Kale et al. (2025) Water evaporation forecasting using a deep learning model based on Perrin sequence CNN and minimization techniques

Identification

• Journal: Theoretical and Applied Climatology
• Year: 2025
• Date: 2025-12-12
• Authors: Jaydeep Narayan Kale, Sanjay Kumar Sharma
• DOI: 10.1007/s00704-025-05935-9

Research Groups

• Department of Computer Science & Engineering, Oriental University, Indore, MP, India

Short Summary

This study introduces a novel deep learning model, the Perrin Sequence Convolutional Neural Network (PS-CNN), for accurate water evaporation forecasting by integrating the Perrin mathematical sequence into its convolutional layers to capture complex spatio-temporal patterns. Tested on a 15-year climate dataset from India, the PS-CNN significantly outperforms traditional and existing deep learning methods, achieving a Mean Absolute Error of 0.17 mm/day and a Coefficient of Determination (R²) of 0.93.

Objective

• To develop and evaluate a novel deep learning model, the Perrin Sequence Convolutional Neural Network (PS-CNN), for accurate water evaporation forecasting under diverse environmental conditions, leveraging advanced data pre-processing and intelligent feature selection.

Study Configuration

• Spatial Scale: Global coverage at 0.25 degree (approximately 25 km) spatial resolution, with specific application and testing across India.
• Temporal Scale: 15-year period (2010-2025) with daily frequency.

Methodology and Data

• Models used:
  • Proposed: Perrin Sequence Convolutional Neural Network (PS-CNN).
  • Comparative: Long Short-Term Memory (LSTM), Convolutional Neural Network (CNN), Support Vector Machine (SVM), Hybrid Machine Learning (Hybrid ML), Penman equation, Dalton equation.
  • Pre-processing techniques: Isolation Forest (outlier detection), K-Nearest Neighbors (KNN) imputation and linear interpolation (missing values), Savitzky–Golay (SG) filter (noise reduction), Min–Max Normalization and Z-score Standardization (feature scaling).
  • Feature Selection: Hyperbolic Tangent based Krill Herd (HT-KH) algorithm.
• Data sources:
  • Global Land Evaporation Amsterdam Model (GLEAM) dataset.
  • Input features: Air temperature (°C), relative humidity (%), solar radiation (W/m²), wind speed (m/s), precipitation (mm), surface soil moisture (m³/m³), and net radiation (W/m²).
  • GLEAM dataset integrates remote sensing data from SMOS, ASCAT, ESA CCI (soil moisture), NDVI, LAI (vegetation indices), CERES, NASA SRB (radiation), temperature measurements, and MSWEP or reanalysis sources (precipitation).

Main Results

• The proposed PS-CNN model achieved superior predictive performance with a Mean Absolute Error (MAE) of 0.17 mm/day, Root Mean Square Error (RMSE) of 0.20 mm/day, Mean Absolute Percentage Error (MAPE) of 6.7%, Relative Absolute Error (RAE) of 0.58, Relative Squared Error (RSE) of 0.50, and a Coefficient of Determination (R²) of 0.93.
• The PS-CNN model significantly outperformed traditional empirical methods (Penman, Dalton) and existing deep learning and hybrid models (LSTM, CNN, SVM, Hybrid ML) across all evaluated metrics.
• The model demonstrated high computational efficiency with a training time of approximately 0.55 seconds and an inference time of about 0.35 seconds.

Contributions

• Introduction of a novel deep learning model, the Perrin Sequence Convolutional Neural Network (PS-CNN), which integrates the Perrin mathematical sequence into its convolutional layers for enhanced capture of spatio-temporal patterns in environmental data. This is one of the first applications of the Perrin sequence in a deep learning model for environmental forecasting.
• Development of a comprehensive data pre-processing pipeline including Isolation Forest for outlier detection, KNN and linear interpolation for missing value imputation, Savitzky–Golay filter for noise reduction, and Min–Max/Z-score scaling for feature normalization.
• Implementation of an intelligent feature selection method using the Hyperbolic Tangent based Krill Herd (HT-KH) algorithm to minimize redundant features and improve model stability and training speed.
• The model effectively learns complex, nonlinear relationships and temporal dependencies between meteorological factors and water evaporation rates, providing highly accurate and reliable forecasts.

Funding

• This research article has not been funded by anyone.

Citation

@article{Kale2025Water,
  author = {Kale, Jaydeep Narayan and Sharma, Sanjay Kumar},
  title = {Water evaporation forecasting using a deep learning model based on Perrin sequence CNN and minimization techniques},
  journal = {Theoretical and Applied Climatology},
  year = {2025},
  doi = {10.1007/s00704-025-05935-9},
  url = {https://doi.org/10.1007/s00704-025-05935-9}
}