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Daily and Multi-step Ahead Forecasting of Potential Evapotranspiration Using Machine Learning Algorithms with Limited Climatic Data (2019-2020)

D. K. Roy
Senior Scientific Officer
Irrigation and Water Management Division, BARI, Gazipur 1701

S. K. Biswas
Senior Scientific Officer
Irrigation and Water Management Division, BARI, Gazipur 1701

M. A. Hossain
Chief Scientific Officer
Irrigation and Water Management Division, BARI, Gazipur 1701

Abstract/ Executive Summary:

Accurate prediction of potential evapotranspiration (ET₀) is essential for efficient planning and management of limited water resources through judicial irrigation scheduling. The FAO-56 Penman-Monteith approach to ET₀ estimation was adopted to compute ET₀ from data obtained during the period 2004–2019 from a weather station located in Gazipur Sadar Upazilla, Bangladesh. These meteorological variables (e.g., daily maximum and minimum temperatures, wind speed, relative humidity and sunshine duration) and computed ET₀ values were used as inputs and outputs, respectively, for modelling daily and one-step ahead ET₀ predictions. For modelling, this study evaluates the prediction accuracy and estimation capability of two deep learning algorithms, a Long-Short Term Memory (LSTM) network and a bi-directional LSTM (Bi- LSTM) network. The prediction accuracy of LSTM and Bi-LSTM networks is compared with six commonly used machine learning algorithms, i.e. Adaptive Neuro Fuzzy Inference System (ANFIS), Gaussian Process Regression (GPR), M5 Model Tree, Multivariate Adaptive Regression Spline (MARS), Probabilistic Linear Regression (PLR), and Support Vector Machine Regression (SVR). Ranking of the prediction models was performed using weights calculated by Shannon’s Entropy that accounts for a set of benefit (higher values indicate better model performance) and cost (smaller values indicate better model performance) performance indices. Results revealed that the LSTM model was found to be the best performer followed by Bi-LSTM, GPR, SVR, MARS (piecewise-linear), ANFIS, MARS (piecewise-cubic), M5 Model Tree, and PLR models. In the next stage, a one-step ahead prediction of ET₀ values was conducted using only the past values of ET₀ time series. Four modelling approaches (LSTM, Bi-LSTM, sequence-to-sequence regression LSTM network (SSR-LSTM) and ANFIS) were used for one-step ahead ET₀ predictions. Partial Auto Correlation Functions were used to obtain the time-lagged information from the ET₀ time series, and to determine the input and output variables for the LSTM, Bi-LSTM, and ANFIS models. On the other hand, in SSR-LSTM the responses are the training sequences with values shifted by one time-step. That is, at each time step of the input sequence, the LSTM network learns to predict the value of the next time step. Results of this modelling work revealed the superiority of Bi-LSTM followed by SSR-LSTM, ANFIS, and LSTM models identified by the ranking values computed using Shannon’s Entropy. The overall results indicate that the deep learning approaches especially LSTM and Bi-LSTM models could be successfully employed to predict daily and one-step ahead ET₀ values, respectively.

Keywords: DL-based prediction model, LSTM, ET0, Weather station, Prediction capability, Machine learning algorithms, Modelling approaches

Location: Gazipur Sadar Upazilla, Gazipur district, Bangladesh

Start Date: 01-01-2014

End Date: 30-06-2019

Program Area: Crop-Soil-Water Management

Non-commodity: Climate change

Objectives:

To: (1) delve into the potential of a DL-based prediction model, LSTM in predicting daily and one-step ahead ET₀ predictions using data obtained from a weather station located in Gazipur Sadar Upazilla; (2) weigh against the prediction capability of the developed LSTM models with that of the commonly used machine learning algorithms; and (3) provide a ranking of the developed modelling approaches using Shannon?s Entropy based decision theory.

Methodology:

Study area and the data The study area is situated in the Gazipur Sadar Upazilla having an aerial extent of 446.38 km². It is located between 23.88°N and 24.18°N latitudes and between 90.33°E and 92.50°E longitudes. Meteorological data including daily maximum and minimum temperatures, wind speed, relative humidity and sunshine duration) for a period of 15.5 years (1 January 2004 to 30 June 2019) were obtained from a weather station located in the Gazipur Sadar upazilla (lat. 24.00°N, long. 90.43°E, elevation of 8.4 m above mean sea level) of Gazipur District, Bangladesh. The study area receives an average annual rainfall of 2036 mm, of which roughly 80% occurs during the monsoon season (May to August). In general, the study area has a subtropical climate, with heavier rainfall events in the summer and lighter rainfall events in winter. Descriptive statistics of the input variables are presented. The mean values of minimum and maximum temperatures range between 21.2 °C and 30.9 °C, while the mean relative humidity across the year is approximately 80%. The wind speed in the study area ranges between 59 km/d and 437 km/d with a mean value of 242 km/d and a standard deviation of 90.69 km/d. The sunshine duration peaks at 11 h on a sunny day, while its minimum value is 0 on a cloudy day with the mean and standard deviations of 5.54 h and 3.09 h, respectively. All meteorological variables showed negative (left) skewness, indicating the data have a longer left tail than right tail in their distribution. The kurtosis values of [10] maximum temperature and relative humidity showed positive values indicating these datasets had “heavy tails” or outliers. The negative kurtosis values of minimum temperatures, wind speed, and sunshine durations indicate “light-tailed” distributions of these variables. The ET₀ values for the study area across the study period were computed from the climatic variables using the FAO-56 PM model. These computed ET₀ values were used as target variables for the developed LSTM and other machine learning based models. This method is widely accepted and has become a common practice in situations where ET0 values are difficult to obtain experimentally (Allen et al., 1998; Feng et al., 2017b; Shiri et al., 2014a). Computed ET₀ values range between 0.92 mm/d and 8.02 mm/d with a mean and standard deviation of 3.80 mm/d and 1.32 mm/d, respectively. Moreover, the skewness and kurtosis values varied between 0.30 and -0.67. The climatic variables and the computed ET₀ constituted the input output training patterns for the machine learning algorithms. Four layers were used for the training purpose: a sequence input layer equivalent to the number of input variables or features, a LSTM layer corresponding to the number of hidden units, fully connected layer associated with the number of output variables or the responses, and a regression layer. For developing LSTM and Bi-LSTM models, all possible combinations of the five input variables (Minimum temperatures, Maximum temperatures, Relative humidity, Wind speed, and Sunshine hours) were used. A total of 31 models were developed based on the 31 combinations (single, two-input combinations, three-inputs combinations, four-inputs combinations, and all five inputs) of input variables. The “model tree” is a technique for dealing with continuous class learning problems. It was developed by Quinlan (1992) and was exemplified in a learning algorithm known as the “M5 model tree”. A model tree is like a regression tree, but it builds trees whose leaves are associated with a multivariate linear model. The nodes are then chosen over the attributes that maximize the expected error reduction as a function of the standard deviation of the output parameters. Building the model tree consists of three steps: Building the initial tree: A decision-tree induction algorithm is introduced to create a tree. Instead of maximizing the information gain at each interior node, a splitting criterion is presented that minimizes the intra-subset variation in the class values down each branch. b) Pruning the tree: this is based on minimizing the estimated absolute error of the multiple linear regression models. It starts from each leaf by using the regression plane rather than a constant value (Solomatine and Yunpeng, 2004). c) Smoothing the tree: this is done to compensate for severe discontinuities that cannot be avoided between adjacent linear models at the leaves of the pruned tree. A MATLAB toolbox “M5PrimeLab” (Jekabsons 2016) was used to develop M5 model trees for predicting daily reference ET₀ values with various climatic variables as inputs and ET₀ values as outputs. Multivariate Adaptive Regression Spline (MARS) An adaptive approach of prediction model formation, MARS (Friedman, 1991) is a rapid and flexible nonparametric technique that is able to build regression models by dividing the total decision space into numerous interludes of input variables. Individual splines or Basis functions are then fitted to each interlude to build the final regression model (Bera et al., 2006). MARS utilizes both a forward and a backward step during the model developmental phase. Initially, MARS builds a relatively large and complex model by utilizing a given number of Basis functions specified by the user in the forward step. The backward step is implemented in MARS to eliminate some input variables that have relatively less influence on predicting the output variable (Salford- Systems, 2016). This backward step also helps keeping the developed model as simple as possible and at the same time prevents model over fitting.

Source of Information: Irrigation and Water Management Division, BARI, Joydebpur, Gazipur

Article Link (Online Journal):

Funding Source:

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Total Budget (Tk.) :

Achievement/Findings:

Precise and reliable prediction of reference evapotranspiration can effectively be employed in developing a sustainable and efficient agricultural water management strategy. This study aimed at developing a robust prediction tool for daily and one-step ahead ET₀ values through deep learning algorithms: Long Shot Term Memory (LSTM) networks and bidirectional LSTM networks. The performance of these two deep learning algorithms were compared with the commonly used machine learning algorithms. For daily ET₀ prediction, a number of meteorological variables were used as inputs to the models whereas the computed ET0 values were used as outputs from the models. For one-step ahead predictions, the suitable daily lag times of ET₀ values were used as inputs to the prediction models while the output from the models is the one-step ahead ET₀ values. The selection of optimal combination of inputs for the models in one-step ahead prediction was executed through careful examination of the PACF functions. In both cases, a set of statistical performance evaluation indices were calculated, and these indices were incorporated to calculate Shannon?s Entropy in order to provide a ranking of these prediction models. The ranking results for daily prediction demonstrated that the LSTM model was the best performer among others based on the proposed ranking method. The ranking of the models was: LSTM>Bi- LSTM>GPR>SVR>MARS_L>ANFIS>MARS_C>M5 Model Tree>PLR. On the other hand, Bi- LSTM model was the best performing model in predicting one-step ahead ET0 predictions, and the ranking of the models was: Bi-LSTM>SSR-LSTM>ANFIS>LSTM. The key findings of this research were (i) deep learning-based LSTM and Bi-LSTM models could be employed in predicting daily and one-step ahead prediction of ET0 values, (ii) Shannon?s Entropy based decision theory could be utilized to provide a ranking of several prediction models in order to make an unbiased decision regarding the suitability of a prediction model. This study investigated the daily and one-step ahead ET0 predictions. However, the performance of the proposed deep learning models needs to be evaluated for predicting multiple-step ahead predictions. Therefore, the study should be continued to evaluate the prediction performance of the proposed models for the multiple-step ahead predictions.

Knowledge Management: Report/Proceedings