0.512***	0.070NS	0.014NS
FC (cm3 cm−3)	0.689***	−0.173NS	0.700***	0.134NS
WP (cm3 cm−3)	0.649***	−0.181NS	0.559***	0.374**

*Significant at p < .05, **significant at p < .01, ***significant at p < .001, NS no significant.

As shown in the Table 5, a exhibited significant negative correlation with sand% and ρ (-0.748) and (-0.934) respectively. On the other hand, silt%, CaCO related in a positive correlation 0.747, 0.680, 0.689, and 0.649 respectively. Saturation θ demonstrated an identical value with a with a high correlation coefficient equal to 0.999 which makes a equal to θ (Fig. 8).

Fig. 8

Identical measured and predicted θ.

b was correlated positively with sand% and ρ with value (0.280) and (0.446) respectively. In contrast a negative correlation with silt%, ρ , and θ with R (-0.315), (-0.311), and (-0.512) respectively. SWR analysis resulted a F test significant only for θ (Table 6), the generated equation is :

Table 6

Correlation coefficient (R), mean square error (MSE), and F test for physical and hydraulic properties prediction equations.

Equation No.	Set	R	MSE	F test	p(1)
10	Training	0.510	2.223	12.086	0.0014
	Validation	0.685	3.554
11	Training	0.913	0.064	θs = 68.831	1.39 × 10−9
				FC = 165.493	1.08 × 10−14
	Validation	0.684	0.157
12	Training	0.606	0.0012	FC = 11.917	0.0015
				WP = 18.287	0.00015
	Validation	0.863	0.0011

1) Significance level at 95% confidence.

Equation (10) preformed a good correlation coefficient 0.510 and MSE 2.223 for training set and correlation of 0.685 and MSE 3.554 for validation set. Fig. 9 depicted the result of equation (10) compared with the measured b for both training and validation sets.

Fig. 9

Measured and predicted b using equation (10).

c shown a highly significant correlation with FC and WP only with (0.700) and (0.559) respectively. SWR analysis generated an equation (11) with tow explanatory variables θ and FC with a significant F test with the value of 68.831 and 165.493 and p = 1.39x10−9 and 1.08 x10−14 respectively.

As shown in Table 6 the training set preformed high correlation 0.913 and MSE 0.063 also validation set preformed 0.684 and MSE 0.157. Fig. 10 illustrated the accuracy of the generated equation within 95% of confidence interval.

Fig. 10

Measured and predicted c using equation (11).

Parameter d was correlated significantly with clay% and WP (0.330) and (0.374) respectively. SWR resulted a significant F test (11.917) and (18.287) with p equal (0.0018) and (0.00015) for FC and WP respectively, the multiple linear equation (12)

Training set showed a significant correlation and low MSE for equation (12) 0.606 and 0.0012 respectively. Validation set also showed good correlation and less MSE (0.863) and (0.0011) respectively, Fig. 11 showed a good identicality between the training and validation set results.

Fig. 11

Measured and predicted d using equation (12).

SWCC prediction validation

Validation set samples covered five different soil types (SiL, L, SL, LS, and S) as shown previously in Table 1. SWCC for all validation soils were measured using filter paper and results of the fitting equation (2) were listed in Table 5. Correlation coefficient and MSE between measured and predicted SWCC were applied to determine the accuracy of PTFs equations.

Level one (L1) used a equal to θ and PTFs equations (10, 11, and 12) to predict (b, c, and d) respectively from measured θ and WP. As shown in (Table 7) and (Fig. 12). High correlation, between measured and predicted SWCC, ranged between 0.945 and 0.996 with very low MSE ranged between 0.0001 and 0.002 for soils 37,38,39, and 41. Soil 40 (LS) showed the lowest correlation and highest MSE (0.945) and (0.002) respectively. As combining all soils result together high correlation was achieved (0.986) with high accuracy MSE (0.0007) (Fig. 13).

Table 7

Correlation coefficient (R) and mean square error (MSE) for different prediction levels (L1 and L2).

Soil No.	Soil Type	Level	R	MSE
37	SiL	L1	0.994	0.0006
		L2	0.995	0.0001
38	L	L1	0.998	0.0001
		L2	0.941	0.0049
39	SL	L1	0.996	0.0008
		L2	0.959	0.0049
40	LS	L1	0.945	0.002
		L2	0.982	0.0033
41	S	L1	0.995	0.0002
		L2	0.99	0.0007
All		L1	0.986	0.0007
		L2	0.952	0.0028

Fig. 12

SWCC prediction using (L1) and (L2) approach for the validation soils (37, 38, 39, 40, 41).

Fig. 13

Comparison of measured and prediction moisture content using (L1) and (L2) approach for all validation data.

Level tow (L2) also used a equal to θ and PTFs equations (8 and 9) to calculate FC and WP which they are inputs in the PTFs equations (10, 11, and 12). Correlation coefficient significantly ranged between 0.945 and 0.998 and MSE as less as 0.0001 to 0.0049 (Table 7) (Fig. 12). Loamy soil (38) showed the lowest correlation (0.941) and highest MSE (0.0049). Combining all soils result together showed an excellent correlation (0.952) with high accuracy MSE (0.0028) (Fig. 13).

Discussion

The sand particles dominated the considered soils in this study 57.83%, with about 50% classified as sandy loam (SL) texture. Elprince et al. (2003) found that more than 60% of 600 soil samples covered all Al-Ahsa regions were SL with an average sand percentage of 75%. Many researchers also had reported nearing results of proofing that sand percentage between 65 and 70% and soil texture SL is dominated the soil type in Al-Ahsa (Al-Barrak and Al-Badawi, 1988, AlJaloud, 1983, Alnajem, 2021). Sand reflects the nature of the parent material from which sand is derived from, i.e., marl and redbeds (Al-Hawas, 1989, Al-Sayari and Zötl, 1978).

Calcite CaCO is a prime constituent element in Al-Ahsa soils formed either from the parent material or as secondary as it was precipitated in soil from the direct irrigation water or water rising through capillarity rise (Al-Barrak, 2000, Elprince, 1985). The calcite CaCO in this study ranged from 1.25% to 71.23%. The variation depends on the sample site's location, depth, and land usage (Al-Barrak, 2000, Alnajem, 2021, Bashour et al., 1983, Elprince, 1985). According to Table 2, CaCO showed a high correlation with silt%, which shows that the majority of CaCO is presented in silt particles (Al-Barrak, 2000, AlJaloud, 1983). That was clear in SiL soils, whereas the mean content of CaCO was 39.93 % and silt% was 61.25%. This result was reported by many studies in Al-Ahsa or other sites worldwide (Machette, 1985). Obviously, in this case, the increase of CaCO will increase the pore ratio in soil, which will improve the hydraulic properties to some extent (Chaudhari et al., 2013, Chen et al., 2020, Hafshejani and Jafari, 2017, Khlosi, 2015).

Bulk density ρ increased as sand% increased while oppositely decreased as CaCO and silt% increased. That can be referred to as the increase of CaCO in soil, which is well documented that CaCO has a low density as reported by (Chaudhari et al., 2013, Chen et al., 2020, Habel, 2013). Applying eq. (6) gave a good estimation result with a high correlation (0.776) with very low MSE (0.018) for training set, also validation set showed a high correlation (0.897) with MSE (0.015). These results indicated the high reliability of using silt content as in equation (6) to estimate ρ, particularly with the absence of organic matter information. This finding has been reported in previous studies and models (Aliku and Oshunsanya, 2018; Saxton and Rawls, 2006).

Saturation θs is highly affected by the ratio of pores and fine particles. Positive correlations with silt% and CaCO were due to increased pore ratio and, in contrast, negative correlation for ρ and sand%. The results parallel with other studies (Al-Qinna and Jaber, 2013, Chaudhari et al., 2013, Du, 2020; Mahdi, 2008; Mahdi and Naji, 2015; Saxton and Rawls, 2006; Sun et al., 2020). Equations (7) performed high identicality in estimating θ with a correlation (-0.929) and neglectable MSE (0.001) for training set. Validation set also showed high accuracy within the limit of 95% confidence interval with corelation (-0.768) and MSE (0.004). These models performed similar to some well-known models (Rawls and Brakensiek, 1982; Saxton and Rawls, 2006; Wösten et al., 1999).

Despite FC and WP were significantly correlated with sand%, silt%, ρ, and θ, only θ offered a significant F test at 95% confidence interval. These findings were supported by previous works except with the absent of organic matter effect (Gao and Sun, 2017; Mbah, 2012; Ostovari et al., 2015; Shiri et al., 2017). Equations (8 and 9) achieved high correlation associated with low MSE for both training and validation sets. θ played a very crucial role in improving the output of the PTFs. This made from θ a very critical property in the developing and improving the accuracy of PTFs prediction, strengthened by many earlier researches (Ghanbarian-Alavijeh and Liaghat, 2009, Grewal et al., 1990; Mbah, 2012; Saxton and Rawls, 2006).

The fitting parameters (a, b, c, and d) in equation (2), a it’s the maximum value for y axis at zero value of x axis, this is more or less equal to θ, as showed before in (van Genuchten, 1980) in his famous paper. Here in this study a correlated identically (0.999) with θ.

b correlated weakly with sand%, silt%, and CaCO and strongly with ρ, and θ. Equation (10) showed a significant F test with θ only, which indicated that θ is the only important variable can affect b value. High MSE for equation (10) is still in the acceptable level, especially that all validation set results within the 95% confidence interval, with more stability for the PTFs than adding more none significant variables, even if highly correlated, to the equation which might improve the under study samples (Rastgou et al., 2020; Zhao et al., 2016). c showed a strong correlation with FC and WP with high significant F test, this is support previous results of Rastgou et al., 2020. Equation (11) resulted a good prediction using FC and WP. b and c PTFs are the crucial to be more stable to reduce the MSE as they working as a shaper parameters for SWCC (Porebska et al., 2006; van Genuchten, 1980).

d showed moderated correlation with clay% and WP which indicated the effect of micro pores on this parameter. Both training and validation sets demonstrated a high correlation and low MSE with made the use of equation (12) very excellent PTFs for d prediction.

Level one (L1) and level tow (L2) approaches both exhibited a high accuracy with very low MSE for SWCC prediction regardless the soil type. The low accuracy of PTFs for b effected the overall accuracy of both approaches.

Generally, the results of using any of the suggested approach challenge the resulted reported in many research in term of simplicity and accuracy

Conclusion

The goal of this study was to establish PTFs related to Al-Ahsa soils by utilizing limited properties. These PTFs in eq. (6), 7, 8, and 9 were led to a very high accuracy for predicting SWCC. This results demonstrated the importance of having more samples analysis in future to improve the accuracy and stability of the local soil PTFs.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.