Daily land surface temperature (LST) forecasting is of great significance for application in climate-related, agricultural, eco-environmental, or industrial studies. Hybrid data-driven prediction models using Ensemble Empirical Mode Composition (EEMD) coupled with Machine Learning (ML) algorithms are useful for achieving these purposes because they can reduce the difficulty of modeling, require less history data, are easy to develop, and are less complex than physical models. In this article, a computationally simple, less data-intensive, fast and efficient novel hybrid data-driven model called the EEMD Long Short-Term Memory (LSTM) neural network, namely EEMD-LSTM, is proposed to reduce the difficulty of modeling and to improve prediction accuracy. The daily LST data series from the Mapoling and Zhijaing stations in the Dongting Lake basin, central south China, from 1 January 2014 to 31 December 2016 is used as a case study. The EEMD is firstly employed to decompose the original daily LST data series into many Intrinsic Mode Functions (IMFs) and a single residue item. Then, the Partial Autocorrelation Function (PACF) is used to obtain the number of input data sample points for LSTM models. Next, the LSTM models are constructed to predict the decompositions. All the predicted results of the decompositions are aggregated as the final daily LST. Finally, the prediction performance of the hybrid EEMD-LSTM model is assessed in terms of the Mean Square Error (MSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE), Pearson Correlation Coefficient (CC) and Nash-Sutcliffe Coefficient of Efficiency (NSCE). To validate the hybrid data-driven model, the hybrid EEMD-LSTM model is compared with the Recurrent Neural Network (RNN), LSTM and Empirical Mode Decomposition (EMD) coupled with RNN, EMD-LSTM and EEMD-RNN models, and their comparison results demonstrate that the hybrid EEMD-LSTM model performs better than the other five models. The scatterplots of the predicted results of the six models versus the original daily LST data series show that the hybrid EEMD-LSTM model is superior to the other five models. It is concluded that the proposed hybrid EEMD-LSTM model in this study is a suitable tool for temperature forecasting.

Multifractal detrended fluctuation analysis (MFDFA) method can examine higher-dimensional fractal and multifractal characteristics hidden in time series. However, removal of local trends in MFDFA is based on discontinuous polynomial fitting, resulting in pseudo-fluctuation errors. In this paper, we propose a two-stage modified MFDFA for multifractal analysis. First, an overlap moving window (OMW) algorithm is introduced to divide time series of the classic MFDFA method. Second, detrending by polynomial fitting local trend in traditional MFDFA is replaced by ensemble empirical mode decomposition (EEMD)-based local trends. The modified MFDFA is named OMW-EEMD-MFDFA. Then, the performance of the OMW-EEMD-MFDFA method is assessed by extensive numeric simulation experiments based on a p-model of multiplicative cascading process. The results show that the modified OMW-EEMD-MFDFA method performs better than conventional MFDFA and OMW-MFDFA methods. Lastly, the modified OMW-EEMD-MFDFA method is applied to explore multifractal characteristics and multifractal sources of daily precipitation time series data at the Mapoling and Zhijiang stations in Dongting Lake Basin. Our results showed that the scaling properties of the daily precipitation time series at the two stations presented a long-range correlation, showing a long-term persistence of the previous state. The strong q-dependence of $H\left(q\right)$ and $\tau \left(q\right)$ indicated strong multifractal characteristics in daily precipitation time series data at the two stations. Positive $\Delta f$ values demonstrate that precipitation may have a local increasing trend. Comparing the generalized Hurst exponent and the multifractal strength of the original precipitation time series data with its shuffled and surrogate time series data, we found that the multifractal characteristics of the daily precipitation time series data were caused by both long-range correlations between small and large fluctuations and broad probability density function, but the broad probability density function was dominant. This study may be of practical and scientific importance in regional precipitation forecasting, extreme precipitation regulation, and water resource management in Dongting Lake Basin.

Because of the complex nonstationary and nonlinear characteristics of annual runoff time series, it is difficult to achieve good prediction accuracy. In this paper, ensemble empirical mode decomposition (EEMD) coupled with Elman neural network (ENN)—namely the EEMD-ENN model—is proposed to reduce the difficulty of modeling and to improve prediction accuracy. The annual runoff time series from four hydrological stations in the lower reaches of the four main rivers in the Dongting Lake basin, and one at the outlet of the lake, are used as a case study to test this new hybrid model. First, the nonstationary and nonlinear original annual runoff time series are decomposed to several relatively stable intrinsic mode functions (IMFs) by using EEMD. Then, each IMF is predicted by using ENN. Next, the predicted results of each IMF are aggregated as the final prediction results for the original annual runoff time series. Finally, five statistical indices are adopted to measure the performance of the proposed hybrid model compared with a back propagation (BP) neural network, EEMD-BP, and ENN models—mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), Pearson correlation coefficient (R) and Nash–Sutcliffe coefficient of efficiency (NSCE). The performance comparison results show that the proposed hybrid model performs better than the BP, EEMD-BP or ENN models. In short, the developed hybrid model can provide a significant improvement in annual runoff time series forecasting.