Selecting models for the estimation of reference evapotranspiration for irrigation scheduling purposes

Alternative models for the estimation of reference evapotranspiration (ETo) are typically assessed using traditional error metrics, such as root mean square error (RMSE), which may not be sufficient to select the best model for irrigation scheduling purposes. Thus, this study analyzes the performance of the original and calibrated Hargreaves-Samani (HS), Romanenko (ROM) and Jensen-Haise (JH) equations, initially assessed using traditional error metrics, for use in irrigation scheduling, considering the simulation of different irrigation intervals/time scales. Irrigation scheduling was simulated using meteorological data collected in Viçosa-MG and Mocambinho-MG, Brazil. The Penman-Monteith FAO-56 equation was used as benchmark. In general, the original equations did not perform well to estimate ETo, except the ROM and HS equations used at Viçosa and Mocambinho, respectively. Calibration and the increase in the time scale provided performance gains. When applied in irrigation scheduling, the calibrated HS and JH equations showed the best performances. Even with greater errors in estimating ETo, the calibrated HS equation performed similarly or better than the calibrated JH equation, as it had errors with greater potential to be canceled during the soil water balance. Finally, in addition to using error metrics, the performance of the models throughout the year should be considered in their assessment. Furthermore, simulating the application of ETo models in irrigation scheduling can provide valuable information for choosing the most suitable model.

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Forecasting Reference Evapotranspiration Using Time Lagged Recurrent Neural Network

WSEAS TRANSACTIONS ON ENVIRONMENT AND DEVELOPMENT ◽

10.37394/232015.2020.16.72 ◽

2020 ◽

Vol 16 ◽

Keyword(s):

Neural Network ◽

Root Mean Square Error ◽

Mean Square Error ◽

Root Mean Square ◽

Network Model ◽

Recurrent Neural Network ◽

Reference Evapotranspiration ◽

Irrigation Scheduling ◽

Mean Square ◽

Time Lagged

The aim of this study is to employ a Time Lagged Recurrent Neural Network (TLRNN) model for forecasting near future reference evapotranspiration (ETo) values by using climate data taken from meteorological station located in Velestino, a village near the city of Volos, in Thessaly, centre of Greece. TLRNN is Multilayer Perceptron Neural Network (MLP-NN) with locally recurrent connections and short-term memory structures that can learn temporal variations from the dataset. The network topology is using input layer, hidden layer and a single output with the ETo values. The network model was trained using the back propagation through time algorithm. Performance evaluations of the network model done by comparing the Mean Bias Error (MBE), Root Mean Square Error (RMSE), Coefficient of Determination (R2) and Index of Agreement (IA). The evaluation of the results showed that the developed TLRNN model works properly and the forecasting ETo values approximate the FAO-56 PM values. A good proximity of predictions with the experimental data was noticed, achieving coefficients of determination (R2) greater than 75% and root mean square error (RMSE) values less than 1.0 mm/day. The forecasts range up to three days ahead and can be helpful to farmers for irrigation scheduling.

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Estimating evapotranspiration using the complementary relationship and the Budyko framework

Journal of Water and Climate Change ◽

10.2166/wcc.2017.148 ◽

2017 ◽

Vol 8 (4) ◽

pp. 771-790 ◽

Cited By ~ 4

Author(s):

Homin Kim ◽

Jagath J. Kaluarachchi

Keyword(s):

Root Mean Square Error ◽

Vegetation Cover ◽

Meteorological Data ◽

Mean Square ◽

Limited Data ◽

Complementary Relationship ◽

Proposed Model ◽

The Usa ◽

Dry Conditions ◽

The Subject

Abstract Several models have been developed to estimate evapotranspiration. Among those, the complementary relationship has been the subject of many recent studies because it relies on meteorological data only. Recently, the modified Granger and Gray (GG) model showed its applicability across 34 diverse global sites. While the modified GG model showed better performances compared to the recently published studies, it can be improved for dry conditions and the relative evaporation parameter in the original GG model needs to be further investigated. This parameter was empirically derived from limited data from wet environments in Canada – a possible reason for decreasing performance with dry conditions. This study proposed a refined GG model to overcome the limitation using the Budyko framework and vegetation cover to describe relative evaporation. This study used 75 eddy covariance sites in the USA from AmeriFlux, representing 36 dry and 39 wet sites. The proposed model produced better results with decreasing monthly mean root mean square error of about 30% for dry sites and 15% for wet sites compared to the modified GG model. The proposed model in this study maintains the characteristics of the Budyko framework and the complementary relationship and produced improved evapotranspiration estimates under dry conditions.

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Coupling a Bat Algorithm with XGBoost to Estimate Reference Evapotranspiration in the Arid and Semiarid Regions of China

Advances in Meteorology ◽

10.1155/2019/9575782 ◽

2019 ◽

Vol 2019 ◽

pp. 1-16 ◽

Cited By ~ 3

Author(s):

Yixiu Han ◽

Jianping Wu ◽

Bingnian Zhai ◽

Yanxin Pan ◽

Guomin Huang ◽

...

Keyword(s):

Air Temperature ◽

Reference Evapotranspiration ◽

Meteorological Data ◽

Bat Algorithm ◽

Irrigation Scheduling ◽

Multivariate Adaptive Regression Splines ◽

Accurate Estimation ◽

Agricultural Irrigation ◽

Semiarid Regions ◽

Arid And Semiarid

Accurate estimation of reference evapotranspiration (ETo) is key to agricultural irrigation scheduling and water resources management in arid and semiarid areas. This study evaluates the capability of coupling a Bat algorithm with the XGBoost method (i.e., the BAXGB model) for estimating monthly ETo in the arid and semiarid regions of China. Meteorological data from three stations (Datong, Yinchuan, and Taiyuan) during 1991–2015 were used to build the BAXGB model, the multivariate adaptive regression splines (MARS), and the gaussian process regression (GPR) model. Six input combinations with different sets of meteorological parameters were applied for model training and testing, which included mean air temperature (Tmean), maximum air temperature (Tmax), minimum air temperature (Tmin), wind speed (U), relative humidity (RH), and solar radiation (Rs) or extraterrestrial radiation (Ra, MJ m−2·d−1). The results indicated that BAXGB models (RMSE = 0.114–0.412 mm·d−1, MAE = 0.087–0.302 mm·d−1, and R2 = 0.937–0.996) were more accurate than either MARS (RMSE = 0.146–0.512 mm·d−1, MAE = 0.112–0.37 mm·d−1, and R2 = 0.935–0.994) or GPR (RMSE = 0.289–0.714 mm·d−1, MAE = 0.197–0.564 mm·d−1, and R2 = 0.817–0.980) model for estimating ETo. Findings of this study would be helpful for agricultural irrigation scheduling in the arid and semiarid regions and may be used as reference in other regions where accurate models for improving local water management are needed.

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Global comparison of 20 reference evapotranspiration equations in a semi-arid region of Iran

Hydrology Research ◽

10.2166/nh.2018.174 ◽

2018 ◽

Vol 50 (1) ◽

pp. 282-300 ◽

Cited By ~ 10

Author(s):

Hadi Farzanpour ◽

Jalal Shiri ◽

Ali Ashraf Sadraddini ◽

Slavisa Trajkovic

Keyword(s):

Arid Region ◽

Reference Evapotranspiration ◽

Meteorological Data ◽

Irrigation Scheduling ◽

Climatic Conditions ◽

Accurate Estimation ◽

Management Scenarios ◽

Global Comparison ◽

Semi Arid Region ◽

Semi Arid

Abstract Accurate estimation of reference evapotranspiration (ETo) is a major task in hydrology, water resources management, irrigation scheduling and determining crop water requirement. There are many empirical equations suggested by numerous references in literature for calculating ETo using meteorological data. Some such equations have been developed for specific climatic conditions while some have been applied universally. The potential for usage of these equations depends on the availability of necessary meteorological parameters for calculating ETo in different climate conditions. The focus of the present study was a global cross-comparison of 20 ETo estimation equations using daily meteorological records of 10 weather stations (covering a period of 12 years) in a semi-arid region of Iran. Two data management scenarios, namely local and cross-station scenarios, were adopted for calibrating the applied equations against the standard FAO56-PM model. The obtained results revealed that the cross-station calibration might be a good alternative for local calibration of the ETo models when proper similar stations are used for feeding the calibration matrix.

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Error propagation approach for estimating root mean square error of the reference evapotranspiration when estimated with alternative data

Journal of Agricultural Engineering ◽

10.4081/jae.2019.909 ◽

2019 ◽

Vol 50 (3) ◽

pp. 120-126

Author(s):

Homayoon Ganji ◽

Takamitsu Kajisa

Keyword(s):

Root Mean Square Error ◽

Mean Square Error ◽

Root Mean Square ◽

Error Propagation ◽

Reference Evapotranspiration ◽

Mean Square ◽

Severe Restriction ◽

Data Set ◽

Model Improvement ◽

Using Data

Estimation of reference evapotranspiration (ET0) with the Food and Agricultural Organisation (FAO) Penman-Monteith model requires temperature, relative humidity, solar radiation, and wind speed data. The lack of availability of the complete data set at some meteorological stations is a severe restriction for the application of this model. To overcome this problem, ET0 can be calculated using alternative data, which can be obtained via procedures proposed in FAO paper No.56. To confirm the validity of reference evapotranspiration calculated using alternative data (ET0(Alt)), the root mean square error (RMSE) needs to be estimated; lower values of RMSE indicate better validity. However, RMSE does not explain the mechanism of error formation in a model equation; explaining the mechanism of error formation is useful for future model improvement. Furthermore, for calculating RMSE, ET0 calculations based on both complete and alternative data are necessary. An error propagation approach was introduced in this study both for estimating RMSE and for explaining the mechanism of error formation by using data from a 30-year period from 48 different locations in Japan. From the results, RMSE was confirmed to be proportional to the value produced by the error propagation approach (ΔET0). Therefore, the error propagation approach is applicable to estimating the RMSE of ET0(Alt) in the range of 12%. Furthermore, the error of ET0(Alt) is not only related to the variables’ uncertainty but also to the combination of the variables in the equation.

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On the comparison between the LISFLOOD modelled and the ERS/SCAT derived soil moisture estimates

Hydrology and Earth System Sciences ◽

10.5194/hess-12-1339-2008 ◽

2008 ◽

Vol 12 (6) ◽

pp. 1339-1351 ◽

Cited By ~ 13

Author(s):

G. Laguardia ◽

S. Niemeyer

Keyword(s):

Soil Moisture ◽

Root Mean Square Error ◽

Mean Square Error ◽

Root Mean Square ◽

Land Surface ◽

Soil Depth ◽

Meteorological Data ◽

Data Retrieval ◽

Mean Square ◽

Mountainous Regions

Abstract. In order to evaluate the reliability of the soil moisture product obtained by means of the LISFLOOD hydrological model (De Roo et al., 2000), we compare it to soil moisture estimates derived from ERS scatterometer data (Wagner et al., 1999b). Once evaluated the effect of scale mismatch, we calculate the root mean square error and the correlation between the two soil moisture time series on a pixel basis and we assess the fraction of variance that can be explained by a set of input parameter fields that vary from elevation and soil depth to rainfall statistics and missing or snow covered ERS images. The two datasets show good agreement over large regions, with 90% of the area having a positive correlation coefficient and 66% having a root mean square error minor than 0.5 pF units. Major inconsistencies are located in mountainous regions such as the Alps or Scandinavia where both the methodologies suffer from insufficiently resolved land surface processes at the given spatial resolution, as well as from limited availability of satellite data on the one hand and the uncertainties in meteorological data retrieval on the other hand.

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Alternative reference evapotranspiration methods for the main climate types of the state of Paraná, Brazil

Pesquisa Agropecuária Brasileira ◽

10.1590/s0100-204x2018000900003 ◽

2018 ◽

Vol 53 (9) ◽

pp. 1003-1010 ◽

Cited By ~ 1

Author(s):

Bruno César Gurski ◽

Daniela Jerszurki ◽

Jorge Luiz Moretti de Souza

Keyword(s):

Root Mean Square Error ◽

Mean Square Error ◽

Root Mean Square ◽

Reference Evapotranspiration ◽

The State ◽

Alternative Methods ◽

Coefficient Of Determination ◽

Mean Square ◽

Standard Values

Abstract: The objective of this work was to define the best alternative methods for estimating the reference evapotranspiration (ETo) in the main climatic types (Cfa and Cfb) of the state of Paraná, Brazil. The methods tested were Budyko, Camargo, Hargreaves-Samani, Linacre, and Thornthwaite, which were compared to the ETo calculated with the Penman-Monteith ASCE (EToPM) method, between 1986 and 2015, in eight meteorological stations. The performance of the alternative methods was obtained from the coefficient of determination (R2), index “d” of agreement, index “c” of performance, and root mean square error (RMSE). The Hargreaves-Samani method has a better performance in estimating the ETo for the main climatic types in the state of Paraná. The Camargo method allows smaller errors between the standard values of ETo, obtained with the Penman-Monteith method, and the estimated values. The methods of Thornthwaite, Linacre, and Budyko are not adequate to estimate the ETo in any climatic type of the state of Paraná, Brazil.

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REDES NEURAIS ARTIFICIAIS, REGRESSÃO E MÉTODOS EMPÍRICOS PARA A MODELAGEM DA EVAPOTRANSPIRAÇÃO DE REFERÊNCIA NA CIDADE DE INHAMBANE, MOÇAMBIQUE

Irriga ◽

10.15809/irriga.2019v24n4p802-816 ◽

2019 ◽

Vol 24 (4) ◽

pp. 802-816

Author(s):

BARTOLOMEU FÉLIX TANGUNE ◽

Rodrigo Máximo Sánchez Román

Keyword(s):

Neural Networks ◽

Artificial Neural Networks ◽

Root Mean Square Error ◽

Mean Square Error ◽

Reference Evapotranspiration ◽

Mean Bias Error ◽

Bias Error ◽

Mean Square ◽

Empirical Methods ◽

E Mail

REDES NEURAIS ARTIFICIAIS, REGRESSÃO E MÉTODOS EMPÍRICOS PARA A MODELAGEM DA EVAPOTRANSPIRAÇÃO DE REFERÊNCIA NA CIDADE DE INHAMBANE, MOÇAMBIQUE BARTOLOMEU FÉLIX TANGUNE1 E RODRIGO MÁXIMO SÁNCHEZ ROMÁN2 1 Departamento de Engenharia Rural, Escola Superior de Desenvolvimento Rural, Universidade Eduardo Mondlane, Vilankulo, Inhambane, Moçambique. E-mail: [email protected]. 2 Departamento de Engenharia Rural, Faculdade de Ciências Agronômicas, Universidade Estadual Paulista (UNESP) Campus de Botucatu. Fazenda Experimental Lageado, Avenida Universitária, nº 3780, Altos do Paraíso, CEP: 18610-034, Botucatu – SP. Brasil. E-mail: [email protected] 1 RESUMO Estimativa precisa da evapotranspiração de referência (ETo) é importante para dimensionar e fazer manejo de sistemas de irrigação. Métodos de estimativa da ETo (11 métodos empíricos, 10 modelos de regressão múltipla: RLM e 10 redes neurais artificias: RNAs) foram avaliados em relação ao método padrão de Penman Monteith FAO 56, utilizando os seguintes índices: MBE (Mean Bias Error), RMSE (Root Mean Square Error) e R2, sendo RMSE utilizado como critério principal de seleção dos métodos. A significância dos métodos foi avaliada com base no teste t utilizando dados de 1985 a 2009. Os dados meteorológicos utilizados (temperatura máxima: Tmax, temperatura mínima: Tmin e temperatura média: T, umidade relativa, velocidade do vento e insolação) são da estação meteorológica convencional da cidade de Inhambane, Moçambique. Os resultados mostraram que o modelo RLM4 apresentou melhor desempenho (MBE = 0,01 mm.d-1; RMSE = 0,15 mm.d-1; R2 = 0,99). Na falta da radiação solar global, os modelos RLM6 (MBE = -0,01 mm.d-1; RMSE = 0,23 mm.d-1; R2 = 0,97) e RLM10 (MBE = 0,01 mm.d-1; RMSE = 0,23 mm.d-1; R2 = 0,97) podem ser utilizados e exigem a medição da T, Tmax e Tmin, respectivamente. Esses modelos não foram estatisticamente diferentes do método padrão. Palavras-chave: evapotranspiração, regressão múltipla, redes neurais. TANGUNE, B. F.; SÁNCHEZ-ROMÁN, R. M. ARTIFICIAL NEURAL NETWORKS, REGRESSION AND EMPIRICAL METHODS FOR REFERENCE EVAPOTRANSPIRATION MODELING IN INHAMBANE CITY, MOZAMBIQUE 2 ABSTRACT Precise estimation of reference evapotranspiration (ETo) is important for designing and managing irrigation systems. Methods of ETo estimation (11 empirical methods, 10 multiple regression models: RLM and 10 artificial neural networks: RNAs) were evaluated against Penman Monteith FAO 56 method using the following indexes: MBE (Mean Bias Error), RMSE (Root Mean Square Error) and R2, and RMSE was used as the main criterion of method selection. The significance of the methods was evaluated on the basis of the t test using data from 1985 to 2009. The meteorological data used (maximum temperature: Tmax, minimum temperature: Tmin and average temperature: T, relative air humidity, wind speed and solar brightness), from 1985 to 2009, are from the conventional meteorological station of the city of Inhambane, Mozambique. The results showed that the RLM4 model presented better performance (MBE = 0.01 mm.d-1; RMSE = 0.15 mm.d-1; R2 = 0.99). In the absence of global solar radiation, RLM6 (MBE = -0.01 mm.d-1; RMSE = 0.23 mm.d-1; R2 = 0.97) and RLM10 (MBE = 0.01 mm. d-1; RMSE = 0.23 mm.d-1; R2 = 0.97) can be used, which require measurement of T, and Tmax and Tmin, respectively. These models were not statistically different from the standard method. Keywords: evapotranspiration, multiple regression, neural networks.

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Comparison of evapotranspiration models

MAUSAM ◽

10.54302/mausam.v53i2.1627 ◽

2022 ◽

Vol 53 (2) ◽

pp. 119-126

Author(s):

R. K. MALL ◽

B. R. D. GUPTA

Keyword(s):

Root Mean Square Error ◽

Model Performance ◽

Uttar Pradesh ◽

The Other ◽

Mean Bias Error ◽

Wheat Crop ◽

Bias Error ◽

Mean Square ◽

Better Than ◽

Computing Models

Actual evapotranspiration of wheat crop during different year from 1978-79 to 1992-93 was measured daily in Varanasi, Uttar Pradesh using lysimeter. In this study three evapotranspiration computing models namely Doorenbos and Pruitt, Thornthwaite and Soil Plant Atmosphere Water (SPAW) have been used. Comparisons of these three methods show that the SPAW model is better than the other two methods for evapotraspiration estimation. In the present study the MBE (Mean-Bias-Error), RMSE (Root Mean Square Error) and t-statistic have also been obtained for better evaluations of a model performance.

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Simulation of the soil water balance of wheat using daily weather forecast messages to estimate the reference evapotranspiration

Hydrology and Earth System Sciences Discussions ◽

10.5194/hessd-6-697-2009 ◽

2009 ◽

Vol 6 (1) ◽

pp. 697-728

Author(s):

J. Cai ◽

Y. Liu ◽

D. Xu ◽

P. Paredes ◽

L. S. Pereira

Keyword(s):

Wind Speed ◽

Water Balance ◽

Soil Water ◽

Minimum Temperature ◽

Reference Evapotranspiration ◽

Weather Forecast ◽

Irrigation Scheduling ◽

Soil Water Balance ◽

Daily Weather ◽

Model Predictions

Abstract. Aiming at developing real time water balance modelling for irrigation scheduling, this study assesses the accuracy of using the reference evapotranspiration (ETo) estimated from daily weather forecast messages (ETo,WF) as model input. A previous study applied to eight locations in China (Cai et al., 2007) has shown the feasibility for estimating ETo,WF with the FAO Penmam-Monteith equation using daily forecasts of maximum and minimum temperature, cloudiness and wind speed. In this study, the global radiation is estimated from the difference between the forecasted maximum and minimum temperatures, the actual vapour pressure is estimated from the forecasted minimum temperature and the wind speed is obtained from converting the common wind scales into wind speed. The present application refers to a location in the North China Plain, Daxing, for the wheat crop seasons of 2005–2006 and 2006–2007. Results comparing ETo,WF with ETo computed with observed data (ETo, obs) have shown favourable goodness of fitting indicators and a RMSE of 0.77 mm d−1. ETo was underestimated in the first year and overestimated in the second. The water balance model ISAREG was calibrated and validated for both years using ETo, obs by comparing the predicted and observed soil water content relative to various irrigation treatments. The calibrated crop parameters were used in the simulations of the same treatments using ETo,WF as model input. Errors in predicting the soil water balance are small, 0.010 and 0.012 m3 m−3 respectively for the first and second year. Other indicators also confirm the goodness of model predictions. It could be concluded that using ETo computed from daily weather forecast messages provides for accurate model predictions, thus making it viable to use an irrigation scheduling model in real time with daily weather forecast messages.

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