The effect of soil porosity size distribution on integral energy content of water in different moisture slopes

Simulation of soil water dynamics in field conditions becomes necessary to understand changes of soil water conditions to develop irrigation guidelines (Birendra et al. 2021; He et al. 2021; Hodges et al. 2022). The bell-shaped curve of soil pore size distribution is the result of plotting the slope of the soil moisture curve versus the equivalent diameter of the pore in a logarithmic scale (Malicki et al. 1992). This is in the condition that the curve is drawn based on the volumetric soil moisture against the natural logarithm of matric suction (Badr & Abuarab 2013; Lal et al. 2017; Qiu et al. 2023). Soil moisture content has a main role in water-food-energy and ecosystem nexus (Liu 2016; Tian et al. 2019; Wolde et al. 2021).

Chen et al. (2022) developed three models including Auto-Regressive Integrated Moving Average (ARIMA), Back-Propagation Artificial Neural Network (BP-ANN), and Least Squares Support Vector Machine (LS-SVM) to simulate the soil water content in the 0–14 cm and 14–33 cm soil layers across the Taihu Lake region of China. Rainfall, evaporation, temperature, humidity and wind speed that affect soil water content changes were considered in the BP-ANN and LS-SVM, but not in ARIMA. The results showed that the variability of soil water content in the 0–14 cm soil layer was greater than that in 14–33 cm. Correlation coefficients of soil water content between simulations and observations were highest (0.9827) using LS-SVM in the 14–33 cm soil layer, while they were the lowest (0.7019) using ARIMA in the 0–14 cm soil layer; but no significant difference in correlation coefficient values was observed between the two soil layers with the BP-ANN model. Rostami et al. (2022) investigated the potential of rainfed agriculture in the ZarrinehRoud basin as this basin is one of the most important sub-basins of Urmia Lake, Iran. For this study, the remote sensing data of surface soil moisture and evapotranspiration were combined with the SWAT model using the Data Assimilation method, Ensemble Kalman Filter (EnKF). Calibration of runoff flow rate in the SWAT model showed the correlation coefficient ranging between 0.69 and 0.84 in the calibration period (2000–2009) and between 0.64 and 0.86 in the validation period (2010–2014). The assimilation of the remote sensing data with the calibrated SWAT model showed that the model simulations for both the variables of surface soil moisture and actual evapotranspiration improved by at least 25%.

Although the total amount of water available for plants has a good correlation with the plant's performance and response, certain energy is required to absorb the unit weight of water in the soil, which justifies the ease of water absorption by the plant (Yan et al. 2022; Zhou et al. 2022; Zhu et al. 2023). Based on this, Minasny & McBratney (2003) presented integral energy as a standard to estimate the plant's usable water.

These researchers showed that the soil moisture curve is a suitable tool for estimating the energy required by the plant to overcome the water energy in the soil and absorb the unit weight of water (Dale et al. 2011; Wei et al. 2023). This energy is a function of the amount of water, or in other words, a function of the starting and ending points of the moisture range in the soil. Researchers believe that in similar soils in terms of the amount of usable water, which is the amount of integral energy, the growth and performance of the plant and, accordingly, the efficiency of water consumption will be different (Minasny & McBratney 2003).

The results of the studies showed that the usable water of the plant is not sensitive to the soil management method (Xu et al. 2022; Wei et al. 2023). With the increase in apparent specific gravity of the soil, the usable water of the plant remains constant due to the corresponding increase in humidity, the field capacity and the wilting point, and the effect of increasing the apparent specific gravity of the soil on the usable water of the plant is not shown (Zhang et al. 2023). But in the same soil, with an increase in apparent specific mass, the integral energy of water will increase (Reynolds et al. 2008, 2009). Asgarzadeh et al. (2011) believed that there is a strong and significant relationship between integral energy, integral water capacity, and suction at a point with resistance equal to 5.1 MPa, as well as between integral energy, minimum limited moisture range, and suction at a point with resistance. Subsidence equivalent to 2 MPa indicates the high dependence of integral energy on the resistance of soil subsidence in its dry range.

The texture and physical quality of the soil is one of the most important issues in improving the efficiency of water consumption in the agriculture and food security sectors. Therefore, in this study, an attempt has been made to investigate the relationship between the distribution of pore size in the soil and the amount of energy required by the plant to absorb water in different soil moisture ranges. In order to evaluate and compare the distribution curves of soil pore size, different indicators of the location and shape of the curve are used. In this regard, three indicators of mode, median and average diameter equivalent of soil porosity are considered as location indicators and three indicators of standard deviation; Skewness and Kurtosis are considered as shape indicators.

The present research was conducted during the years 2019–2022 at the research station of Chongqing Institute of Geology and Mineral Resources in China with an average height of 244 m above sea level and geographical coordinates of 102° and 21 min to 108° and 41 min of longitude and 28° and 11 min to 34° and 27 min of latitude. The soil of this station has been classified into entisol category. Generally, the surface layer had medium to light texture. Forty-five points with different texture, structure and organic matter were selected (Xu et al. 2022) and different soil characteristics were prepared from 0 to 30 cm depth, including one damaged sample and one intact sample using metal cylinders with a diameter of 6 cm and a height of 8 cm. In this study, the coefficients of the soil moisture curve, by fitting the Wegner-Houghton by the particle emission optimization model to the soil moisture data in suctions of 0, 10, 20, 40, 60, 80 and 100 cm using a sand box device and suctions of 500, 1,000, 10,000 and 15,000 cm were obtained using pressure plates.

In these formulas, θ_v is the volumetric moisture content in matric suction h, d_e is the equivalent pore diameter (μm), γ is the surface tension of water inside equivalent pore (72.8 g s⁻²), ρ_w is the specific weight of equivalent water (0.998 g cm⁻³), g is the equivalent acceleration of gravity (980 centimeter per square second) and ω is the contact angle of water with soil porosity, which is considered almost equal to 0.

Different humidity levels are included in the calculation of integral energy, so first the values of usable water range, minimum limited humidity range and integral water capacity were determined.

In this way, the difference in soil moisture at the field capacity point (suction 100 and 330 cm) and permanent wilting (suction 15,000 cm) was considered as usable plant water. The humidity range with the minimum limit was determined by calculating the difference between the upper limit (the smaller value between the moisture of the field capacity and the humidity of ventilation porosity of 10%) and the lower limit (the larger value between the permanent wilting humidity and the resistance of 2 MPa).

In this study, the integral energy of water for usable plant water and humidity range with the minimum limit (field capacity in suction 100 and 330 cm (EW100 and EW330)) and the integral capacity of water are shown as CW100 and CW330, respectively. To perform integral calculations in order to determine the integral energy index value of water, a subprogram has been prepared in Python.

In order to determine the statistical relationship between the shape indices and the location of the pore size distribution curve with the integral energy of water in different humidity ranges, Pearson's correlation and multivariate linear regression were also used in Python programming.

The results of measuring and determining the soil texture and the amounts of sand components in the studied samples are briefly shown in Table 1. The results indicate that 36% of the studied soil samples had loam texture, 27% silty loam texture, 12% silty clay loam texture, 18% clay loam texture and 7% sandy loam texture. The specific mass and organic carbon in the studied soil samples had a range between 1.56 and 1.29 and an average of 45.1 g/cm³ and 26–0.05 and an average of 53.0%. Using the soil moisture curve coefficients, the indices of the pore size distribution curve of the soil samples were calculated (Zhang et al. 2023). Table 2 briefly shows the values of the mentioned indices in the studied soil samples.

The results showed that, on average, pores with a diameter of 57 μm are the most frequent in the examined soil samples. The difference between the minimum and maximum average pore diameter of 26 μm, as well as the range of calculated standard deviation changes, indicates the diversity of pore size in the soil samples, or in other words, the presence of pores with different sizes in the studied soils.

The results indicate that the average value of the integral energy of water in the humidity range with the minimum limit, in which, in addition to the humidity at the field capacity points and permanent wilting, ventilation restrictions and soil subsidence resistance, are also considered, from the average value of this factor in the water range. The usable capacity of the plant (corresponding field capacity) is less. Another noteworthy point is the average amount of integral water energy in the range of integral water capacity, which is lower than the value of this index in the humidity range.

It can be stated that the index of integral water capacity by taking into account the limitations of water absorption by the plant as a continuous function of water suction in the soil and calculating the integral energy according to the effect of these limitations, is a better measure to express the availability of water for the plant. The results of other researchers also showed that, on average, the amount of integral energy was the lowest in the range of integral water capacity and the highest in the range of plant usable water. The statistical relationship between the indices of the pore size distribution curve and the integral energy values of water in different humidity ranges is presented in the form of Pearson's correlation coefficient in Table 4.

The results showed that the mean and mode indices of soil pore diameter have no significant statistical relationship with the values of integral energy of water in different humidity ranges. Among the three indices of soil pore size distribution curve position, only the average pore diameter index had a significant negative relationship with integral water energy in EW100, EW330 and ECW. In this regard, the elongation index also showed a negative and significant effect on the integral energy of ECW, CW100, CW330 and EW100 of water, in which the increase in the diameter of the soil pores leads to a decrease in the integral energy of water in the mentioned moisture ranges and facilitates the absorption of water by the plant. The results of the study of the relationship between the standard deviation of the pore size distribution curve or the variation of the pore size with the values of the integral energy of water in different moisture ranges showed that with the decrease of the variation of the diameter of the pores in the soil, the integral energy of water in ECW decreases. The increase in the uplift index of the soil pore size distribution curve in the studied soil samples showed a significant decrease in the integral energy of water in ECW. This means that the curve is longer in the center and its traces are longer at both ends of the curve compared to the normal log state.

This article does not contain any studies with animals performed by any of the authors.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.