Multi-step ahead forecasting of daily reference evapotranspiration using deep learning
Introduction
Computation of evapotranspiration (ET) is required in water resource management, hydrological studies, irrigation scheduling and crop modeling studies. In addition, some drought indices are computed based on ET (Tian et al., 2020). There are different alternatives to estimate ET of a particular crop, however, the use of reference evapotranspiration (ETo) and crop coefficient (Kc) is the most common approach (Pereira et al., 2015). ETo can be estimated using the FAO-56 Penman-Monteith (FAO56-PM) equation, which is widely used and accepted due to its good performance (Allen et al., 1998, Pereira et al., 2015).
In addition to estimation of ETo from past and current periods, prediction of ahead ETo values (i.e., ETo forecasting) can be useful for irrigation planning. This future information can improve real-time irrigation scheduling, allowing to make better decisions. However, ETo forecasting studies are not as common in the literature as ETo estimation studies.
Trajkovic et al. (2003) forecasted monthly ETo based on previous ETo values using artificial neural network (ANN). Landeras et al. (2009) employed autoregressive integrated moving average (ARIMA) and ANN to forecast weekly ETo. Torres et al. (2011) forecasted daily ETo (computed using the Hargreaves-Samani equation) up to seven days ahead using ANN and multivariate relevance vector machine (MVRVM). Karbasi (2018) forecasted multi-step ahead daily ETo using gaussian process regression (GPR) and wavelet-GPR. The author observed that by increasing the forecasting time period from 1 to 30 days, the accuracy was reduced. Ashrafzadeh et al. (2020) forecasted monthly ETo up to 24 months ahead using seasonal autoregressive integrated moving average (SARIMA), group method of data handling (GMDH) and SVM. Nourani et al. (2020) forecasted multi-step ahead ETo based on monthly lagged meteorological data (up to 12 months). The authors used support vector machine (SVM), adaptive neuro fuzzy inference system (ANFIS), ANN and multiple linear regression (MLR) individually and in a multi-model approach (ensemble). The multi-model approach provided the best performance. In Brazil, Alves et al. (2017) forecasted one-day ahead daily ETo with high accuracy using ANN with only mean air temperature from the previous day as input.
In contrast to the studies presented above, some studies forecast ETo based on forecasted meteorological data, such as public weather forecasts (Cai et al., 2007, Perera et al., 2014, Traore et al., 2017, Yang et al., 2019), or with a combination of past local meteorological data and forecasted meteorological data (Bachour et al., 2016). In this study, ETo is forecasted based on past meteorological data. This approach has the advantage of not requiring external data, using only data measured on a local weather station.
The most common approach to forecast ETo with machine learning is to use only lagged ETo values as input data (Ashrafzadeh et al., 2020, Landeras et al., 2009, Trajkovic et al., 2003). However, the use of meteorological data related to ETo (i.e., temperature, relative humidity, solar radiation, wind speed and extraterrestrial radiation) and the day of the year as additional input data could provide performance gains. Thus, this is also investigated in the present study.
As presented above, traditional machine learning models, such as ANN and SVM, have been used for ETo forecasting. However, deep learning models can also be used for this task. The deep learning field has gained much attention in recent years and has been applied in several areas, outperforming traditional machine learning models and achieving state-of-the-art performances (Ferreira and da Cunha, 2020, Gao et al., 2019, Haidar and Verma, 2018, Kamilaris and Prenafeta-Boldú, 2018, Lecun et al., 2015, Lee et al., 2020, Saggi and Jain, 2019). A review of deep learning for water resources scientists is presented by Shen (2018). For time series forecasting, long short-term memory (LSTM) (Son and Kim, 2020, Tian et al., 2018, Zhou et al., 2019) and one-dimensional convolutional neural network (1D CNN) (Amarasinghe et al., 2017, Barzegar et al., 2020, Sayeed et al., 2020, Tian et al., 2018) can be used. In addition, 1D CNN can be combined with LSTM, creating a hybrid model (CNN-LSTM) (Barzegar et al., 2020, Kim and Cho, 2019, Huang and Kuo, 2018). Although deep learning has exhibited great performance in several cases, it is still poorly explored in the hydrology/climatology field. For ETo forecasting, studies using deep learning are very scarce.
For multi-step ahead forecasting, different modeling strategies can be employed (Taieb et al., 2010, Taieb et al., 2012, Ye and Dai, 2019). Iterated and direct strategies are the most common alternatives (Ye and Dai, 2019). In iterated strategy, a model is built to perform a one-step ahead forecasting. The result is fed back as input to predict the following value until the desired prediction horizon has been reached. In direct strategy, to predict the H next values of the time series, H models are constructed. Each model predicts a specific value of the prediction horizon. In contrast to iterated strategy, this method avoids accumulation of prediction errors. However, it has higher computational cost since more models are constructed.
In addition to iterated and direct strategies, multiple input multiple output (MIMO) strategy can be used (Taieb et al., 2010, Taieb et al., 2012, Ye and Dai, 2019). In MIMO, all the H next values of the time series are predicted at the same time. Thus, instead of a scalar value, a vector of future values is predicted. The advantages of MIMO against iterated and direct strategies are that it avoids accumulation of prediction errors and requires only a single model. In addition, compared to direct strategy, MIMO preserves the stochastic dependency characterizing the forecasted time series. However, to use MIMO, models that can predict multiple values, such as ANN and random forest (RF), are required. According to our knowledge, so far, multiple forecasting strategies have not been compared in ETo forecasting studies.
Considering the importance of ETo forecasts, this study assesses the potential of deep learning models (LSTM, 1D CNN and CNN-LSTM) and traditional machine learning models (ANN and RF), in regional and local scenarios, to forecast multi-step ahead daily ETo (seven days) using iterated, direct and MIMO forecasting strategies. The use of additional input variables to lagged ETo (meteorological data and day of the year) is also assessed.
Section snippets
Database, study sites and data management
Data from 53 automatic weather stations of the Brazilian National Institute of Meteorology (INMET) were used. The data length varied according to the stations, with a mean length of 11.7 ± 1.34 years. All the stations have data up to the year 2018. Maximum and minimum air temperature, maximum and minimum relative humidity, solar radiation and wind speed were obtained. Wind speed, measured at 10 m height, was converted to 2 m, according to Allen et al. (1998). The data, collected on an hourly
Baselines
Generally, B2 (i.e., baseline based on long-term mean monthly ETo) exhibited better performance than B1 (i.e., baseline based on mean ETo from the last seven days) (Table 3). Comparing mean RMSE values over the prediction horizon and weather stations, B2 showed RMSE (ind) (i.e., RMSE computed considering individual ETo values observed on each day of the prediction horizon, mm d−1) equal to 0.93, while B1 had RMSE (ind) equal to 0.98. Similarly, for RMSE (acc) (i.e., RMSE computed considering
Conclusions
This study assesses the potential of deep learning models (LSTM, 1D CNN and CNN-LSTM) and traditional machine learning models (ANN and RF) to forecast multi-step ahead daily ETo (seven days) using different forecasting strategies. Three input data combinations were assessed. For comparison purposes, two baselines were also used.
Although there were no large performance differences between the forecasting strategies, for the traditional machine learning models, direct and MIMO performed slightly
CRediT authorship contribution statement
Lucas Borges Ferreira: Conceptualization, Methodology, Software, Formal analysis, Writing - original draft. Fernando França da Cunha: Conceptualization, Writing - review & editing, Formal analysis, Supervision.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The present study was supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001 and CNPq, National Council for Scientific and Technological Development - Brazil. The authors wish to thank the Brazilian National Institute of Meteorology (INMET) for the meteorological data used.
References (45)
- et al.
A review and comparison of strategies for multi-step ahead time series forecasting based on the NN5 forecasting competition
Expert Syst. Appl.
(2012) - et al.
Multiple-output modeling for multi-step-ahead time series forecasting
Neurocomputing
(2010) - et al.
Estimating reference evapotranspiration with the FAO Penman-Monteith equation using daily weather forecast messages
Agric. For. Meteorol.
(2007) - et al.
A data-driven multi-model methodology with deep feature selection for short-term wind forecasting
Appl. Energy
(2017) - et al.
Estimation of reference evapotranspiration in Brazil with limited meteorological data using ANN and SVM – A new approach
J. Hydrol.
(2019) - et al.
A methodology for energy multivariate time series forecasting in smart buildings based on feature selection
Energy Build.
(2019) - et al.
Evaluation of CatBoost method for prediction of reference evapotranspiration in humid regions
J. Hydrol.
(2019) - et al.
Predicting residential energy consumption using CNN-LSTM neural networks
Energy
(2019) - et al.
Forecasting daily reference evapotranspiration for Australia using numerical weather prediction outputs
Agric. For. Meteorol.
(2014) - et al.
Reference evapotranspiration estimation and modeling of the Punjab Northern India using deep learning
Comput. Electron. Agric.
(2019)
Using a deep convolutional neural network to predict 2017 ozone concentrations, 24 hours in advance
Neural Networks
Developing a hybrid drought index: Precipitation Evapotranspiration Difference Condition Index
Clim. Risk Manag.
Forecasting daily potential evapotranspiration using machine learning and limited climatic data
Agric. Water Manag.
Evaluation of six equations for daily reference evapotranspiration estimating using public weather forecast message for different climate regions across China
Agric. Water Manag.
MultiTL-KELM: A multi-task learning algorithm for multi-step-ahead time series prediction
Appl. Soft Comput. J.
Explore a deep learning multi-output neural network for regional multi-step-ahead air quality forecasts
J. Clean. Prod.
Reference evapotranspiration forecasting by artificial neural networks
Eng. Agric.
Deep neural networks for energy load forecasting
IEEE Int. Symposium Industrial Electronics
Comparative Study of Time Series Models, Support Vector Machines, and GMDH in Forecasting Long-Term Evapotranspiration Rates in Northern Iran
J. Irrig. Drain. Eng.
Wavelet-multivariate relevance vector machine hybrid model for forecasting daily evapotranspiration
Stoch. Environ. Res. Risk Assess.
Short-term water quality variable prediction using a hybrid CNN–LSTM deep learning model
Stoch. Environ. Res. Risk Assess.
Cited by (91)
Machine-learning-based short-term forecasting of daily precipitation in different climate regions across the contiguous United States
2024, Expert Systems with ApplicationsInnovative approach for predicting daily reference evapotranspiration using improved shallow and deep learning models in a coastal region: A comparative study
2024, Journal of Environmental ManagementApplications of machine learning to water resources management: A review of present status and future opportunities
2024, Journal of Cleaner ProductionEvaluating the ability of deep learning on actual daily evapotranspiration estimation over the heterogeneous surfaces
2024, Agricultural Water ManagementStatistical and deep learning models for reference evapotranspiration time series forecasting: A comparison of accuracy, complexity, and data efficiency
2023, Computers and Electronics in Agriculture