Iranian Journal of Soil and Water Research

Iranian Journal of Soil and Water Research

Digital Mapping of Soil Surface Calcium Carbonate Equivalent in a Semi-Arid Region Using Gene Expression Programming Algorithm (Case Study: Abyek Plain, Qazvin)

Document Type : Research Paper

Authors
Mohsen Davirand 1
Fereydoon Sarmadian 2
sajjad teimouri bardyani 3
1 Department of Soil Science, Faculty of Agriculture and Natural Resources, University of Tehran, Karaj, Iran
2 soil science department< faculty of agricultural engineering and technology, university of Tehran
3 Department of Soil Science and Engineering, Faculty of Agriculture and Natural Resources, University of Tehran, Karaj, Iran
10.22059/ijswr.2026.404804.670039
Abstract
Predicting soil calcium carbonate equivalent (CCE) is essential for effective land management in semi-arid regions characterized by high soil and topographic variability. This study evaluated the performance of Gene Expression Programming (GEP) for spatial prediction of CCE. Environmental predictors included seven Landsat 8 spectral bands, 15 derived spectral indices, nine ASTER-derived spectral indices, and 20 topographic variables derived from the digital elevation model (DEM). Recursive Feature Elimination based on Support Vector Machines (RFE-SVM) was employed for feature selection, reducing the predictor set by 84%. The optimized GEP model, consisting of three independent genes linked by an additive function, generated an explicit and interpretable mathematical equation for CCE prediction. Model performance demonstrated moderate predictive capability, with R² and RMSE values of 0.62 and 4.13 in the training phase, and 0.52 and 4.25 in the testing phase, respectively. However, regression slopes of 0.509 and 0.487 for the training and testing datasets indicated substantial regression toward the mean and underestimation of prediction variability. The resulting prediction map revealed a distinct north–south spatial gradient consistent with regional hydrological and topographic conditions. Overall, the integrated RFE-SVM–GEP framework provides a practical basis for digital CCE mapping in semi-arid environments. Nevertheless, improving the quality and spatial representativeness of training data, incorporating more informative environmental predictors, and integrating hybrid modeling approaches are recommended to enhance prediction accuracy, particularly for extreme CCE values.
Keywords
Gene Expression Programming (GEP)
Calcium Carbonate Equivalent (CCE)
Semi-arid regions
Digital Soil Mapping
Subjects

Objective

The precise spatial delineation of Calcium Carbonate Equivalent (CCE) in the surface horizon (0–30 cm) is a critical prerequisite for advanced pedological research and the operationalization of sustainable land management (SLM) in water-stressed, semi-arid environments. Conventional Digital Soil Mapping (DSM) techniques, particularly those leveraging opaque 'black-box' machine learning algorithms, often preclude the necessary mechanistic understanding of pedogenic factors governing CCE distribution, thereby impeding scientific knowledge transfer. This study was conceived to rigorously assess the capacity of Gene Expression Programming (GEP)—an evolutionary computation paradigm designed to yield explicit, parsimonious mathematical models—for spatially predicting CCE content. The core aim was to derive a transparent, non-linear, and fully interpretable predictive pedotransfer function within the heterogeneous Abyek Plain, Qazvin, offering a demonstrable scientific advantage over correlative, non-mechanistic models for enhanced environmental stewardship.

Research Method

The study was executed within the Abyek Plain, Iran, an expansive pedoscape (approximately 60,000 ha) characterized by a semi-arid climate, thermic soil temperature regime, and diverse Quaternary geomorphic surfaces. A total of 240 georeferenced surface soil samples were acquired, ensuring representative coverage across the region's stratified pedological heterogeneity. Laboratory characterization confirmed the soil matrix as strongly alkaline and highly calcareous (mean CCE: 11.30%; pH: 7.88). The initial ancillary data catalogue comprised 51 covariates extracted at a 30-meter spatial resolution from multi-temporal median composite imagery (Landsat 8, ASTER) and an ALOS Digital Elevation Model (DEM). To address inherent multicollinearity and optimize the model’s predictive stability, the Recursive Feature Elimination (RFE) algorithm was systematically employed. RFE successfully pruned the catalogue to the optimal subset of eight predictors, including the Brightness Index, Wind Exposition, Wetness Index, DEM, Convergence Index, and PCA3. The finalized dataset was randomly partitioned into an 80% calibration set and a 20% independent validation set. The GEP framework was configured with 30 chromosomes and 6 genes, utilizing the additive fitness function to minimize the Root Mean Square Error (RMSE) and facilitate the evolution of a multi-genic prediction model.

Findings

The GEP-derived model exhibited commendable performance and robustness in spatially modeling the CCE concentration. The calibration phase yielded a Coefficient of Determination of R² = 0.62 and a minimal RMSE of 4.13%. Crucially, the model maintained its predictive efficacy on the independent validation set, achieving a statistically acceptable R² = 0.52 and an RMSE of 4.25%. This performance affirms the model's generalized applicability across the pedoscape. The explicit mathematical architecture generated by GEP facilitated the quantifiable assessment of predictor contributions:

The Brightness Index emerged as the single most influential covariate, contributing 23% of the model’s predictive power. This strong positive correlation (r=0.48) is mechanistically linked to the high spectral albedo associated with surficial salt and carbonate accumulation zones, particularly in poorly-drained, evaporative depressions. Wind Exposition followed with a substantial 18% contribution, suggesting that wind-driven sediment transport (aeolian processes) and micro-relief significantly regulate the redistribution of CCE. The Wetness Index demonstrated a significant negative correlation (r=-0.44), consistent with the hydrogeomorphic mechanism of CCE leaching in well-drained or topographically lower accumulation areas.

Conclusion

This investigation successfully demonstrated the utility of the GEP algorithm as a superior, mechanistically transparent alternative for the Digital Soil Mapping of CCE in complex semi-arid environments. The synthesis of RFE for predictor selection and GEP for model derivation resulted in an explicit, yet highly accurate, predictive model (R² = 0.52 validation). The resultant multi-genic pedotransfer function not only provides high-resolution spatial predictions but also offers unparalleled interpretability into the geo-environmental controls—such as spectral response linked to surficial salinization/carbonation and topographic features—that govern CCE distribution. This transparent modeling output constitutes an invaluable evidence base for precision agricultural intervention (e.g., targeted amendments, optimized irrigation scheduling) and informed environmental policy in calcareous, water-scarce regions, thereby supporting the tenets of sustainable land management. Future research should prioritize integrating time-series covariates to capture the dynamic spatio-temporal fluxes influencing CCE distribution.

Funding

The study was funded by the University of Tehran, Country Iran.

Authorship contribution

Conceptualization, Fereydoon Sarmadian; methodology, Fereydoon Sarmadian; software, Mohsen Davirand; validation, Fereydoon Sarmadian; formal analysis, Fereydoon Sarmadian; investigation, Mohsen Davirand, Sajjad Teimouri; resources, Mohsen Davirand ; data curation, Fereydoon Sarmadian; writing—original draft preparation, Mohsen Davirand; writing—review and editing, Mohsen Davirand; visualization, Mohsen Davirand; supervision, Fereydoon Sarmadian; project administration, Fereydoon Sarmadian; funding acquisition, Fereydoon Sarmadian.

All authors have read and agreed to the published version of the manuscript.

All authors contributed equally to the conceptualization of the article and writing of the original and subsequent drafts.

Declaration of Generative AI and AI-assisted technologies in the writing process

The authors declare that any AI and AI-assisted software was not used for writing process.

Data availability statement

Data available on request from the authors.

Acknowledgements

The authors sincerely appreciate the support and facilities provided by University of Tehran.

Ethical considerations

The authors avoided data fabrication, falsification, and plagiarism, and any form of misconduct.

Conflict of interest

The authors declare no conflict of interest.

AbdelRahman, M. A., Metwaly, M. M., Yossif, T. M., & Moursy, A. R. (2025). Using hyperspectral data to estimate and map surface and subsurface soil salinity, pH, and calcium carbonates in arid region. Environmental Sustainability, 8(2), 367-387.
Adeli, H., et al. (2024). Application of machine learning models for soil property prediction: A systematic review and meta-analysis. Geoderma, 443, 115049. (This is a comprehensive and recent review supporting the use of ML in soil science).
Ahangar, A. G., & Piri, J. (2026). Evaluation of standard, black-box, and bayesian RSM-SVR models in the semi-arid area of south-eastern Iran for predicting soil chemical properties. Scientific Reports, 16(1), 11183.
Alijani, Z., & Sarmadian, F. (2014). The role of topography in changing of soil carbonate content. India J Sci Res, 6, 263-271.
Asgari Hafshejani, N., & Jafari, S. (2023). The study of particle size distribution of calcium carbonate and its effects on some soil properties in khuzestan province. Iran Agricultural Research, 36(2), 71-80.
Awad, M., & Fraihat, S. (2023). Recursive feature elimination with cross-validation with decision tree: Feature selection method for machine learning-based intrusion detection systems. Journal of Sensor and Actuator Networks, 12(5), 67.
Ben-Dor, E., & Banin, A. (1994). Visible and near-infrared (0.4–1.1 μm) analysis of arid and semiarid soils. Remote Sensing of Environment, 48(3), 261-274.
Bolan, N., Srivastava, P., Rao, C. S., Satyanaraya, P. V., Anderson, G. C., Bolan, S., ... & Kirkham, M. B. (2023). Distribution, characteristics and management of calcareous soils. Advances in agronomy, 182, 81-130. https://doi.org/10.1016/bs.agron.2023.06.002
Emamgolizadeh, S., Mousavi, S. R., & Taghizadeh-Mehrjardi, R. (2023). Predicting soil organic carbon using gene expression programming in a semi-arid region of Iran. Journal of Soils and Sediments, 23(4), 1567–1580.
Fayyaz, M., Davatgar, N., Mousavi, S. H., & Emamgolizadeh, S. (2024). Gene Expression Programming (GEP) for predicting soil properties: A review. Journal of Environmental Management, 350, 119565.
Ferreira, C. (2001). Gene expression programming: a new adaptive algorithm for solving problems. arXiv preprint cs/0102027.
Gallant, J. C., & Dowling, T. I. (2003). A multiresolution index of valley bottom flatness for mapping depositional areas. Water resources research, 39(12).
Gholami, A., Fathabadi, A., & Taghizadeh-Mehrjardi, R. (2022). Machine learning approaches for predicting soil properties in semi-arid regions. Environmental Earth Sciences, 81(18), 456.
Gholizadeh, H., Gamon, J. A., Zygielbaum, A. I., Wang, R., Schweiger, A. K., & Cavender-Bares, J. (2018). Remote sensing of biodiversity: Soil correction and data dimension reduction methods improve assessment of α-diversity (species richness) in prairie ecosystems. Remote Sensing of Environment, 206, 240-253.
Gorelick, N., Hancher, M., Dixon, M., Ilyushchenko, S., Thau, D., & Moore, R. (2017). Google Earth Engine: Planetary-scale geospatial analysis for everyone. Remote sensing of Environment, 202, 18-27. https://doi.org/10.1016/j.rse.2023.113567
Guo, J., Wang, K., & Jin, S. (2022). Mapping of Soil pH Based on SVM-RFE Feature Selection Algorithm. Agronomy, 12(11), 2742. https://doi.org/10.3390/agronomy12112742
Hartemink, A. E., & Barrow, N. J. (2023). The effects of pH on nutrient availability depend on both soils and plants. Plant and Soil, 487(1), 21-37.
Hengl, T., Mendes de Jesus, J., Heuvelink, G. B., Ruiperez Gonzalez, M., Kilibarda, M., Blagotić, A., ... & Kempen, B. (2017). SoilGrids250m: Global gridded soil information based on machine learning. PLoS one, 12(2), e0169748.
Hodson, T. O. (2022). Root mean square error (RMSE) or mean absolute error (MAE): When to use them or not. Geoscientific Model Development Discussions, 2022, 1-10.
Karbakhsh-ravari, E. and Sarmadian, F. (2025). Land suitability assessment using the Marcos method and its comparison with the parametric method. Iranian Journal of Soil and Water Research, 56(7), 1821-1838. doi: 10.22059/ijswr.2025.394553.669933.in Persian
Kuhn, M., & Johnson, K. (2013). Applied predictive modeling (Vol. 26, p. 13). New York: Springer.
Kumar, S. (2017). A survey of deep learning methods for relation extraction. arXiv preprint arXiv:1705.03645.
Lawal, A. I., Kwon, S., Hammed, O. S., & Idris, M. A. (2021). Blast-induced ground vibration prediction in granite quarries: An application of gene expression programming, ANFIS, and sine cosine algorithm optimized ANN. International Journal of Mining Science and Technology, 31(2), 265-277.
Lotfollahi, L., Delavar, M. A., Biswas, A., Jamshidi, M., & Taghizadeh-Mehrjardi, R. (2023). Modeling the spatial variation of calcium carbonate equivalent to depth using machine learning techniques. Environmental monitoring and assessment, 195(5), 607. https://doi.org/10.1007/s10661-023-11126-8
Lu, T., Luo, P., Wang, J., Lu, Y., Huo, A., & Liu, L. (2025). Soil salinity accumulation and groundwater degradation due to overexploitation over recent 40-year period in Yaoba Oasis, China. Soil and Tillage Research, 248, 106398.
Mahmoudabadi, E., Karimi, A., Haghnia, G. H., & Sepehr, A. (2017). Digital soil mapping using remote sensing indices, terrain attributes, and vegetation features in the rangelands of northeastern Iran. Environmental monitoring and assessment, 189(10), 500.
Makhamreh, Z. (2006). Analysis of Spectral Reflectance for Estimation of Soil Quality along a Climatic Gradient in the Eastern Mediterranean Region.
Metternicht, G. I., & Zinck, J. A. (2003). Remote sensing of soil salinity: potentials and constraints. Remote sensing of environment, 85(1), 1-20.
Montesinos López, O. A., Montesinos López, A., & Crossa, J. (2022). Overfitting, model tuning, and evaluation of prediction performance. In Multivariate statistical machine learning methods for genomic prediction (pp. 109-139). Cham: Springer International Publishing.
Mousavi, S. , Sarmadian, F. , Omid, M. and Bogaert, P. (2021). Modeling the Vertical Soil Calcium Carbonate Equivalent Variation by Machine Learning Algorithms in Qazvin Plain. Water and Soil, 35(5), 719-734. https://doi: 10.22067/jsw.2021.71748.1076. in Persian.
Mousavi, S. R., Sarmadian, F., Omid, M., & Bogaert, P. (2022). Three-dimensional mapping of soil organic carbon using soil and environmental covariates in an arid and semi-arid region of Iran. Measurement, 201, 111706.
Mousavi, S. R., Taghizadeh-Mehrjardi, R., & Rostaminia, M. (2023). Digital mapping of soil organic carbon stocks in a semi-arid region using machine learning and remote sensing. Catena, 224, Article 106985. https://doi.org/10.1016/j.catena.2023.106985
Mulder, V. L., De Bruin, S., Schaepman, M. E., & Mayr, T. R. (2011). The use of remote sensing in soil and terrain mapping—A review. Geoderma, 162(1-2), 1-19.
Nawar, S., & Mouazen, A. M. (2021). Machine learning approaches for soil classification and prediction of soil properties using proximal sensing. Soil and Tillage Research, 209, Article 104966. https://doi.org/10.1016/j.still.2021.104966
Nenkam, A. M., Wadoux, A. M. C., Minasny, B., Silatsa, F. B., Yemefack, M., Ugbaje, S. U., ... & McBratney, A. B. (2024). Applications and challenges of digital soil mapping in Africa. Geoderma, 449, 117007.
Nguyen, T. T., Shoukry, A. E., & Saraji, S. (2025). Investigating reactive transport and precipitation patterns of calcium carbonate in fractured porous media. Journal of Colloid and Interface Science, 679, 467-480.
Omondiagbe, O. P., Roudier, P., Lilburne, L., Ma, Y., & Mcneill, S. (2024). Quantifying uncertainty in the prediction of soil properties using mid-infrared spectra. Geoderma, 448, 116954.
Pereira, P., Bogunovic, I., Muñoz-Rojas, M., & Brevik, E. C. (2018). Soil ecosystem services, sustainability, valuation and management. Current Opinion in Environmental Science & Health, 5, 7-13.
Phillips, J. D. (2009). Soils as extended composite phenotypes. Geoderma, 149(1-2), 143-151.
Rahmani Siyalarz, S. , Keshavarzi, A. , Sarmadian, F. and Farahbakhsh, M. (2024). Assessment of environmental indices for soil lead contamination in a part of Shahr-e-Ray, Tehran Province. Iranian Journal of Soil and Water Research, 55(9), 1485-1503. doi: 10.22059/ijswr.2024.378270.669735. in Persian.
Ramezan, C. A. (2022). Transferability of recursive feature elimination (RFE)-derived feature sets for support vector machine land cover classification. Remote Sensing, 14(24), 6218.
Rasaei, Z., Sarmadian, F., & Jafari, A. (2025). Improving the Disaggregation of Soil Map Units Using the DSMART Method: Integrating Tree-Based Models and New Soil Profile Data. Iranian Journal of Soil and Water Research, 56(6), 1609-1629.in Persian.
Rillig, M. C., Van der Heijden, M. G., Berdugo, M., Liu, Y. R., Riedo, J., Sanz-Lazaro, C., ... & Delgado-Baquerizo, M. (2023). Increasing the number of stressors reduces soil ecosystem services worldwide. Nature Climate Change, 13(5), 478-483.
Sarmadian, F. and GHavami, M. J. (2020). Land Suitability Evaluation Using TOPSIS Method and Its Comparison with Parametric Methods for Maize Production in Part of Qazvin. Iranian Journal of Soil and Water Research, 50(9), 2275-2287. doi: 10.22059/ijswr.2019.273788.668095.in Persian.
Shahabi, A., Nabiollahi, K., Davari, M., Zeraatpisheh, M., Heung, B., Scholten, T., & Taghizadeh-Mehrjardi, R. (2022). Spatial prediction of soil properties through hybridized random forest model and combination of reflectance spectroscopy and environmental covariates. Geocarto International, 37(27), 18172-18195.
Sherrod, L. A., Erskine, R. H., & Green, T. R. (2015). Spatial Patterns and Cross‐Correlations of Temporal Changes in Soil Carbonates and Surface Elevation in a Winter Wheat–Fallow Cropping System. Soil Science Society of America Journal, 79(2), 417-427.
Shirazi, F. R. A., Shahbazi, F., Rezaei, H., & Biswas, A. (2024). Multi-property digital soil mapping at 30-m spatial resolution down to 1 m using extreme gradient boosting tree model and environmental covariates. Remote Sensing Applications: Society and Environment, 33, 101123.
Soil Survey Staff. (2022). Kellogg Soil Survey Laboratory Methods Manual. USDA Natural Resources Conservation Service.
Sun, Y. and Ellwood, M.J. (2025) Calcium Carbonate Cycling in the Southern Ocean: Insights from Dissolved Calcium and Potential Alkalinity Tracers. Limnology and Oceanography Letters.
Tadić, J. M., et al. (2023). Satellite imagery and digital elevation models for soil mapping: A review. ISPRS Journal of Photogrammetry and Remote Sensing, 197, 308-325.
Taghizadeh, R. Amirian Chekan, A. Sarmadian. And Mohammadi, J.(2018). Study of lateral and vertical distribution of soil calcium carbonate using geostatistics and spline functions. Applied Soil Research, 5(2), 1-15. in Persian.
Taghizadeh-Mehrjardi, R., Minasny, B., Toomanian, N., & Zeraatpisheh, M. (2021). Digital soil mapping: A review of challenges and opportunities in Iran. Geoderma Regional, 25, Article e00390.
Taghizadeh-Mehrjardi, R., Zeraatpisheh, M., Amirian-Chakan, A., & Scholten, T. (2024). A brief review of digital soil mapping in Iran. Remote Sensing of Soil and Land Surface Processes, 217-228.
Teimouri Bardyani, S., & Sarmadian, F. (2024). Digital mapping of soil properties (Calcium Carbonate and soil clay percentage) using landsat 8 and Prisma satellite images by the random forest algorithm. Iranian Journal of Soil and Water Research, 55(3), 381-399. in Pesrsian.
Tejedor, M., Jiménez, C. C., & Díaz, F. (2003). Use of volcanic mulch to rehabilitate saline‐sodic soils. Soil Science Society of America Journal, 67(6), 1856-1861.
UNCCD. (2017). Global Land Outlook, first edition. United Nations Convention to Combat Desertification.
Wadoux, A. M. C., Samuel‐Rosa, A., Poggio, L., & Mulder, V. L. (2020). A note on knowledge discovery and machine learning in digital soil mapping. European Journal of Soil Science, 71(2), 133-136.
Waschkowski, F., Li, H., Deshmukh, A., Grenga, T., Zhao, Y., Pitsch, H., ... & Sandberg, R. D. (2025). Gradient information and regularization for gene expression programming to develop data-driven physics closure models. Flow, Turbulence and Combustion, 114(1), 145-175
White, P. J., & Holland, J. E. (2018). Calcium in plant physiology and its availability from the soil. In White, PJ & Holland, JE Proceedings of the International Fertiliser Society 827: Calcium in Plant Physiology and its Availability from the Soil. (pp. 1-32).
Wilford, J., De Caritat, P., & Bui, E. (2015). Modelling the abundance of soil calcium carbonate across Australia using geochemical survey data and environmental predictors. Geoderma, 259, 81-92.
Yu, Z., Kuang, L., Jiang, Y., Li, W., Zhang, J., Zhou, Y., ... & Ye, Y. (2024). Soil attributes are more important than others in shaping the diversity of cultivated land quality types, southern China. Ecological Indicators, 166, 112472.
Zeng, S., Liu, Z., Jiang, Y., Goldscheider, N., Yang, Y., Zhao, M., ... & Shi, L. (2025). A greening Earth has reversed the trend of decreasing carbonate weathering under a warming climate. Nature Communications, 16(1), 2583.
Zeraatpisheh, M., Ayoubi, S., Jafari, A., Tajik, S., & Finke, P. (2019). Digital mapping of soil properties using multiple machine learning in a semi-arid region, central Iran. Geoderma, 338, 445-452.
Zhou, H., Wang, X., Wu, Y., & Zhang, X. (2021). Mechanical properties and micro-mechanisms of marine soft soil stabilized by different calcium content precursors based geopolymers. Construction and Building Materials, 305, 124722. https://doi.org/10.1016/j.conbuildmat.2021.124722
Zhou, J., Tian, Q., Nazar, S., & Huang, J. (2024). Hyper-tuning gene expression programming to develop interpretable prediction models for the strength of corncob ash-modified geopolymer concrete. Materials Today Communications, 38, 107885.
Zou, J., Wei, Y., Zhang, Y., Liu, Z., Gai, Y., Chen, H., ... & Song, Q. (2024). Remote sensing inversion of soil organic matter in cropland combining topographic factors with spectral parameters. Frontiers in Environmental Science, 12, 1420557.
       
Iranian Journal of Soil and Water Research
Volume 57, Issue 6
August 2026
Pages 1421-1445