University of Oulu

Seifi, A., Ehteram, M., Nayebloei, F. et al. GLUE uncertainty analysis of hybrid models for predicting hourly soil temperature and application wavelet coherence analysis for correlation with meteorological variables. Soft Comput 25, 10723–10748 (2021).

GLUE uncertainty analysis of hybrid models for predicting hourly soil temperature and application wavelet coherence analysis for correlation with meteorological variables

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Author: Seifi, Akram1; Ehteram, Mohammad2; Nayebloei, Fatemeh3;
Organizations: 1Department of Water Science & Engineering, College of Agriculture, Vali-e-Asr University of Rafsanja, Rafsanjan, Iran
2Department of Water Engineering and Hydraulic Structures, Faculty of Civil Engineering, Semnan University, Semnan, Iran
3Department of Irrigation and Drainage Engineering, Tarbiat Modares University, Tehran, Iran
4School of Engineering, University of Guelph, Guelph, ON, NIG 2W1, Canada
5Water, Energy and Environmental Engineering Research Unit, University of Oulu, P.O. Box 4300, FIN90014, Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 2.5 MB)
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Language: English
Published: Springer Nature, 2021
Publish Date: 2022-07-12


Accurate prediction of soil temperature (Ts) is critical for efficient soil, water and field crop management. In this study, hourly Ts variations at 5, 10, and 30 cm soil depth were predicted for an arid site (Sirjan) and a semi-humid site (Sanandaj) in Iran. Existing machine learning models have high performance, but suffer from uncertainty and instability in prediction. Therefore, GLUE approach was implemented to quantify model uncertainty, while wavelet coherence was used to assess interactions between Ts and meteorological parameters. Standalone machine learning models (adaptive neuron fuzzy interface system (ANFIS), support vector machine model (SVM), radial basis function neural network (RBFNN), and multilayer perceptron (MLP)) were hybridized with four optimization algorithms (sunflower optimization (SFO), firefly algorithm (FFA), salp swarm algorithm (SSA), particle swarm optimization (PSO)) to improve Ts prediction accuracy and reduce model uncertainty. For both arid and semi-humid sites, ANFIS-SFO produced the most accurate performance at studied soil depths. At best, hybridization with SFO (ANFIS-SFO, MLP-SFO, RBFNN-SFO, SVM-SFO) decreased RMSE by 5.6%, 18%, 18.3%, and 18.2% at 5 cm, 11.8%, 10.4%, 10.6%, and 12.5% at 10 cm, and 9.1%, 12.1%, 13.9%, and 14.2% at 30 cm soil depth compared with the respective standalone models. GLUE analysis confirmed the superiority of hybrid models over the standalone models, while the hybrid models decreased the uncertainty in Ts predictions. ANFIS-SFO covered 95%, 94%, and 96% observation data at 5, 10, and 30 cm soli depths, respectively. Wavelet coherence analysis demonstrated that air temperature, relative humidity, and solar radiation, but not wind speed, had high coherence with Ts at different soil depths at both sites, and meteorological parameters mostly influenced Ts in upper soil layers. In conclusion, uncertainty analysis is a necessary and powerful technique to obtain an accurate and realistic prediction of Ts. In contrast, wavelet coherence analysis is a useful tool to investigate the most effective variables that strongly affect predictions.

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Series: Soft computing
ISSN: 1432-7643
ISSN-E: 1433-7479
ISSN-L: 1432-7643
Volume: 25
Issue: 16
Pages: 10723 - 10748
DOI: 10.1007/s00500-021-06009-4
Type of Publication: A1 Journal article – refereed
Field of Science: 1171 Geosciences
Copyright information: © The Author(s) 2021. This is a post-peer-review, pre-copyedit version of an article published in Soft Computing. The final authenticated version is available online at: