Integrating Piecewise And Symbolic Regression With Remote Sensing Data For Spatiotemporal Analysis Of Surface Water Total Dissolved Solids In The Karun River, Iran

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Integrating piecewise and symbolic regression with remote sensing data for spatiotemporal analysis of surface water total dissolved solids in the Karun River, Iran

This research article addresses the critical need for cost-effective water quality monitoring by developing a novel hybrid approach to estimate Total Dissolved Solids (TDS) in Iran’s Karun River. Since traditional monitoring is often logistically and financially burdensome, the researchers integrated Landsat-9 satellite imagery—specifically the red and near-infrared bands—with advanced machine learning techniques to enable spatiotemporal analysis. The study evaluated four distinct modeling methods: nonlinear regression (NLR), the M5P model tree, multivariate adaptive regression splines (MARS), and symbolic regression (SR). Field sampling was conducted along a four-kilometer stretch of the river to calibrate these algorithms, synchronizing in-situ measurements with satellite overpasses. Data processing was facilitated by the Google Earth Engine platform, which provided a cloud-based environment for atmospheric correction and image analysis.

To ensure the reliability of the predictions, the authors introduced an innovative framework for quantifying uncertainty using fuzzy-based interval analysis and the Analytic Hierarchy Process (AHP) weighting. The efficiency of each model was then assessed using the Composite Uncertainty Index (CUI). Results indicated that standard nonlinear regression was insufficient for capturing the complex dynamics of TDS. While symbolic regression showed high simulation efficiency, it also exhibited the widest uncertainty bandwidth. Ultimately, the MARS and M5P models were identified as the most effective performers, achieving CUI values of 0.83 and 0.72, respectively. MARS proved superior under conditions of low uncertainty, whereas M5P was more robust in scenarios with higher input uncertainty due to its lower sensitivity. These findings provide water managers with a transformative tool for identifying pollution hotspots and supporting evidence-based decision-making in sustainable watershed management.

Figure 1: a) The red and b) near-infrared reflectance bands of Landsat-9 Collection 2 for the May 24, 2024, sampling date by QGIS (The blue points represent sampling points), and c) a Google Earth Pro image accessed on May 2024, with sampling locations.

Reference:

Zahiri, J., Nikoo, M. R., Moradi-Sabzkouhi, A., Cheraghi, M., & Nawi, N. M. (2025). Integrating piecewise and symbolic regression with remote sensing data for spatiotemporal analysis of surface water total dissolved solids in the Karun River, Iran. Results in Engineering, 25, 104159.

Link:

https://doi.org/

Reference:

Zahiri, J., Nikoo, M. R., Moradi-Sabzkouhi, A., Cheraghi, M., & Nawi, N. M. (2025). Integrating piecewise and symbolic regression with remote sensing data for spatiotemporal analysis of surface water total dissolved solids in the Karun River, Iran. Results in Engineering, 25, 104159. https://doi.org/10.1016/j.rineng.2025.104159

Date of Input: 27/02/2026 | Updated: 27/02/2026 | ainzubaidah

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This research article addresses the critical need for cost-effective water quality monitoring by developing a novel hybrid approach to estimate Total Dissolved Solids (TDS) in Iran’s Karun River. Since traditional monitoring is often logistically and financially burdensome, the researchers integrated Landsat-9 satellite imagery—specifically the red and near-infrared bands—with advanced machine learning techniques to enable spatiotemporal analysis. The study evaluated four distinct modeling methods: nonlinear regression (NLR), the M5P model tree, multivariate adaptive regression splines (MARS), and symbolic regression (SR). Field sampling was conducted along a four-kilometer stretch of the river to calibrate these algorithms, synchronizing in-situ measurements with satellite overpasses. Data processing was facilitated by the Google Earth Engine platform, which provided a cloud-based environment for atmospheric correction and image analysis. To ensure the reliability of the predictions, the authors introduced an innovative framework for quantifying uncertainty using fuzzy-based interval analysis and the Analytic Hierarchy Process (AHP) weighting. The efficiency of each model was then assessed using the Composite Uncertainty Index (CUI). Results indicated that standard nonlinear regression was insufficient for capturing the complex dynamics of TDS. While symbolic regression showed high simulation efficiency, it also exhibited the widest uncertainty bandwidth. Ultimately, the MARS and M5P models were identified as the most effective performers, achieving CUI values of 0.83 and 0.72, respectively. MARS proved superior under conditions of low uncertainty, whereas M5P was more robust in scenarios with higher input uncertainty due to its lower sensitivity. These findings provide water managers with a transformative tool for identifying pollution hotspots and supporting evidence-based decision-making in sustainable watershed management.


Figure 1: a) The red and b) near-infrared reflectance bands of Landsat-9 Collection 2 for the May 24, 2024, sampling date by QGIS (The blue points represent sampling points), and c) a Google Earth Pro image accessed on May 2024, with sampling locations.

Reference: Zahiri, J., Nikoo, M. R., Moradi-Sabzkouhi, A., Cheraghi, M., & Nawi, N. M. (2025). Integrating piecewise and symbolic regression with remote sensing data for spatiotemporal analysis of surface water total dissolved solids in the Karun River, Iran. Results in Engineering, 25, 104159.

Link: https://doi.org/