Najib et al. (2026) Quantile mapping using the Alpha Power Transformed X-Lindley (APTXL) distribution for bias correction of Coupled Model Intercomparison Project Phase 6 (CMIP6) outputs: a case study over the Toba Lake region

Identification

• Journal: Theoretical and Applied Climatology
• Year: 2026
• Date: 2026-01-01
• Authors: Mohamad Khoirun Najib, Sri NURDIATI, Elis Khatizah, Aulia Rizki Firdawanti, Hendri Irwandi, Mirza Farhan Azhari, Nicholas Abisha
• DOI: 10.1007/s00704-025-05975-1

Research Groups

• Division of Computational Mathematics, IPB University, Bogor, Indonesia
• Division of Statistical Modelling and Data Analysis, IPB University, Bogor, Indonesia
• Research Center for Climate and Atmosphere, National Research and Innovation Agency (BRIN), Central Jakarta, Indonesia
• Applied Mathematics, IPB University, Bogor, Indonesia

Short Summary

This study evaluates various quantile mapping (QM) approaches for bias correction of CMIP6 monthly rainfall outputs over the Toba Lake region, Indonesia. It finds that the Alpha Power Transformed X-Lindley (APTXL) distribution, particularly when combined with a Sliding 3-Month Window parametric QM, provides the most consistent and robust improvements in correcting rainfall magnitude and variability, despite not always being the statistically best-fitting distribution.

Objective

• To introduce and evaluate a quantile mapping framework using the Alpha Power Transformed X-Lindley (APTXL) distribution for bias correction of CMIP6 monthly rainfall outputs over the Toba Lake region.
• To compare the APTXL-based method against other parametric, semi-parametric, and non-parametric quantile mapping approaches, including a sliding 3-month window technique, to identify the most effective strategy for tropical rainfall bias correction.

Study Configuration

• Spatial Scale: The Toba Lake region in North Sumatra, Indonesia, covering a catchment area of approximately 2,486 square kilometers. The study utilized data from 13 meteorological observation stations within and around the basin.
• Temporal Scale: Monthly precipitation records over a 34-year period (1981–2014). This period was divided into a 20-year calibration period (1981–2000) and a 14-year validation period (2001–2014).

Methodology and Data

• Models used:
  • Climate Models: Four Coupled Model Intercomparison Project Phase 6 (CMIP6) General Circulation Models (GCMs): ACCESS-ESM1-5, BCC-CSM2-MR, CNRM-ESM2-1, and EC-Earth3-Veg-LR.
  • Bias Correction Methods: Non-parametric Quantile Mapping (EQM), Semi-parametric Quantile Mapping (SPQM), Parametric Quantile Mapping (PQM), and Parametric Quantile Mapping with a Sliding 3-Month Window technique.
  • Probability Distributions: Alpha Power Transformed X-Lindley (APTXL), Gamma, Lognormal, Weibull, Exponential, Normal, Log-logistic, Generalized Extreme Value (GEV), Inverse Gaussian, and Logistic distributions.
  • Statistical Tests: Augmented Dickey–Fuller (ADF) test for stationarity and Mann–Kendall (MK) test with Sen’s slope estimator for trend detection.
  • Interpolation: Bilinear interpolation to extract model outputs at station locations.
  • Evaluation Metrics: Taylor Diagram (spatial correlation coefficient, standard deviation, centered root-mean-square difference), Interannual Variability Skill (IVS), Mean Absolute Error (MAE), and Comprehensive Rating Index (CRI).
• Data sources:
  • Observational Data: Monthly precipitation records from 13 meteorological stations operated by Indonesia’s Meteorological, Climatological, and Geophysical Agency (BMKG).
  • CMIP6 Model Data: Raw monthly precipitation outputs from the selected CMIP6 GCMs, obtained from the Copernicus Climate Data Store (CDS).

Main Results

• Raw CMIP6 models systematically overestimate median rainfall in the Toba Lake region and exhibit substantial biases in variability and extreme events.
• All 13 observational rainfall series were found to be stationary (ADF test), with mixed increasing, decreasing, or no significant monotonic trends (Mann–Kendall test).
• While classical distributions like Weibull, Gamma, Lognormal, and GEV frequently provided the best statistical fit to raw rainfall data, the Alpha Power Transformed X-Lindley (APTXL) distribution showed the most consistent and robust performance in the bias correction framework.
• The Parametric Quantile Mapping (PQM) approach using the APTXL distribution consistently ranked among the top methods across all evaluation metrics (low cRMSE and MAE, IVS close to zero, high CC).
• The Sliding 3-Month Window PQM–APTXL approach achieved the highest Comprehensive Rating Index (CRI = 0.712) among all tested methods and distributions, demonstrating superior correction skill, improved seasonal responsiveness, and stable parametric behavior.
• Post-correction evaluation revealed that the EC-Earth3-Veg-LR model consistently performed best, followed by ACCESS-ESM1-5, while the multi-model ensemble mean generally outperformed individual GCMs.
• The SlidingQM–APTXL method delivered substantial reductions in rainfall magnitude errors, with average MAE improvements ranging from 10% to 40% across stations and models, and an average improvement of 30.8% for the ensemble mean.

Contributions

• Introduces and rigorously evaluates the Alpha Power Transformed X-Lindley (APTXL) distribution as a highly effective parametric distribution for bias correction of climate model rainfall outputs in complex tropical environments.
• Demonstrates that statistical goodness-of-fit alone is an insufficient criterion for selecting optimal distributions for bias correction; functional correction performance, as assessed by a comprehensive rating index (CRI), is critical.
• Highlights the superior performance of a seasonally adaptive (Sliding 3-Month Window) parametric quantile mapping approach, particularly when combined with APTXL, for effectively addressing strong seasonal dynamics and preserving interannual variability.
• Provides a robust, validated methodology for improving the reliability of CMIP6 rainfall projections, enhancing their applicability for hydrological modeling and climate-impact assessments in data-scarce, topographically complex tropical regions like the Toba Lake basin.

Funding

• IPB University, "Dana Masyarakat IPB Tahun Anggaran 2025", under the "Skema Penelitian Dosen Muda Tahun Anggaran 2025", Grant Number 10816/IT3.D10/PT.01.03/P/B/2025.

Citation

@article{Najib2026Quantile,
  author = {Najib, Mohamad Khoirun and NURDIATI, Sri and Khatizah, Elis and Firdawanti, Aulia Rizki and Irwandi, Hendri and Azhari, Mirza Farhan and Abisha, Nicholas},
  title = {Quantile mapping using the Alpha Power Transformed X-Lindley (APTXL) distribution for bias correction of Coupled Model Intercomparison Project Phase 6 (CMIP6) outputs: a case study over the Toba Lake region},
  journal = {Theoretical and Applied Climatology},
  year = {2026},
  doi = {10.1007/s00704-025-05975-1},
  url = {https://doi.org/10.1007/s00704-025-05975-1}
}