Estimation and validation of daily global solar radiation by day of the year-based models for different climates in China

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A total of 7 empirical models and 7 machine learning models are established and validated in this study.

Measured data from 1994 to 2015 at 35 stations are analyzed, covering all the climate zones in China.

A novel hybrid 3rd order polynomial and sine wave equation is introduced to improve estimation accuracy.

ANFIS-CFA and ANFIS-WOASAR are newly proposed, which demonstrate superb adaptability to diverse climatic conditions.


Day of the year-based (DYB) models can achieve great accuracy in daily global solar radiation estimation without specific meteorological elements. Many empirical models (EMs) and machine learning (ML) methods have been proposed for DYB models. However, the number of their comparative studies based on diverse climates is limited. In this study, a grand total of 14 DYB models are established to estimate daily global solar radiation based on measured data from 1994 to 2015 at 35 meteorological stations in six climate zones of China. Detailed tasks are as follows: (1) Seven EMs and seven ML models are trained for solar radiation estimation. (2) A new EM and two novel ML models are proposed, i.e. hybrid 3rd order polynomial and sine wave model, adaptive neuro-fuzzy inference system (ANFIS) optimized by chaotic firefly algorithm (CFA) and ANFIS optimized by whale optimization algorithm with simulated annealing and roulette wheel selection (WOASAR). (3) Four statistical indicators are utilized to compare those models, and the best model for each station is decided. (4) We discuss the model parameters and climate variances of six specific stations in different climate zones. The comparison results demonstrate superb estimation precision and climate adaptability of the newly proposed models.


Global solar radiation estimation

Day of the year

Empirical models

Machine learning

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