Enhanced forecasting of multi-step ahead daily soil temperature using advanced hybrid vote algorithm-based tree models

Soil temperature (T_S) is a very important factor in the earth environment; it is mainly included in various meteorology studies, water soil dynamics, water evaporation, deep and slow water infiltration, and the quantification of water requirements for irrigation purposes. However, despite those important roles of T_S, important challenges remain in its estimation process, including an exact quantification over time and space, which is mainly related to the soil plant atmosphere behaviour (Taheri et al. 2023). Soil temperature is affected by various external factors, especially climatic variables, plants, and soil structure (Ma et al. 2023). Due to the complexity of soil structure and composition, several approaches have been adopted for soil temperature (T_S) estimation and three different approaches are mainly adopted including (i) direct in situ measurement, (ii) remote sensing estimation, and (iii) model application (Taheri et al. 2023).

Machine-learning methods, especially artificial neural networks (ANNs), have been found to provide reliable forecasts for some hydrological and meteorological variables in evapotranspiration modelling (Adnan et al. 2021), water quality indices (Abba et al. 2021), and irrigation system modelling (Kisi et al. 2021). ANNs were the most commonly used in hydrological and meteorological modelling, and numerous studies have employed ANNs to estimate T_S. ANN models have been used to estimate daily and annual T_S and they have demonstrated strong performance in forecasting the spatial variations of T_S (Mihalakakou 2002). Tabari et al. (2011) found that ANN methods perform better than multivariate linear regression when predicting daily T_S at six soil depths and they found that the most important variables for these predictions were air temperature and relative humidity. Bilgili (2010) compared linear regression, nonlinear regression, and ANN models to estimate monthly T_S at five soil depths and found that the ANN model was the most effective. Kisi et al. (2015) estimated monthly T_S at several soil depths by modelling with multi-layer perceptron neural networks (MLPNNs), radial basis neural networks (RBNNs), generalized regression neural networks (GRNNs), and multiple linear regression (MLR). The results indicated that the RBNN model was best for predicting T_S at shallow depths (i.e., 5 and 10 cm), but the MLR and GRNN models were better at deeper soil depths (50 and 100 cm, respectively). Tabari et al. (2015) used an ANN model to forecast T_S 1 day in advance at six depths and realized good accuracy in that short-term prediction.

Kim & Singh (2014) evaluated the adaptive neuro-fuzzy inference systems (ANFIS) and multi-layer perceptron (MLP) models for calculating daily T_S. An extreme learning machine (ELM) was optimized by self-adaptive evolutionary modelling to predict daily T_S at six depths (Nahvi et al. 2016). Both models produced accurate estimates, but the optimized ELM model performed marginally better than the original ELM model. Talaee (2014) used a co-active neuro-fuzzy inference system (CANFIS) to model T_S in arid and semi-arid regions and found that CANFIS produced accurate results. Abyaneh et al. (2016) utilized both ANN and CANFIS modelling to estimate T_S in moderate air temperature conditions in humid and dry climates and found that they were more effective models in arid settings. T_S was predicted monthly by ANN and ANFIS models using data collected at 31 stations in Iran and ANFIS was found to be the more effective model (Mehdizadeh et al. 2017). Several other models have been tested as well. These include genetic programming (GP) (Kisi et al. 2017), gene expression programming (Samadianfard et al. 2018), and genetic-based neural networks (Kazemi et al. 2018). Khosravi et al. (2022a) developed several ML models including KStar, instance-based K-nearest learner, and locally weighted learner coupled with bagging (BA) and dagging (DA) for T_S prediction in Iran. They finally stated that for soil depth of 5 cm, BA-KStar is superior while for soil depth of 50 cm, DA-KStar outperforms other algorithms. Malik et al. (2022) applied support vector machine (SVM), MLP, and ANFIS models optimized with slime mould algorithm, particle swarm optimization, and spotted hyena optimizer algorithms for T_S prediction in a semi-arid region of Punjab, India. Their finding showed the higher performance of SVM models at multiple depths.

Ozbek (2023) compared long short-term memory (LSTM) deep learning, the ANFIS with fuzzy c-means clustering algorithm, the autoregressive integrated moving average, and the autoregressive moving average models for forecasting 1-h-ahead soil temperature. They reported that the LSTM was more accurate compared to the other models at different sites. Farhangmehr et al. (2023) used the convolutional neural network (CNN) and the MLPNN models for predicting hourly soil temperature using large features, namely precipitation, surface pressure, evaporation, wind gust, dewpoint temperature, surface solar radiation, surface thermal radiation, and air temperature. According to the obtained results, the authors highlighted the importance of the air temperature as the first relevant feature, while the surface thermal radiation was the poorest one. Furthermore, the CNN was the most accurate, significantly higher than the MLPNN model. Ebtehaj et al. (2023) introduced a new machine-learning model called the emotional neural network (ENN) for predicting T_S at 10 and 20 cm depths. They developed the modelling framework according to two scenarios, namely (i) modelling T_S using climatic variables, i.e., air temperature, wind speed, and solar radiation and (ii) time series modelling. By comparison with the least square support vector machine, the GP and the multivariate adaptive regression splines machine-learning models demonstrated the superiority of the ENN. Alizamir et al. (2020) compared ELM, the MLPNN, the classification and regression trees, and the group method of data handling for modelling monthly T_S at different depths using four climatic variables, namely air temperature, solar radiation, wind speed, and relative air humidity. The authors reported that at 5, 10 and 50 cm, the ELM model was more accurate, and the best performances can be obtained using only air temperature; however, at 10 cm depth, it is necessary to include solar radiation and wind speed. Sattari et al. (2020) compared three ensemble machine-learning models, namely decision tree (DT), gradient boosted trees (GBT), and hybrid DT-GBT models for predicting daily soil temperature at 5, 10, and 20 cm depths. The proposed models were developed using mean, maximal and minimal air temperature, sunshine duration, and precipitation. From the obtained results, hybrid DT-GBT was found to be most accurate at 5 cm depth, while the DT exhibited high accuracy at 10 and 20 cm depths.

Though researchers have attempted predictions of T_S on daily or monthly intervals, predicting values for shorter periods (half an hour, for instance) is uncommon. There are questions regarding the appropriateness of machine-learning modelling of T_S over short intervals, but such models may yield a valuable high-resolution insight for modelling water resources and agronomy to improve crop yields (Singh et al. 2018; Xing et al. 2018). There has been a supportive discussion of these opportunities (Sanikhani et al. 2018). On the one hand, T_S measuring is time-consuming, and on the other hand, finding a reliable and practical model as a cost-effective model is required. This study investigates the potential of (1) three standalone machine-learning models: M5Prime (M5P), random forest (RF), and random tree (RT), (2) their ensembles with the vote (V) algorithm: V-M5P, V-RF, and V-RT, (3) effect of different input scenarios, and (4) involving different easily available input variables for forecasting T_S at two depths (5 and 50 cm) 1–3 days in advance. To the best of the author's knowledge, the vote algorithm is rarely used in geoscience and their ensembles with tree-based algorithms are new and has a high performance for predicting geoscience phenomena.

The simple Pearson's correlation coefficients (r-values) between the model's input variables of T_M, T_X, T_N, E_pan, S_R, and S_H and output variable (T_S at two depths) were used to develop the input variable list. The simple r-value approach is commonly used to build model's potential input successfully (Khosravi et al. 2020, 2021a, 2021b, 2021c, 2021d, 2021e; Kargar et al. 2021; Meshram et al. 2021; Panahi et al. 2021). The r-values of the variable-output pairs suggested six inputs for modelling based on the strength of the relationships (Tables 2 and 3). The most effective input combination was determined and used for model training.

In the present study, all developed models are implemented in the Waikato Environment for Knowledge Analysis (WEKA 3.9). WEKA software was developed at the University of Waikato, New Zealand, and is a free software licensed under the GNU General Public License. Three machine learnings were proposed in the present study, namely M5P, RF, RT, and the V. These models have been broadly reported in the literature as having high forecasting capabilities (Hanoon et al. 2021; Irwan et al. 2023).

In the current study, the identification of all model parameters was performed in the WEKA 3.9 software. First, the default value is considered and each model is trained based on the existence condition. Second, lower and higher values that are default values are generated and fed to them, and again each model is implemented. This approach is continued until the optimum value for each parameter is determined. In this case, root mean square error (RMSE) is applied for comparing and determining the optimum value, as the lower the RMSE, the better the model parameter would be.

This study compared three ensemble machine-learning models to forecast soil temperature (T_S) at depths of 5 and 50 cm. The models, V-M5P, V-RF, and V-RT, were trained and validated using four performance metrics: RMSE, MAE, NSE, and R. The results were scrutinized for both depths.

Based on the achieved results (Table 3), T_m has the highest impact on T_S for all three ahead days forecasting at two different depths, while S_R is the variable with the lowest impact. In addition, input scenario No. 2, in which T_M and T_X are involved, is determined as the most effective input scenario with the lowest RMSE value. Only the results from the best input scenario are considered for further modelling and analysis.

Similarly, 3-day forecasting revealed decreased performance for V-RF and V-M5P and no change in performance for V-RT (Table 4, Figures 6 and 7). Error scores produced by V-RF were 9.86% higher RMSE and 12.54% higher MAE than those values for V-M5P. In addition, these values for V-MVP were 13.51 and 16.96% better than the V-RT model. Comparing the models' 1- and 3-day forecasts, V-M5P's values for all metrics decreased: R by 4.21%, NSE by 7.95%, RMSE by 20.18%, and MAE by 18.18%. V-RF's scores declined at lower rates: R by 2.10%, NSE by 4.49%, RMSE by 13.80%, and MAE by 9.32%.

In this paper, we present a new method to forecast T_S measured at two different depths and we apply it to T_S measured at the Isfahan region in Iran. Our method is based on the comparison between three single and hybrid models using the voting algorithm, i.e., V-M5P, V-RF, and V-RT. However, our method was inspired by several previous studies for which the T_S was modelled using meteorological variables, especially, the mean, maximal, and minimal air temperatures. As commented in the previous results section, the T_S was mostly influenced by air temperature, whereas combining these six meteorological variables produces different results at different depths and different forecasting horizons. Compared to the results reported in the literature, our T_S estimations are consistent and encouraging. Note that, although the importance of air temperature is quite important, it seems to be sufficient for an accurate prediction of soil temperature as previously confirmed in the same site using the same data by Sattari et al. (2017) and Khosravi et al. (2022a). Comparing our numerical results with those reported in the literature, the inclusion of two temperatures, i.e., the mean and the maximal, shows a lower error at all depths and all forecasting horizons. However, given the high correlation coefficient reported in Table 3, we can consider that both variables have a positive effect on soil temperature. In addition, in this new modelling study, we demonstrate the importance of the vote algorithm in the improvement of model performances. Focusing on the proposed methods, the V-RF at 1-, 2- and 3-day forecast provides statistically high performances compared to V-M5P and V-RT. Additionally, the results of the proposed vote method provide a good forecast at 50 cm depth more than at 5 cm depth for all three forecasting horizons. Overall, the results show that with the hybrid vote method proposed in the present study, we can forecast the soil temperature with high NSE values approximately equal to 0.89.

This study investigated the use of three ensemble machine-learning models for 1-, 2-, and 3-day forecasts of T_S at depths of 5 and 50 cm. The three models compared were V-M5P, V-RF, and V-RT. The novelty of this study is the use of the vote ensemble algorithm. The T_S forecasting models were validated using in situ measurements from one station. The model inputs included daily air temperature measurements (i.e., minimum, maximum, and mean), solar radiation, evaporation, and sunshine hours. Though each model accurately forecasted T_S, thus demonstrating that each could be a powerful tool, the accuracies of the forecasts ranged from one model to another and for each forecasting horizon. There was an apparent increase in error statistics for T_S forecasts at the depth of 5 cm among all three models as forecast horizons increased from 1 to 3 days; mean RMSE and MAE for 1-day forecasts were 3.697 and 2.830°C but increased by 11.56 and 9.10% in the 3-day forecast. This increased error was less apparent for T_S forecasts at 50 cm depths. The T_S forecasts of the three models improved with increasing forecast horizon: RMSE and MAE decreased in the 3-day forecast by 4.30 and 3.20%, respectively. Though the performance metrics of V-M5P and V-RF were similar (V-M5P showed slight superiority), both exceeded the performance of V-RT. The strong performances of all three models, however, depend largely on the number of input variables included in the models, and the variables may be relatively high in number. It would be beneficial to test models that could achieve similar or better results using fewer input variables. It is highly recommended that other potential input variables, such as atmospheric pressure, precipitation, relative humidity, and wind speed, which may have a high impact on T_S prediction and their effectiveness, need to be investigated.

The publication has been prepared with the support of the RUDN University Strategic Academic Leadership Program.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.