Rehamnia et al. (2025) Evaluating the role of dimensionality and complexity structure in time series models for precipitation simulation

Identification

• Journal: Modeling Earth Systems and Environment
• Year: 2025
• Date: 2025-10-18
• Authors: Issam Rehamnia, Mohammad Nazeri Tahroudi, Mehri Saeidinia
• DOI: 10.1007/s40808-025-02649-9

Research Groups

• Badji Mokhtar University, Annaba, Algeria
• Lorestan University, Khorramabad, Iran

Short Summary

This study evaluates various linear and nonlinear time series models for monthly precipitation simulation across 12 stations in Algeria, finding that the optimal model depends on input variables and station-specific precipitation dynamics rather than a universal best fit.

Objective

• To model monthly precipitation in the Kébir-Rhumel watershed, Algeria, by evaluating the performance of a novel ensemble of linear, nonlinear, and hybrid time series models under two scenarios to assess the impact of input dimensionality and station-specificity.

Study Configuration

• Spatial Scale: Kébir-Rhumel watershed in northeastern Algeria (8,908 km² area, 532 km perimeter), covering 12 weather stations: Ain Fakroun, Bella, Bir Drimil, Bir el Arch, Chelghoum Laid, Constantine-ONM, Djemila, El Kheneg, El Milia, Ferdj Mzala, Redjas Ferada, and Settara.
• Temporal Scale: Monthly precipitation and temperature data from January 1981 to December 2019 (39 years).

Methodology and Data

• Models used:
  • CARMA-ARCH (CA)
  • CARMA-GARCH (CG)
  • Optimized-CARMA-ARCH (OCA)
  • Optimized-CARMA-GARCH (OCG)
  • Bayesian-Optimized-CARMA-ARCH (BOCA)
  • Bayesian-Optimized-CARMA-GARCH (BOCG)
  • Bilinear-ARCH (BL)
  • Bilinear-GARCH (BLG)
• Data sources: Monthly precipitation and temperature data from 12 weather stations in the Kébir-Rhumel watershed, provided by the National Agency of Hydraulic Resources (ANRH).

Main Results

• Scenario 1 (Uniform inputs: Temperature at lags 0 and 1):
  • Simple hybrid models (CA, CG) and their optimized versions (OCA, OCG) performed well, yielding an average error of 17 mm.
  • Bilinear-based models (BL, BLG) exhibited the weakest performance.
  • Bayesian optimization did not significantly improve the performance of base models.
  • All models showed acceptable performance, with correlation coefficients exceeding 0.90 between observed and simulated precipitation.
• Scenario 2 (Station-specific, increased inputs including precipitation lags):
  • The average error decreased by 12 mm compared to Scenario 1.
  • The top-performing models shifted towards Bilinear-based models (BL, BLG), especially with the addition of temperature at lags 3 and 6 and precipitation at lag 6.
  • Bilinear models demonstrated superior performance due to their ability to handle increased fluctuations caused by precipitation lags.
  • Bayesian optimization degraded performance at most stations in this scenario.
  • All models demonstrated acceptable performance, with Nash-Sutcliffe Efficiency (NSE) coefficients exceeding 0.72 across all stations.
  • The range of Root Mean Square Error (RMSE) values decreased, and the performance gap between the worst and best models narrowed significantly (maximum difference reduced by approximately 44%).
  • Percentage improvement in RMSE from Scenario 1 to Scenario 2 for the best-performing models ranged from 0.4% to 11%.
• Overall: No single universally optimal model exists; the best model depends critically on the input variables and the specific memory effects and volatility patterns present at each station.

Contributions

• Integration of bilinear and GARCH structures into a novel comparative framework for evaluating a diverse suite of linear, bilinear, and heteroskedastic models under consistent scenarios.
• Introduction of an innovative two-scenario experimental framework to explicitly evaluate the effects of input dimensionality and station-specificity on model performance, challenging conventional one-size-fits-all modeling paradigms.
• Empirical evidence demonstrating that model performance is intrinsically linked to local precipitation-generating processes, particularly the memory of volatility and the relevance of long-lag inputs.
• Provision of a framework for selecting model complexity based on data availability, enhancing forecasting accuracy.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Citation

@article{Rehamnia2025Evaluating,
  author = {Rehamnia, Issam and Tahroudi, Mohammad Nazeri and Saeidinia, Mehri},
  title = {Evaluating the role of dimensionality and complexity structure in time series models for precipitation simulation},
  journal = {Modeling Earth Systems and Environment},
  year = {2025},
  doi = {10.1007/s40808-025-02649-9},
  url = {https://doi.org/10.1007/s40808-025-02649-9}
}