Nivar

Nivar

Validation of Combined Empirical Mode Decomposition with Normal Transformation in Climate Elements Forecasting

Document Type : Original Article

Author
Azarbaijan Shahid Madani University
Abstract
The non-stationary nature and skewness of time series due to various factors, including human activities, have created a new challenge in forecasting climate elements. To increase the accuracy of the forecasting process and overcome the skewness of time series, an algorithm was proposed and evaluated in three climates: arid, semi-arid, and very humid with maximum temperature data and total sunshine hours. The algorithm is based on time series decomposition using the empirical mode decomposition (EMD) approach and then normalizing the decomposed series. Series decomposition and then normalization of subseries were able to significantly improve modeling performance, so that the average reduction in root mean square error at five stations from the maximum temperature data without decomposition to series decomposition and normalization of decomposed subseries was 11.22 and 22.94 percent, respectively. The proposed algorithm had minimal error in modeling average temperature and total sunshine hours in dry and very humid climates, respectively. In the case of maximum temperature, except for the Birjand station, all other stations have underestimates, and in the case of sunshine hour data, only stations in arid climates have underestimates. Therefore, the type of climate can affect the modeling performance. The type of normalized sub-series can also affect the evaluation statistics. Combining empirical mode decomposition with normal transformation has satisfactory performance, especially in the case of non-stationary series, which can play an effective role as an efficient tool in complex modeling.
Keywords
Subjects

 1.       Pezeshki, Z., Geraylo, H., & Soleimani Ivari, S. A. (2018). Noise removal of temperature using wavelet transform and temperature prediction with SVM and inverse wavelet method. Scientific Journal of Research in Computer Sciences, (10), 1–18. (In Persian; )
2.       Roshangar, K., & Abdolzadeh, S. (2023). River discharge prediction using a hybrid long short-term memory, wavelet transform, and empirical mode decomposition approach in semi-arid and humid climates. Iranian Journal of Irrigation and Drainage, 17(4), 703–717. (In Persian)
3.       Shahi Nejad, B., & Dehghani, R. (2016). Application of wavelet neural networks in estimating mean air temperature of Sari County. Climatological Research, 7(27), 75–86. (In Persian)
4.       Salehi, S. M., Radmanesh, F., Zarei, H., Mansouri, B., & Selgi, A. (2018). Groundwater level prediction using a hybrid time series–wavelet model (Case study: Firuzabad Plain). Irrigation Sciences and Engineering, 41(4), 1–16. (In Persian)
5.       Agnieszka, W., & Dawid, K. (2022). Modeling seasonal oscillations in GNSS time series with complementary ensemble empirical mode decomposition. GPS Solutions, 26(4), 101. https://doi.org/10.1007/s10291-022-01300-1
6.       Cho, D., Yoo, C., Son, B., Im, J., Yoon, D., & Cha, D. H. (2022). A novel ensemble learning for post-processing of NWP model’s next-day maximum air temperature forecast in summer using deep learning and statistical approaches. Weather and Climate Extremes, 35, 100410. https://doi.org/10.1016/j.wace.2021.100410
7.       Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N. C., Tung, C. C., & Liu, H. H. (1998). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 454(1971), 903–995. https://doi.org/10.1098/rspa.1998.0193
8.       Kang, Y., Cheng, X., Chen, P., Zhang, S., & Yang, Q. (2023). Monthly runoff prediction by a multivariate hybrid model based on decomposition-normality and Lasso regression. Environmental Science and Pollution Research, 30(10), 27743–27762. https://doi.org/10.1007/s11356-022-24145-3
9.       Licer, M., Belmajdoub, H., & Minaoui, K. (2025). Enhanced deep learning approach for improved maximum temperature forecasting: A case study in the Sahara region, Morocco. Theoretical and Applied Climatology, 156(1), 1–14. https://doi.org/10.1007/s00704-024-04628-3
10.   Lin, M. L., Tsai, C. W., & Chen, C. K. (2021). Daily maximum temperature forecasting in changing climate using a hybrid of multi-dimensional complementary ensemble empirical mode decomposition and radial basis function neural network. Journal of Hydrology: Regional Studies, 38, 100923. https://doi.org/10.1016/j.ejrh.2021.100923
11.   Liu, Z., Cheng, M., Li, Z., Huang, Z., Liu, Q., Xie, Y., & Chen, E. (2024). Adaptive normalization for non-stationary time series forecasting: A temporal slice perspective. Advances in Neural Information Processing Systems, 36.
12.   Muchtadi-Alamsyah, I., Viltoriano, R., Harjono, F., Nazaretha, M., Susilo, M., Bayu, A., Josaphat, B., Hakim, A., & Syuhada, K. (2024). Support vector regression–based heteroscedastic models for cryptocurrency risk forecasting. Applied Soft Computing, 111792. https://doi.org/10.1016/j.asoc.2024.111792
13.   Salarijazi, M., Ghorbani, K., Mohammadi, M., Ahmadianfar, I., Mohammadrezapour, O., Naser, M. H., & Yaseen, Z. M. (2023). Spatial–temporal estimation of maximum temperature high return periods for annual time series considering stationary and nonstationary approaches in Iranian urban areas. Urban Climate, 49, 101504. https://doi.org/10.1016/j.uclim.2023.101504
14.   Shamshirband, S., Mohammadi, K., Khorasanizadeh, H., Yee, L., Lee, M., Petković, D., & Zalnezhad, E. (2016). Estimating the diffuse solar radiation using a coupled support vector machine–wavelet transform model. Renewable and Sustainable Energy Reviews, 56, 428–435. https://doi.org/10.1016/j.rser.2015.11.055
15.   Stallone, A., Cicone, A., & Materassi, M. (2020). New insights and best practices for the successful use of empirical mode decomposition, iterative filtering, and derived algorithms. Scientific Reports, 10(1), 15161. https://doi.org/10.1038/s41598-020-72166-6
16.   Velivelli, S., Satyanarayana, G. C., & Ali, M. M. (2024). Predicting daily maximum temperature over Andhra Pradesh using machine learning techniques. Theoretical and Applied Climatology, 155(9), 8567–8585. https://doi.org/10.1007/s00704-023-04677-8
17.Volvach, A., Kurbasova, G., & Volvach, L. (2024). Wavelets in the analysis of local time series of the Earth’s surface air temperature. Heliyon, 10(1), e23741. https://doi.org/10.1016/j.heliyon.2024.e23741
Volume 49, 130-131 - Serial Number 130
October 2025
Pages 160-176

  • Receive Date 17 February 2025
  • Revise Date 17 March 2025
  • Accept Date 19 May 2025
  • Publish Date 23 September 2025