Modeling Soil Available Water Using Neuro-fuzzy, Gene Expression Programming and Random Forest Methods

Document Type : Research Article

Authors

• M. Hasanpour Kashani ¹
• Sh. Asghari ²

¹ Department of Water Engineering, Water Management Research Center, Faculty of Agriculture and Natural Resources, University of Mohaghegh Ardabili, Ardabil, Iran

² Department of Soil Sciences and Engineering, Faculty of Agriculture and Natural Resources, University of Mohaghegh Ardabili, Ardabil, Iran

10.22067/jsw.2025.92342.1470

Abstract

Introduction
Soil available water (SAW) is defined as the difference between field capacity (FC) and permanent wilting point (PWP). FC is the amount of soil water content held by the soil after the gravitational water was drained from the soil. PWP is defined as a minimum water content of a soil which is needed for the crop survival and if the water content decreases lower than PWP, a plant wilts and can no longer recover itself. The direct measurement of FC and PWP soil water contents is very costly and time consuming; therefore, it is useful the use of different intelligent models such as neuro-fuzzy (NF), gene expression programming (GEP) and random forest (RF) to estimate FC, PWP and SAW through easily accessible and low-cost soil characteristics. The objectives of this research were: (1) to obtain NF, GEP and RF models for estimating SAW from the easily accessible soil variables in the cultivated lands of Ardabil plain, and (2) to compare the accuracy of the mentioned models in estimating SAW using the coefficient of determination (R²), root mean square error (RMSE), mean error (ME) and Nash-Sutcliffe coefficient (NS) criteria.
 
 Materials and Methods
 The measured data from 102 soil samples taken from 0-10 cm soil depth of the cultivated lands of Ardabil plain, northwest of Iran, were used in this study. Sand, clay, mean geometric diameter (d_g) and geometric standard deviation (σ_g) of soil particles, bulk density (BD) and organic carbon (OC) were introduced as input variables to the applied three intelligent models for estimating soil available water (SAW). Data randomly were divided in two series as 82 data for training and 20 data for testing of models. In all models, six different input variables combinations were used; SPSS 22 software with stepwise method was applied to select the input variables. MATLAB, Gene Xpro Tools 4.0 and Weka softwares were used to derive neuro-fuzzy (NF), gene expression programming (GEP) and random forest (RF) models, respectively. One of the important steps by using NF method is selecting the appropriate membership functions (MFs) and its numbers. Based on a trial and error procedure, 3 numbers of MFs and 50 to 100 optimum replications were found for the NF modeling. Also, the input MFs were chosen as “triangular”, “trapezoid”, “generalized bell” and “pi” and the output MF was selected as “constant”. A set of optimal parameters were chosen before developing a best GEP model. The number of chromosomes and genes, head size and linking function were selected by the trial and error method, and they are 30, 3, 8, and +, respectively. The rates of genetic operators were chosen according to literature studies. Various tree numbers were analyzed for choosing the best random forest (RF) method. Increasing the tree numbers beyond 100 made lower variations in the average squared error values for the SAW estimation cases. The accuracy of NF, GEP and RF models in estimating SAW was evaluated by coefficient of determination (R²), root mean square error (RMSE), mean error (ME) and Nash-Sutcliffe coefficient (NS) statistics.
 
Results and Discussion
The studied soils were loam (n= 53), clay loam (n= 26), sandy loam (n= 15), silt loam (n= 6) and clay (n= 2) textural classes. The values of sand (24.40 to 68.00 %), clay (3.80 to 42.90 %), dg (0.02 to 0.26 mm), σ_g (7.48 to 19.41), BD (1.04 to 1.70 g cm^-3), OC (0.31 to 1.52 %) and SAW (5.10 to 25.10 % g g^-1) indicated good variations in the soils of studied region. Significant correlations were found between SAW and BD (r = -0.59), clay (r = 0.56^**), OC (r = 0.45^**), and sand (r = -0.44^**). NF, GEP and RF models were applied to estimate SAW using six different combinations of input soil variables (sand, clay, dg, σ_g, BD and OC). The results of the best NF, GEP and RF models indicated that the most appropriate input variables to predict SAW were OC and BD. The values of R², RMSE, ME and NS criteria were obtained equal 0.73, 2.51 % g g^-1, 0.09 % g g^-1and 0.71, and 0.76, 3.10 % g g^-1, - 1.41 % g g^-1 and 0.56, 0.68, 3.30 % g g^-1, - 1.45 % g g^-1, 0.50 for the best NF, GEP and RF models in the testing data set, respectively. Numerous investigations also showed that there is significant negative correlation between SAW with BD and sand and positive correlation between SAW with OC and clay.  
 
Conclusion
The results from the three investigated intelligent models indicated that organic carbon (OC) and bulk density (BD) were the most important and readily available soil variables for predicting soil available water (SAW) in the study area. Among the models, the Neuro-Fuzzy (NF) approach demonstrated the highest accuracy, as evidenced by the lowest root mean square error (RMSE) and the highest Nash–Sutcliffe efficiency (NS) values. In contrast, the Random Forest (RF) model provided the least accurate estimates of SAW, performing worse than both the NF and Gene Expression Programming (GEP) models.

Keywords

• Intelligent models
• Prediction
• Readily variables
• Soil water

Main Subjects

• Soil science

©2025 The author(s). This is an open access article distributed under Creative Commons Attribution 4.0 International License (CC BY 4.0).

References

• Amirabedi, H., Asghari, Sh., Mesri, T., & Keivan behjo, F. (2013). Estimating of field capacity, permanent wilting point and available water content in Ardabil plain using regression and artificial neural network models. Applied Soil Research, 1(1), 60-72. (In Persian with English abstract)
• Bauer, A., & Black, A.L. (1992). Organic carbon effects on available water capacity of three soil textural groups. Soil Science Society of America Journal, 56, 248-254. https://doi.org/10.2136/sssaj1992.03615995005600010038x
• Blake, G.R., & Hartge, K.H. (1986). Bulk density. p. 363-375. In: Klute A. (ed). Methods of Soil Analysis Part 1, Physical and Mineralogical Methods. 2nd ed. American Society of Agronomy, Madison, WI. https://doi.org/ 10.2136/sssabookser5.1.2ed.c13
• Breiman, L. (2001). Random forests. Machine Learning, 45, 5-32.
• Cheema, S.J., Shah, S.H.H., Farooque, A.A., Jamei, M., Abbas, F., Esau, T.J., & Grewal, K.S. (2024). A comprehensive analytical and computational assessment of soil water characteristics curves in Atlantic Canada: Application of a novel SelectKbestbased GEP model. Agricultural Water Management, 298, 108868. https://doi.org/10.1016/j.agwat.2024.108868
• Ferreira, C. (2006). Gene Expression Programming: Mathematical modeling by an artificial intelligence. Springer, Berlin, Heidelberg, New York, p. 478.
• Gardner, W.H. (1986). Water content. p. 493-544. In: Klute A. (ed). Methods of Soil Analysis. Part 1. 2nd ed. Agronomy. Monograph. 9. ASA, Madison, WI.
• Gee, G.W., & Or, D. (2002). Particle-size analysis. p. 255–293. In: Dane J. H., & Topp G. C. (eds.). Methods of Soil Analysis. Part 4. SSSA Book Series No. 5. Soil Science Society of America, Madison, WI. https://doi.org/10.2136/sssabookser5.4.c12
• Ghorbani, M.A., Deo, R.C., Kashani, M.H., Shahabi M., & Ghorbani, S. (2019). Artificial intelligence-based fast and efficient hybrid approach for spatial modeling of soil electrical conductivity. Soil and Tillage Research, 186, 152–164. https://doi.org/10.1016/j.still.2018.09.012
• Jafari, M.M., Ojaghlou, H., & Karbasi, M. (2021). Comparison of the performance of artificial neural networks and gene expression programming in estimating the forest soil water characteristic curve. Iranian Journal of Soil and Water Research, 52(8), 2093-2109.
• Jury, W., & Horton, R. (2004). Soil Physics. John Wiley and Sons, Inc.
• Kiani, R., & Bayat, H. (2024). Capability of regression and random forest methods to estimate soil water retention curve by developing pseudo-continuous pedotransfer functions. Journal of Soil and Plant Science (Water and Soil Science), 34(4), 15-36. https://doi.org/10.3390/w12123425
• Kozak, E., Pachepsky, Y.A., Sokolowski, S., Sokolowska, Z., & Stepniewski, W. (1996). A modified number-based method for estimating fragmentation fractal dimensions of soils. Soil Science Society of America Journal, 60, 1291-1297. https://doi.org/10.2136/sssaj1996.03615995006000050002x
• Merdun, H., Cinar, O., Meral, R., & Apan, M. (2006). Comparison of artificial neural network and regression pedotransfer functions for prediction of soil water retention and saturated hydraulic conductivity. Soil and Tillage Research, 90, 108–116. https://doi.org/10.1016/j.still.2005.08.011
• Nelson, D.W., & Sommers, L.E. (1982). Total carbon, organic carbon, and organic matter. p. 539–579. In: A.L. Page et al. (ed.) Methods of Soil Analysis. Part 2. 2^nd Agron. Monogr. 9. ASA and SSSA, Madison, WI. https://doi.org/10.2134/agronmonogr9.2.2ed.c29
• Ostovari, Y., Asgari, K., & Cornelis, W. (2015). Performance evaluation of pedotransfer functions to predict field capacity and permanent wilting point using UNSODA and HYPERS datasets. Arid Land Research Management, 29, 383-398. https://doi.org/10.1080/15324982.2015.1029649
• Rastgou, M., Bayat, H., Mansoorizadeh, M., & Gregory, A.S. (2020). Estimating the soil water retention curve: comparison of multiple nonlinear regression approach and random forest data mining technique. Computer and Electronics in Agriculture, 174, 1-13. https://doi.org/10.1016/j.compag.2020.105502
• Shirazi, M.A., & Boersma, L. (1984). A unifying quantitative analysis of soil texture. Soil Science Society American Journal, 48(1), 142–147. https://doi.org/10.2136/sssaj1984.03615995004800010026x
• Shiri, J., Keshavarzi, A., Kisi, O., & Karimi, S. (2017). Using soil easily measured parameters for estimating soil water capacity: Soft computing approaches. Computers and Electronics in Agriculture, 141, 327-339. https://doi.org/10.1016/j.compag.2017.08.012
• Shojaei, S., Farhadi Bansouleh, B., Fatehi, Sh., & Rahmani, M. (2023). Comparison of pedotransfer functions based on machine learning methods to estimate soil moisture at field capacity and permanent wilting point (Case study: Ravansar District, Kermanshah Province). Journal of Water and Soil Conservation, 30(1), 27-47. https://doi.org/10.3390/w13192639
• Waseem, M., Mani, N., Andiego, G., & Usman, M. (2017). A review of criteria of fit for hydrological models. International Research Journal of Engineering and Technology, 4(11), 1765-1772.
• Zhang, R., & Zhang, S. (2024). Coefficient of permeability prediction of soils using gene expression programming. Engineering Applications of Artificial Intelligence, 128 (107504). https://doi.org/10.1016/j.engappai.2023.107504