Boukdire et al. (2025) Interpolation and Machine Learning Methods for Sub-Hourly Missing Rainfall Data Imputation in a Data-Scarce Environment: One- and Two-Step Approaches

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Identification

• Journal: Hydrology
• Year: 2025
• Date: 2025-11-10
• Authors: Mohamed Boukdire, Çağrı Alperen İnan, Giada Varra, Renata Della Morte, Luca Cozzolino
• DOI: 10.3390/hydrology12110297

Research Groups

Not specified in the provided text.

Short Summary

This study develops and evaluates machine learning and interpolation approaches for imputing missing 10-minute rainfall data, demonstrating that a two-step machine learning approach, which first classifies rain/no-rain periods, consistently outperforms direct methods and traditional interpolation techniques.

Objective

• To develop and test machine learning (Multilayer Perceptron, Random Forest) and interpolation methods (Inverse Distance Weighting, Ordinary Kriging) for the imputation of missing 10-minute rainfall data, particularly under data-scarce conditions.

Study Configuration

• Spatial Scale: Two distinct environments in the Campania region (Southern Italy): mountainous and coastal. Spatial scenarios included using all nearby stations, stations within the same cluster, and the three most highly correlated stations.
• Temporal Scale: 10-minute rainfall data. Tests included using data from the imputed time interval only and data from a time window containing several time intervals before and after the imputed time interval.

Methodology and Data

• Models used: Multilayer Perceptron (MLP), Random Forest (RF) for machine learning; Inverse Distance Weighting (IDW), Ordinary Kriging (OK) for interpolation. A Random Forest classifier was specifically used in the first step of the two-step approach.
• Data sources: Sub-hourly rainfall depth observations from rain gauges, under data-scarce conditions where rainfall depth was the only available variable.

Main Results

• The two-step approach consistently improved imputation accuracy across all spatial and temporal scenarios compared to the direct approach.
• The Random Forest classifier in the two-step approach showed strong performance in classifying rain/no-rain periods, with an average weighted F1 score of 0.961 (mountainous) and 0.957 (coastal), and average Accuracy of 0.928 (mountainous) and 0.946 (coastal).
• For the regression step, Random Forest achieved the highest performance in the mountainous area with an R² of 0.541 and a Root Mean Square Error (RMSE) of 0.109 mm, considering all stations.
• Using time windows with lagged data significantly improved results by capturing atmospheric dynamics and connecting rainfall instances across different time levels and stations.
• Machine learning models consistently outperformed spatial interpolation methods due to their ability to manage complex data structures.

Contributions

• Introduction and validation of a novel two-step imputation approach that separates rain/no-rain classification from rainfall depth estimation, leading to improved accuracy for sub-hourly rainfall data.
• Demonstration of the significant benefits of incorporating time-lagged data windows for capturing atmospheric dynamics in rainfall imputation.
• Confirmation that machine learning models are superior to traditional spatial interpolation methods for high-resolution rainfall data imputation, especially in data-scarce conditions.
• Evaluation of these methods in diverse geographical settings (mountainous and coastal) under challenging data-scarce conditions.

Funding

Not specified in the provided text.

Citation

@article{Boukdire2025Interpolation,
  author = {Boukdire, Mohamed and İnan, Çağrı Alperen and Varra, Giada and Morte, Renata Della and Cozzolino, Luca},
  title = {Interpolation and Machine Learning Methods for Sub-Hourly Missing Rainfall Data Imputation in a Data-Scarce Environment: One- and Two-Step Approaches},
  journal = {Hydrology},
  year = {2025},
  doi = {10.3390/hydrology12110297},
  url = {https://doi.org/10.3390/hydrology12110297}
}