Zhao et al. (2026) Analysis of urban design rainstorm patterns based on parameter estimation and model approaches

Identification

• Journal: Stochastic Environmental Research and Risk Assessment
• Year: 2026
• Date: 2026-04-01
• Authors: Jun Zhao, Lin Yang, Long Zhu, Cuishan Liu, Zhenxin Bao, Min Liu, Qiyan Huang, Sadashiv Chaturvedi, Y. L. Liu, Yuhan Zhao
• DOI: 10.1007/s00477-026-03202-5

Research Groups

• Nanjing University of Information Science and Technology, Nanjing, Jiangsu Province, China
• Nanjing Hydraulic Research Institute, Nanjing, Jiangsu Province, China
• Yangtze Institute for Conservation and Development, Nanjing, Jiangsu Province, China
• Jiangxi Yuanhuiqu Project Management Bureau, Xinyu, Jiangxi Province, China
• Dipartimento di Ingegneria Civile, Edile e Ambientale (DICEA), University of Naples Federico II, Naples, Italy
• Institute of Environment and Sustainable Development (IESD), Banaras Hindu University, Varanasi, India
• IUSS, Pavia, University Institute of Higher Studies, Pavia, Italy
• College of Hydraulic and Architectural Engineering, Tarim University, Alar, Xinjiang Uygur Autonomous Region, China

Short Summary

This study develops an integrated multi-scale framework for urban design storm characterization in Nanjing, China, by evaluating sampling methods and parameter estimation techniques for Pearson Type III distribution and proposing a hybridized approach for constructing design rainstorm patterns across various durations. The findings recommend the annual multiple sampling method and the double weight function for optimal parameter estimation, and an integrated framework for hyetograph construction, enhancing urban flood risk assessment and climate-adaptive engineering.

Objective

• To establish a comprehensive, multi-dimensional framework for urban design storm characterization in Nanjing, China, by systematically comparing statistical sampling and parameter estimation methods for rainstorm frequency analysis, identifying dominant rainstorm patterns, and developing an integrated multi-scale approach for constructing design rainstorm hyetographs across various durations and return periods.

Study Configuration

• Spatial Scale: Nanjing, China, a pivotal riparian hub in the lower Yangtze River basin, utilizing data from seven rainfall stations.
• Temporal Scale: Rainfall series spanning 1988–2015 (28 years). Analysis of storm durations from 10800 seconds (3 hours) to 86400 seconds (24 hours), and return periods of 0.1%, 1%, and 5% (equivalent to 1000, 100, and 20 years, respectively).

Methodology and Data

• Models used:
  • Distribution: Pearson Type III (P-III) distribution.
  • Parameter Estimation: Curve-fitting method (CFM) (using Ordinary Least Squares (OLS), Absolute Sum (ABS), Weighted Least Squares (WLS) criteria with Levenberg–Marquardt and Hooke-Jeeves algorithms), Double Weight Function (DWF) method, L-moments (LM) method, Probability Weighted Moments (PWM) method.
  • Sampling Methods: Annual Maximum Series (AMS), Annual Multiple Method (AMM, with k=3 events per year).
  • Rainstorm Pattern Recognition: Fuzzy pattern recognition (categorizing into 7 archetypal rainfall profiles).
  • Design Rainstorm Pattern Construction: Chicago method (for 10800 s to 86400 s durations), Pilgrim & Cordery (P&C) method (for 10800 s duration), Same-frequency analysis method (for 86400 s duration).
  • Statistical Tests: Bootstrap confidence bands (95% confidence level, 1000 replications), Kolmogorov–Smirnov (K-S) test, Analysis of Variance (ANOVA), Root Mean Square Error (RMSE).
• Data sources: High-resolution rainfall series from 7 automatic rain gauges in Nanjing, China, obtained from the Nanjing Hydrological Bureau. Data quality control and homogeneity correction were performed.

Main Results

• Sampling Methods: The Annual Multiple Method (AMM) is recommended for urban environments, providing a superior representation of frequent, lower-magnitude events critical for urban resilience. Differences between AMM and Annual Maximum Series (AMS) are generally within ±5% for common hydrological designs but diverge more at extreme return periods.
• Parameter Estimation (for P-III distribution):
  • Unbiasedness: The Double Weight Function (DWF) method consistently demonstrated the highest unbiasedness (smallest mean deviation) across different distribution scenarios.
  • Robustness: The DWF method exhibited the best robustness against outliers (e.g., average deviation of +4.6% at 0.1% exceedance probability), followed by the L-moments method. The curve-fitting method showed the weakest robustness.
  • Goodness-of-Fit: For low-frequency events (5% exceedance probability), the L-moments method achieved the lowest RMSE (0.0055 m). For high-frequency (extreme) events (<1% exceedance probability), the DWF method achieved the lowest RMSE (0.0092 m) and optimal confidence band convergence.
• Rainstorm Patterns (Nanjing): Fuzzy pattern recognition identified three dominant regional hyetotypes: single-peak (most frequent, 54.10–64.25%), multi-peak (23.16–28.42%), and uniform (12.63–18.95%). Type I (front-peak) was the most common.
• Design Rainstorm Pattern Construction:
  • Chicago Method: Demonstrated good reliability for total rainfall intensity (relative deviation <4% compared to the IDF formula), with highest accuracy for short durations (e.g., 10800 s, ~ -2% deviation). It primarily generates single-peak patterns.
  • Pilgrim & Cordery (P&C) Method: For 10800 s duration, it revealed multiple rainfall peaks, with the second peak being the largest, and showed good statistical representativeness for local storm events.
  • Same-Frequency Analysis Method: For 86400 s duration, it effectively preserved peak intensity and rainfall depth within sub-periods, reducing sensitivity to individual extreme events.
• Integrated Framework: A hybridized approach is proposed: the Chicago method for medium-duration (10800 s to 86400 s) parametric standardization; the P&C method for preserving short-duration (10800 s) stochastic peak complexities; and same-frequency scaling for 86400 s watershed-scale flood control.

Contributions

• Establishes a comprehensive, multi-dimensional, and non-stationarity-adaptive framework for urban design storm analysis by integrating sample selection, probability distribution fitting, parameter estimation, and multi-duration pattern construction.
• Provides empirical evidence for rainstorm sampling strategies in rapidly urbanizing regions, validating the applicability and stability of the annual multiple method for urban drainage engineering design.
• Offers regional empirical evidence and a transferable technical approach for parameter estimation of high-intensity rainstorms in the East Asian monsoon region, recommending the Double Weight Function method for its superior unbiasedness and robustness.
• Reveals the temporal distribution characteristics of rainstorm intensity across various durations, providing important guidance for hydrometeorological forecasting and early warning.
• Presents a case study in method integration and regional adaptability analysis for global urban rainstorm pattern research by incorporating multiple internationally recognized rainfall pattern construction methods.
• Provides a more reliable scientific basis and technical standard for urban flood control planning, risk management, climate-adaptive municipal engineering, and disaster mitigation strategies.

Funding

• National Key Research and Development Program of China (No. 2022YFC3202300)
• National Natural Science Foundation of China (NSFC) Projects (Nos. U2240203, 52121006)
• Project funded by Ningbo City 'Ke Chuang Yongjiang 2035' Key R&D Program (2025Z036)
• Science and Technology Program of Ili Kazakh Autonomous Prefecture, China (No. YHZ2024B02)

Citation

@article{Zhao2026Analysis,
  author = {Zhao, Jun and Yang, Lin and Zhu, Long and Liu, Cuishan and Bao, Zhenxin and Liu, Min and Huang, Qiyan and Chaturvedi, Sadashiv and Liu, Y. L. and Zhao, Yuhan},
  title = {Analysis of urban design rainstorm patterns based on parameter estimation and model approaches},
  journal = {Stochastic Environmental Research and Risk Assessment},
  year = {2026},
  doi = {10.1007/s00477-026-03202-5},
  url = {https://doi.org/10.1007/s00477-026-03202-5}
}