Daily Prediction and Multi-Step Forward Forecasting of Reference Evapotranspiration Using LSTM and Bi-LSTM Models

Abstract

Precise forecasting of reference evapotranspiration (ET0) is one of the critical initial steps in determining crop water requirements, which contributes to the reliable management and long-term planning of the world's scarce water sources. This study provides daily prediction and multi-step forward forecasting of ET0 utilizing a long short-term memory network (LSTM) and a bi-directional LSTM (Bi-LSTM) model. For daily predictions, the LSTM model's accuracy was compared to that of other artificial intelligence-based models commonly used in ET0 forecasting, including support vector regression (SVR), M5 model tree (M5Tree), multivariate adaptive regression spline (MARS), probabilistic linear regression (PLR), adaptive neuro-fuzzy inference system (ANFIS), and Gaussian process regression (GPR). The LSTM model outperformed the other models in a comparison based on Shannon's entropy-based decision theory, while the M5 tree and PLR models proved to be the lowest performers. Prior to performing a multi-step-ahead forecasting, ANFIS, sequence-to-sequence regression LSTM network (SSR-LSTM), LSTM, and Bi-LSTM approaches were used for one-step-ahead forecasting utilizing the past values of the ET0 time series. The results showed that the Bi-LSTM model outperformed other models and that the sequence of models in ascending order in terms of accuracies was Bi-LSTM > SSR-LSTM > ANFIS > LSTM. The Bi-LSTM model provided multi-step (5 day)-ahead ET0 forecasting in the next step. According to the results, the Bi-LSTM provided reasonably accurate and acceptable forecasting of multi-step-forward ET0 with relatively lower levels of forecasting errors. In the final step, the generalization capability of the proposed best models (LSTM for daily predictions and Bi-LSTM for multi-step-ahead forecasting) was evaluated on new unseen data obtained from a test station, Ishurdi. The model’s performance was assessed on three distinct datasets (the entire dataset and the first and the second halves of the entire dataset) derived from the test dataset between 1 January 2015 and 31 December 2020. The results indicated that the deep learning techniques (LSTM and Bi-LSTM) achieved equally good performances as the training station dataset, for which the models were developed. The research outcomes demonstrated the ability of the developed deep learning models to generalize the prediction capabilities outside the training station.

Multiple Linear Regression Models with Limited Data for the Prediction of Reference Evapotranspiration of the Peloponnese, Greece

“…In other words, MLR aims to find the linear function that minimizes the sum of the squares of errors (SSE) between the observed and the predicted data. An advantage of this method is the easy interpretation of the coefficients, which are generated in the model with low computational effort, in comparison to more complex techniques, such as energy balance methods and artificial intelligence algorithms [13][14][15][16][17][18][19][20][21][24][25][26][27][28][29][30][37][38][39][40][41][42][43][67][68][69][70][71][72][73][74][75]. For the MLR model, the response (dependent) variable y is assumed to be a function of k independent variables x i .…”

“…The measurement of the ETo is demanding. Therefore, several methods for estimating ETo have been developed, ranging from simple empirical or physically based models [13,14] to complex algorithms and techniques, such as fuzzy logic and machine learning (ML) [15][16][17][18][19][20][21]. These methods employ data from meteorological stations, or retrieved data via remote sensors [22][23][24][25][26][27][28][29][30][31][32].…”

Dam inflow prediction using large-scale climate variability and deep learning approach: a case study in South Korea

“…A Long Short-Term Memory (LSTM) network model, presented by Hochreiter & Schmidhuber (1997), is one of the recurrent neural network (RNN)-based algorithms. The LSTM model was introduced to solve gradient vanishing and optimization errors occurring in the RNN model and capture long-term dependence that exists at various steps in the sequential time series data (Han & Morrison 2022;Roy et al 2022). The LSTM model is an extensible method for dealing with sequence time series data such as speech recognition and language translation.…”

“…The LSTM model is an extensible method for dealing with sequence time series data such as speech recognition and language translation. Specifically, in the hydrologic field, it has been widely used to predict various hydrological factors, such as precipitation and runoff (Kratzert et al 2018;Han & Morrison 2022;Roy et al 2022). A diagram of the model structure of the LSTM cell is represented in Figure 3.…”

Fault diagnosis in asynchronous motors based on an optimal deep bidirectional long short-term memory networks

“…In the input layer, the raw signal is processed in segments to construct input samples that satisfy the timelength requirement. The Bid-LSTM network layer extracts characteristic information at different scales, and the number of memory units in each LSTM layer is not the same [62]. The larger the number of memory units, the shorter the length of data processed by each memory unit in terms of time dimension, and the stronger the ability to extract high-frequency features in the signal.…”