Abstract
Air temperature is a vital meteorological variable required in many applications, such as agricultural and soil sciences, meteorological and climatological studies, etc. Given the importance of this variable, this study seeks to estimate minimum (Tmin), maximum (Tmax), and mean (T) air temperatures by applying a linear autoregressive (AR) time series model and then developing a hybrid model by means of coupling the AR and a non-linear time series model, namely autoregressive conditional heteroscedasticity (ARCH). Hence, the hybrid AR-ARCH model was tested. To that end, the Tmin, Tmax, and T data from 1986 to 2015 at two weather stations located in Northwestern Iran were used for both daily and monthly time scales. The results showed that the hybrid time series model (i.e., AR-ARCH) performed better than the single AR for estimating the air temperature parameters at the study sites. Multi-layer perceptron (MLP) was then employed to estimate the air temperatures using lagged temperature data as input predictors. Next, the single AR and hybrid AR-ARCH time series models were utilized to implement the hybrid MLP-AR and MLP-AR-ARCH models. It is worth noting that developing the hybrid MLP-AR and MLP-AR-ARCH models, as well as AR-ARCH one is the novelty of this study. Three statistical metrics including root mean square error (RMSE), mean absolute error (MAE), and normalized RMSE (NRMSE) were used to investigate the performance of whole the developed models. The hybrid MLP-AR and MLP-AR-ARCH models were found to perform better than the single MLP when estimating the daily and monthly Tmin, Tmax, and T; however, the MLP-AR models outperformed the MLP-AR-ARCH ones. At the end of this study, the performance of MLP was evaluated under an external condition (i.e., estimating the temperature components at any particular site using the temperature data of an adjacent location). The results indicated that the temperature data of a nearby station can be used for estimating the temperatures of a desired station. Most accurate results during the test stage were obtained under a local assessment through the hybrid MLP-AR(1) at the Tabriz station when estimating the monthly Tmax (RMSE = 0.199 °C, MAE = 0.159 °C, NRMSE = 1.012%) and hybrid MLP-AR(12) at the Urmia station when estimating the daily Tmax (RMSE = 0.364 °C, MAE = 0.277 °C, NRMSE = 1.911%).
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References
Azad A, Kashi H, Farzin S, Singh VP, Kisi O, Karami H, Sanikhani H (2020) Novel approaches for air temperature prediction: A comparison of four hybrid evolutionary fuzzy models. Meteorol Appl 27(1):e1817
Behmanesh J, Mehdizadeh S (2017) Estimation of soil temperature using gene expression programming and artificial neural networks in a semiarid region. Environ Earth Sci. https://doi.org/10.1007/s12665-017-6395-1
Bilgili M, Sahin B (2010) Prediction of long-term monthly temperature and rainfall in Turkey. Energy Sources 32(1):60–71
Box GEP, Jenkins GM (1976) Time series analysis: forecasting and control, Revised. Holden-Day, San Francisco
Cifuentes J, Marulanda G, Bello A, Reneses J (2020) Air temperature forecasting using machine learning techniques: a review. Energies 13(16):4215
Cobaner M, Citakoglu H, Kisi O, Haktanir T (2014) Estimation of mean monthly air temperatures in Turkey. Comput Electron Agric 109:71–79
de Martonne E (1925) Traité de Géographie Physique, 3 tomes. Paris
Deo RC, Ghorbani MA, Samadinfard S, Maraseni T, Bilgili M, Biazar M (2018) Multi-layer perceptron hybrid model integrated with the firefly optimizer algorithm for windspeed prediction of target site using a limited set of neighboring reference station data. Renew Energy 116:309–323
Dombayc OA, Golcu M (2009) Daily means ambient temperature prediction using artificial neural network method: a case study of Turkey. Renew Energy 34(4):1158–1161
Engle RF (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50(4):987–1007
Fang Y, Fataliyev K, Wang L, Fu X, Wang Y (2014) Improving the genetic-algorithm-optimized wavelet neural network for stock market prediction. In 2014 IEEE International Joint Conference on Neural Networks (IJCNN) pp. 3038–3042
Fathian F, Mehdizadeh S, Kozekalani Sales A, Safari MJS (2019) Hybrid models to improve the monthly river flow prediction: integrating artificial intelligence and non-linear time series models. J Hydrol 575:1200–1213
Gupta S, Wang LP (2010) Stock forecasting with feedforward neural networks and gradual data sub-sampling. Aus J Intell Inform Proc Syst 11(4):14–17
Guan Y, Mohammadi B, Pham BQ, Adarsh S, Balkhair KS, Ur Rahman K, Linh NTT, Quang Tri D (2020) A novel approach for predicting daily pan evaporation in the coastal regions of Iran using support vector regression coupled with krill herd algorithm model. Theor Appl Climatol 142(1–2):349–367
Hudson G, Wackernagel H (1994) Mapping temperature using kriging with external drift: theory and example from Scotland. Int J Climatol 14:77–91
Jahani B, Mohammadi B (2019) A comparison between the application of empirical and ANN methods for estimation of daily global solar radiation in Iran. Theor Appl Climatol 137(1–2):1257–1269
Kaymaz B (2005) Hazards and their impact on human. 29.IMISE (International Movement for Interdisciplinary Study of Estrangement) Conference. The American University of Paris: Paris, 4–9
Khatib T, Mohamed A, Sopian K, Mahmoud M (2012) Estimating ambient temperature for Malaysia using generalized regression neural network. Int J Green Energy 9:195–201
Kisi O, Sanikhani H (2015) Prediction of long-term monthly precipitation using several soft computing methods without climatic data. Int J Climatol 3(14):4139–4150
Lu X, Ju Y, Wu L, Fan J, Zhang F, Li Z (2018) Daily pan evaporation modeling from local and cross-station data using three tree-based machine learning models. J Hydrol 566:668–684
Mehdizadeh S (2018a) Assessing the potential of data-driven models for estimation of long-term monthly temperatures. Comput Electron Agric 144:114–125
Mehdizadeh S (2018b) Estimation of daily reference evapotranspiration (ETo) using artificial intelligence methods: offering a new approach for lagged ETo data-based modeling. J Hydrol 559:794–812
Mehdizadeh S (2020) Using AR, MA, and ARMA time series models to improve the performance of MARS and KNN approaches in monthly precipitation modeling under limited climatic data. Water Resour Manage 34(1):263–282
Mehdizadeh S, Kozekalani Sales A (2018) A comparative study of autoregressive, autoregressive moving average, gene expression programming and Bayesian networks for estimating monthly streamflow. Water Resour Manage 32(9):3001–3022
Mehdizadeh S, Behmanesh J, Khalili K (2017) A comparison of monthly precipitation point estimates using integration of soft computing methods and GARCH time series model. J Hydrol 554:721–742
Mehdizadeh S, Behmanesh J, Khalili K (2018a) Comprehensive modeling of monthly mean soil temperature using multivariate adaptive regression splines and support vector machine. Theor Appl Climatol 133(3–4):911–924
Mehdizadeh S, Behmanesh J, Khalili K (2018b) New approaches for estimation of monthly rainfall based on GEP-ARCH and ANN-ARCH hybrid models. Water Resour Manage 32(2):527–545
Mehdizadeh S, Fathian F, Adamowski JF (2019a) Novel hybrid artificial intelligencetime series models for monthly streamflow modeling. Appl Soft Comput 80:873–887
Mehdizadeh S, Fathian F, Safari MJS, Adamowski JF (2019b) Comparative assessment of time series and artificial intelligence models to estimate monthly streamflow: A local and external data analysis approach. J Hydrol 579:124225
Mehdizadeh S, Mohammadi B, Pham QB, Khoy DN, Nhi PTT (2020a) Implementing novel hybrid models to improve indirect measurement of the daily soil temperature: Elman neural network coupled with gravitational search algorithm and ant colony optimization. Measurement 165:108127
Mehdizadeh S, Ahmadi A, Kozekalanai Sales A (2020b) Modelling daily soil temperature at different depths via the classical and hybrid models. Meteorol Appl 27(4):e1941
Mehdizadeh S, Kozekalani Sales A, Safari MJS (2020c) Estimating the short-term and long-term wind speeds: implementing hybrid models through coupling machine learning and linear time series models. SN Appl Sci. https://doi.org/10.1007/s42452-020-2830-0
Mehdizadeh S, Fathian F, Safari MJS, Khosravi A (2020d) Developing novel hybrid models for estimation of daily soil temperature at various depths. Soil Till Res 197:104513
Mehdizadeh S, Ahmadi A, Danandeh Mehr A, Safari MJS (2020e) Drought modeling using classic time series and hybrid wavelet-gene expression programming models. J Hydrol 587:125017
Moazenzadeh R, Mohammadi B (2019) Assessment of bio-inspired metaheuristic optimisation algorithms for estimating soil temperature. Geoderma 353:152–171
Mohammadi B, Aghashariatmadari Z (2020) Estimation of solar radiation using neighboring stations through hybrid support vector regression boosted by Krill Herd algorithm. Arab J Geosci 13(10)
Mohammadi B, Ahmadi F, Mehdizadeh S, Guan Y, Pham QB, Linh NTT, Tri DQ (2020a) Developing novel robust models to improve the accuracy of daily streamflow modeling. Water Resour Manage 34:3387–3409
Mohammadi B, Linh NTT, Pham QB, Ahmed AN, Vojteková J, Guan Y, Abba SI, El-Shafie A (2020b) Adaptive neuro-fuzzy inference system coupled with shuffled frog leaping algorithm for predicting river streamflow time series. Hydrol Sci J 65(10):1738–1751
Mohammadi B, Mehdizadeh S (2020) Modeling daily reference evapotranspiration via a novel approach based on support vector regression coupled with whale optimization algorithm. Agric Water Manage 237:106145
Noi PT, Degener J, Kappas M (2017) Comparison of multiple linear regression Cubist regression, and random forest algorithms to estimate daily air surface temperature from dynamic combinations of MODIS LST data. Remote Sens 9(5):398
Pang B, Yue J, Zhao G, Xu Z (2017) Statistical downscaling of temperature with the random forest model. Adv Meteorol 7265178:1–11
Paniagua-Tineo A, Salcedo-Sanz S, Casanova-Mateo C, Ortiz-Garcia EG, Cony MA, Hernandez-Martin E (2011) Prediction of daily maximum temperature using a support vector regression algorithm. Renew Energy 36(11):3054–3060
Ramesh K, Anitha R (2014) MARSpline model for lead seven-day maximum and minimum air temperature prediction in Chennai. India J Earth Syst Sci 123(4):665–672
Sahin M (2012) Modelling of air temperature using remote sensing and artificial neuralnetwork in Turkey. Adv Space Res 50(7):973–985
Salcedo-Sanz S, Deo RC, Carro-Calvo L, Saavedra-Moreno B (2016) Monthly prediction of air temperature in Australia and New Zealand with machine learning algorithms. Theor Appl Climatol 125(1–2):13–25
Sanikhani H, Kisi O (2012) River flow estimation and forecasting by using two different adaptive neuro-fuzzy approaches. Water Resour Manag 26(6):1715–1729
Sanikhani H, Deo RC, Samui P, Kisi O, Mert C, Mirabbasi R, Gavili S, Yaseen ZM (2018) Survey of different data-intelligent modeling strategies for forecasting air temperature using geographic information as model predictors. Comput Electron Agric 152:242–260
Smith BA, Hoogenboom G, McClendon RW (2009) Artificial neural networks for automated year-round temperature prediction. Comput Electron Agric 68(1):52–61
Sotomayor KAL (2010) Comparison of adaptive methods using multivariate regression splines (MARS) and artificial neural networks backpropagation (ANNB) for the forecast of rain and temperatures in the Mantaro river basin. Hydrol Days. pp. 58–68
Teo KK, Wang L, Lin Z (2001) Wavelet packet multi-layer perceptron for chaotic time series prediction: effects of weight initialization. In: International Conference on Computational Science. Springer: Berlin Heidelberg. pp. 310–317
Ustaoglu B, Cigizoglu HK, Karaca M (2008) Forecast of daily minimum, maximum and mean temperature time series by three artificial neural network methods. Meteorol Appl 15(4):431–445
Wagle S, Uttamani S, Dsouza S, Devadkar K (2019) Predicting surface air temperature using convolutional long short-term memory networks ICCCE. Springer, Singapore, pp 183–188
Wang L, Fu X (2006) Data mining with computational intelligence. Springer, New York
Wang L, Teo KK, Lin Z (2001) Predicting time series with wavelet packet neural networks. In IJCNN'01 IEEE International Joint Conference on Neural Networks. Proceedings (Cat. No. 01CH37222). 3: 1593–1597
Webber H, Ewert F, Kimball BA, Siebert S, White JW, Wall GW, Ottman MJ, Trawally DNA, Gaiser T (2016) Simulating canopy temperature for modelling heat stress in cereals. Environ Model Softw 77:143–155
Zhu M, Wang L (2010) Intelligent trading using support vector regression and multilayer perceptrons optimized with genetic algorithms. In: The 2010 IEEE International Joint Conference on Neural Networks (IJCNN) pp. 1–5
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Mohammadi, B., Mehdizadeh, S., Ahmadi, F. et al. Developing hybrid time series and artificial intelligence models for estimating air temperatures. Stoch Environ Res Risk Assess 35, 1189–1204 (2021). https://doi.org/10.1007/s00477-020-01898-7
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DOI: https://doi.org/10.1007/s00477-020-01898-7