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Potential evapotranspiration (PET) is key input in water resources, agricultural and environmental modelling. For many decades, numerous approaches have been proposed for the consistent estimation of PET at several time scales of interest. The most recognized is the Penman-Monteith formula, which is yet difficult to apply in data-scarce areas, since it requires simultaneous observations of four meteorological variables (temperature, sunshine duration, humidity, wind velocity). For this reason, parsimonious models with minimum input data requirements are strongly preferred. Typically, these have been developed and tested for specific hydroclimatic conditions, but when they are applied in different regimes they provide much less reliable (and in some cases misleading) estimates. Therefore, it is essential to develop generic methods that remain parsimonious, in terms of input data and parameterization, yet they also allow for some kind of local adjustment of their parameters, through calibration. In this study we present a recent parametric formula, based on a simplified formulation of the original Penman-Monteith expression, which only requires mean daily or monthly temperature data. The method is evaluated using meteorological records from different areas worldwide, at both the daily and monthly time scales. The outcomes of this extended analysis are very encouraging, as indicated by the substantially high validation scores of the proposed approach across all examined data sets. In general, the parametric model outperforms well-established methods of the everyday practice, since it ensures optimal approximation ofpotential evapotranspiration.
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Agriculture and Agricultural Science Procedia 4 ( 2015 ) 2 – 9
2210-7843 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of Data Research and Consulting
doi: 10.1016/j.aaspro.2015.03.002
Available online at www.sciencedirect.com
ScienceDirect
IRLA2014. The Effects of Irrigation and Drainage on Rural and Urban Landscapes, Patras, Greece
Evaluation of a Parametric Approach for Estimating Potential
Evapotranspiration across Different Climates
Aristoteles Tegos
a
*, Andreas Efstratiadisa, Nikolaos Malamosb, Nikolaos Mamassisa,
Demetris Koutsoyiannisa
aDepartment of Water Resources, School of Civil Engineering, National Technical University of Athens, Heroon Polytechneiou 5, GR-157 80
Zographou, Greece
bDepartment of Agricultural Technology, Technological Educational Institute of Western Greece, Amaliada, Greece
Abstract
Potential evapotranspiration (PET) is key input in water resources, agricultural and environmental modelling. For many decades,
numerous approaches have been proposed for the consistent estimation of PET at several time scales of interest. The most
recognized is the Penman-Monteith formula, which is yet difficult to apply in data-scarce areas, since it requires simultaneous
observations of four meteorological variables (temperature, sunshine duration, humidity, wind velocity). For this reason,
parsimonious models with minimum input data requirements are strongly preferred. Typically, these have been developed and
tested for specific hydroclimatic conditions, but when they are applied in different regimes they provide much less reliable (and
in some cases misleading) estimates. Therefore, it is essential to develop generic methods that remain parsimonious, in terms of
input data and parameterization, yet they also allow for some kind of local adjustment of their parameters, through calibration. In
this study we present a recent parametric formula, based on a simplified formulation of the original Penman-Monteith expression,
which only requires mean daily or monthly temperature data. The method is evaluated using meteorological records from
different areas worldwide, at both the daily and monthly time scales. The outcomes of this extended analysis are very
encouraging, as indicated by the substantially high validation scores of the proposed approach across all examined data sets. In
general, the parametric model outperforms well-established methods of the everyday practice, since it ensures optimal
approximation ofpotential evapotranspiration.
© 2015 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of Technological Educational Institute of Epirus, Hydroconcept R&D (www.hydroconcept.gr)
Keywords: Potential evapotranspiration; Penman-Monteith formula; parametric model; calibration
* Corresponding author. Tel.: +30 2121029102 E-mail address: tegosaris@yahoo.gr
© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of Data Research and Consulting
3
Aristoteles Tegos et al. / Agriculture and Agricultural Science Procedia 4 ( 2015 ) 2 – 9
1. Introduction
The accurate estimation of evapotranspiration has a great importance in hydrological modeling, irrigation
planning and water resources management. Several related studies have been performed during past decades and the
attempts of estimating water requirements for irrigation purposes; go back to 1890 in U.S.A (Jensen and Haise,
1963).
More than 50 important evapotranspiration models can be found in literature (Lu et al., 2005, McMahon et al.
2013), which can be grouped into seven categories: (i) empirical, (ii) water budget (iii) energy budget, (iv) mass
transfer, (v) combination, (vi) radiation and (vii) measurement (Xu and Singh, 2000).
The variety of models and frameworks is related to the complexity of the natural phenomenon and depends on
the wide range of input climate data and local climate conditions.
The Penman-Monteith formulation (Monteith, 1981) for computing potential ET proposed from FAO as
standardized method (Allen et al., 1998) That method had numerous successful applications in the fields of
hydrology and agrometeorology and in a variety of hydroclimatic regimes (Wang and Georgakakos, 2007). Basic
disadvantage of PenmanMonteith model is the simultaneous requirement of several meteorological data as
temperature, wind speed, relative humidity and sunshine measures.
The interdependence of these meteorological parameters and their variability in space and time, lead in
difficulties to formulate an equation that can be used to estimate ET from various crops under different climate
conditions (Temesgen B. et al., 2005). Notably, the difficulties due the sparse hydrometeorological networks in
several regions like Africa and the instability in the records of radiation and relative humidity (Samani, 2000)
reveals the demand of new simplifies models.
Therefore parsimonious model developed and implemented worldwide, such as radiation-based or temperature-
based models (Valiantzas, 2013). From numerous publications (Tabari, 2010; Samaras et al., 2014) demonstrated
that radiation-based methods are powerful models for the ET estimation.
In this study a new radiation based model is proposed, which include a new strategy in the estimation of potential
evapotranspiration (PET).
2. Overview of PET models
2.1. Penman- Monteith model
The classic model of the Penman-Monteith (1963) equation to estimate potential evaporation or
evapotranspiration is represented from the form:
PET = , γ΄ = γ (1 + rs/ra)"(1)
where PET is potential evaporation or evapotranspiration (mm/d), Rn is net radiation at the surface, Δ is the slope of
the saturation vapor pressure curve,γis psychometric coefficient while rs and ra are the surface and aerodynamic
resistance factors.
The FAO PenmanMonteith method was developed by defining the reference crop as a hypothetical crop with an
assumed height of 0.12 m having a surface resistance of 70 s m1 and an albedo of 0.23.
2.2. Radiation- Based Methods
Jensen and Haise (1963)evaluated 3000 observations of PET as determined by soil sampling procedures over a
35-year period, and developed the following relation. This equation has only known the average daily temperature
and extraterrestrial radiation and calculated easily form:
4 Aristoteles Tegos et al. / Agriculture and Agricultural Science Procedia 4 ( 2015 ) 2 – 9
nt
40
aaTR
PET ?
(2)
One decade later Mcguiness and Bordne (1972) using measured values of lysimeter suggested a slight modification
of Jensen’s formulation with the expression:
nt
68
)5( -
?aa TR
PET
(3)
Another widely used approach is the Hargreaves model (Hargeanes and Samani, 1982) that estimates the
reference evapotranspiration at the monthly and daily scale by:
PET = 0.0023 (Tα + 17.8) (Tmax Tmin)0.5 (4)
The method has received considerable attention because it can produce very acceptable results under diverse
climates using only temperature measurements. According to several researchers (Samani, 2000;Xu and Singh
2002) the method tends fails in extreme humidity and wind conditions.
A recent research (Oudinet al., 2005) evaluated a number of evapotranspiration methods, on the basis of
precipitation and streamflow data from a large sample of catchments in U.S., France and Australia. After extended
analysis with the use of four hydrological models, the researchers proposed a modification of Jensen and McGuiness
model:
nt
100
)5( -
?a
T
a
R
PET
(5)
In the four radiation-based formulas PET(mm/d) is the potential evapotranspiration, Ra (kJ m-2d-1) is the
extraterrestrial shortwave radiation, Ta (°C) is the air temperature, λ latent heat of vaporization (kj/kgr) and p is the
water density (kgL-1).
3. Implementation of the parametric approach
3.1. The PET parametric model
Koutsoyiannis and Xanthopoulos (1999), Tegos et al. (2013), Tegos et al. (2015) examined the structure and the
sensitivity of input data in Penmann-Monteith model. They concluded that there are “one to one” relationship
between potential evapotranspiration, extraterrestrial radiation and temperature. In the parametric simplification of
the Penman-Monteith formula, the numerator is approximated by a linear function of extraterrestrial solar radiation,
Ra, while the denominator is approximated by a linear descending function of temperature.
The generalized mathematic equation of the parametric model is:
a
cT
baS
PET /
/
?1
0
(6)
where PET (mm) is the potential evapotranspiration, S0 (kJ m-2) is the extraterrestrial shortwave radiation, Ta (°C)
is the air temperature, and c (°C-1), a (kgkJ-1) and b (kg m-2) are parameters.
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Aristoteles Tegos et al. / Agriculture and Agricultural Science Procedia 4 ( 2015 ) 2 – 9
The mode parameters have physical interpretation of model parameters while:
The dimensionless term a / λρ represents the average percentage of the energy provided by the sun (in terms of
Ra) and, after reaching the Earth’s terrain, is transformed to latent heat, thus driving the evapotranspiration
process.
Parameter b lumps the missing information associated with aerodynamic processes, driven by the wind and the
vapour deficit in the atmosphere.
The term 1 c Ta approximates 1 + γ΄/Δwhich is function of surface and aerodynamic resistance and Δ is the
slope vapour pressure curve, which is function of Ta.
3.2. Study areas and processes
We used monthly meteorological data from 37 stations distributed over Greece, run by the National
Meteorological Service of Greece, from 39 stations of CIMIS hydrometeological network in California, 10 from
Germany and finally 4 from Spain.
The organization of the time series and the calculation of potential evapotranspiration with different methods
(Penman-Monteith, Parametric, Hargreaves) were carried out using the Hydrognomon software. Finally, the other
expression (Jensen, Mcguiness and Oudin) modeled through appropriate spreadsheets.
Every time series was split to two control periods (calibration and validation), where in the first developed the
parametric model and in the second tested its predictive ability. At each station, the three parameters of parametric
model were calibrated against the reference potential evapotranspiration timeseries. This procedure was
automatically employed via a least square optimization technique, embedded in the evapotranspiration module of
Hydrognomon. The optimized values of a, b and c were next embedded to the parametric model.
3.3. Evaluation of the new parametric formula in Greece
The distribution of the coefficient of efficiency (CE),introduced by Nash and Sutcliffe (1970), is presented in the
Table 1. The results for the parametric model are satisfactory while CE values are greater than 95% at all locations
(90% for validation). The globally used radiation-based approaches by McGuiness et al. (1972) and Oudin et al.
(2005) present moderate results.
In order to provide a further parsimonious parametric formulas alternative parameterizations were also examined
through optimization techniques, i.e. (a) by omitting parameter b, and (b) by omitting b and substituting c by its
average value over Greece; in formulation (a) the reduction of CE was negligible.
Table 1 : Distribution of CE values of radiation-based approaches in Greece
CE
Parametric
Mcguiness
Oudin
Val
Cal
Val
Cal
Val
95-100
30
0
2
5
2
90-95
6
8
9
5
9
70-90
1
12
19
12
15
50-70
0
15
6
12
7
<50
0
2
1
3
4
3.4. Evaluation of the new parametric formula in California and in Europe
The distribution of the CE for the CIMIS stations is presented in Table 2 and for European stations in Table 3.
The results for both period and in different climatic regimes are satisfactory for the parametric model, while the
average CE in calibration are 94.80% (CIMIS), 96.52% (European) and in validation period are 94.34% (CIMIS)
and 90.06% (European). Similar satisfactory results shown Hargreaves model especially in CIMIS network (average
6 Aristoteles Tegos et al. / Agriculture and Agricultural Science Procedia 4 ( 2015 ) 2 – 9
CE 94.39% for the calibration period and 91.80% for the validation period) where the model has been developed,
while in European stations the indexes are lower (91.80% in validation period and 87.53% in calibration period).
Mcguiness model gives lower results than parametric and Hargreaves with 87.14% in calibration period and 87.76%
in the validation period.
Oudin’s model which is a modern improved version of radiation-based methods presents moderate results in
CIMIS network (52.18% calibration and 46.82% validation period) but quite better results in European stations
(89.37 % calibration and 82.82% validation period).
By combining the results with the previous study (Tegos et al., 2013) the model’s performance is more
acceptable in humid than in arid climatic regimes. Finally, Jensen-Haise model totally failed to produce physical
results.
Table 2: Distribution of CE values of radiation-based approaches in CIMIS network
CE
Parametric
Hargreaves
Jensen-Haise
Mcguiness
Oudin
Cal
Val
Cal
Val
Cal
Val
Cal
Val
Cal
Val
95-100
26
26
26
23
0
7
16
15
0
0
90-95
11
5
10
7
0
2
6
7
0
0
80-90
2
8
3
9
1
2
10
10
1
0
70-80
0
0
0
0
6
3
3
3
3
5
60-70
0
0
0
0
1
6
2
3
7
4
50-60
0
0
0
0
3
4
1
1
12
6
0-50
0
0
0
0
16
9
1
0
16
24
<0
0
0
0
0
12
6
0
0
0
0
Table3 : Distribution of CE values of radiation-based approaches in European stations
CE
Parametric
Hargreaves
Jensen-Haise
Mcguiness
Oudin
Cal
Val
Cal
Val
Cal
Val
Cal
Val
Cal
Val
95-100
10
9
6
0
0
0
0
0
9
1
90-95
4
4
4
6
0
0
0
0
2
8
80-90
0
0
3
7
0
0
0
0
0
2
70-80
0
0
1
1
0
0
7
1
1
1
60-70
0
0
0
0
0
0
3
1
1
1
50-60
0
0
0
0
0
0
3
1
1
0
0-50
0
1
0
0
5
1
2
9
0
1
<0
0
0
0
0
9
13
1
2
0
0
4. Spatial variability of the parameters
4.1. Mapping of the parameters over Greece
Assuming the simplified parameterization, in which b is omitted, we re-calibrated the local values of a and c, and
mapped them over Greece, using typical interpolation tools (e.g. Inverse Distance Weighting, Kriging etc.).
7
Aristoteles Tegos et al. / Agriculture and Agricultural Science Procedia 4 ( 2015 ) 2 – 9
As shown in Figure 1 parameter a exhibits a systematic geographical pattern, since it increases from SE to NW
Greece, following the increase of sunshine duration and wind velocity as moving from the continental to insular
Greece, while parameter c is site-specific.
Fig. 1. Geographical distribution of parameters a and c over Greece
4.2. Spatial interpolation of models parameters over California
We implemented three well-known interpolation methods, i.e. Inverse Distance Weighting (I.D.W.), Kriging,
Natural Neighbours (NaN) and a recently proposed Bilinear Surface Smoothing (Malamos and Koutsoyiannis, in
press) in California territory.
After extended analysis with these alternatives interpolation techniques in a validation set of 11 stations, the
Inverse Weighting Distance, i.e. the simplest of interpolation methods, provides the more accurate point estimations
of model parameters.
The mapping of the three parameters over California through the I.D.W. approach is illustrated in Figure 2.
Generally, we detect that the parameters a, c increase from North to SE and the opposite occurs for the parameter b.
Par a
Par c
8 Aristoteles Tegos et al. / Agriculture and Agricultural Science Procedia 4 ( 2015 ) 2 – 9
Fig. 2. Geographical distribution of the parameters over California
5. Conclusions
The proposed parametric model can be considered as simplification of the Penman-Monteith formula, in an
attempt to compromise parsimony, in terms of model structure and data requirements, and physical consistency. The
parameters a, b and c have some physical background, since they substitute, to some extent, the three missing
meteorological variables.
The model ensures excellent predictive capacity (in terms of reproducing monthly PET estimations through the
Penman-Monteith) in all examined locations in Greece and California, as well as in Germany and Spain (full results
shown in Tegos et al. 2015). Additionally even simpler parameterizations in Greece through optimization (i.e. the
formulation with two parameters, a and c ) provide similarly good results.
The appropriateness of the method is further revealed through extensive comparisons with other radiation-based
approaches, most of which exhibit poor performance.
The comparisons across different climates reveal the great advantage of parametric approaches against radiation-
based ones, since calibration allows the coefficients that are involved in the mathematical formulas to be fitted to
local climatic conditions.
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Aristoteles Tegos et al. / Agriculture and Agricultural Science Procedia 4 ( 2015 ) 2 – 9
Reliable estimations of PET, both at point basis as well as over extended areas of interest (i.e. river basins), can
be obtained by interpolating the known (i.e., locally optimized) parameter values and next employing the parametric
formula.
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... The Parametric model is a temperature-based model that requires only temperature data and utilizes a parsimonious expression for the potential evapotranspiration (PET) estimation [9]. It replaces some of the variables and constants that are used in the standard Penman-Monteith model by regionally varying parameters, which are estimated through calibration [10][11][12]. The large-scale Parametric model application was satisfactory, and it outperformed the efficiency of several simplified models such as Hargreaves, Thornthwaite, Oudin, and Jensen-Haise. ...
... The Parametric model employs physically consistent parameters distributed over the globe, overcoming the main weakness of the Penman-Monteith model, which is the necessity of simultaneous observations of four meteorological variables [10][11][12][13][14]. ...
... where PET is the potential evapotranspiration (mm), R a (kJ m −2 ) is the extra-terrestrial radiation, a (kg kJ −1 ), and c ( • C −1 ) are the calibrated parameters and T ( • C) is the monthly mean air temperature. As already stated in Tegos et al. [12], the parameters have some physical correspondence to the Penman-Monteith equation, since the product a R a represents the overall energy term (i.e., incoming minus outgoing solar radiation), while the quantity 1 − c T approximates the denominator term of the Penman-Monteith formula. More information about the parameters a and c and their spatial patterns across the globe can be found in [12]. ...
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... Penman (1948) [28] is a radiation based method and requires measured values of temperature, relative humidity, wind speed and net radiation for the estimation of potential evaporation. The Thornthwaite (1948) method on the other hand is the most simplified method and requires only temperature measurements for the estimation of [35]. As explained later in the climate change section, reliable estimates of future climate variables, apart from precipitation and temperate, are difficult to obtain; therefore, the Thornthwaite (1948) method with a modification proposed by Pereira and Pruitt (2004) was used for the estimation of the in this research [36]. ...
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Reference Evapotranspiration (ET0) is a key parameter in hydrology. It has a variety of practical applications, ranging from understanding the hydrological cycle to estimating crop water needs for efficient irrigation in agriculture. The FAO PENMAN–MONTEITH (FAO-PM) method is largely adopted and is the recommended method by the FAO for ET0 estimation. However, it requires multiple measured meteorological parameters that are, in some conditions, difficult to obtain. This work fills this gap and leverages the potential of data-driven methods, namely machine learning and deep learning models, to accurately estimate ET0 while using a limited number of easy-to-obtain parameters. The study uses physical-based models (FAO-PM and Hargreaves) as ET0 learning data providers for data-driven models. First, physical models were fed with meteorological data covering the period 2013–2020 at an hourly scale to estimate ET0. The data were sourced from the in-situ local weather station of our study area in the Tensift basin (center of Morocco) and from the Copernicus ERA5-Land reanalysis data. Next, as a preprocessing step, feature engineering was performed using a decision tree-based approach. We evaluated the predictive importance of weather parameters for ET0 estimation. Scores between 0 and 1 were assigned to each parameter, indicating their efficacy. Notably, mean air temperature and global solar radiation stood out, collectively surpassing an 86% importance threshold. In contrast to the rest of the parameters that have a low importance of 10%. This emphasizes the critical significance of mean air temperature and global solar radiation as essential predictors for accurate ET0 estimation. Finally, during the modeling phase, three deep-learning models Long Short-Term Memory (LSTM), Gated Recurrent Unit, and Convolutional Neural Network are highlighted. Notably, the LSTM model exhibits superior performance, delivering comparable coefficients of determination (R²) and root mean square error (RMSE) results, surpassing its counterparts. In terms of univariate predictions using the Hargreaves and FAO-56 PM methods, the LSTM consistently achieves high R² values of 0.90 across all data sources, accompanied by impressive accuracy reflected in low MAE, MSE, and RMSE values ranging from 0.004 to 0.07 mm/day. In addition, the ensemble learning model XGBoost had the best prediction performance with R² = 0.93 and RMSE = 0.03 mm/day. This confirms that machine learning models outperform deep learning architectures for small and medium-sized datasets. The proposed models will be integrated into an under-development agricultural decision support system.
... 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 . ...
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The aim of this study was to investigate the utility of multiple linear regression (MLR) for the estimation of reference evapotranspiration (ETo) of the Peloponnese, Greece, for two representative months of winter and summer during 2016–2019. Another objective was to test the number of inputs needed for satisfactorily accurate estimates via MLR. Datasets from sixty-two meteorological stations were exploited. The available independent variables were sunshine hours (N), mean temperature (Tmean), solar radiation (Rs), net radiation (Rn), wind speed (u2), vapour pressure deficit (es − ea), and altitude (Z). Sixteen MLR models were tested and compared to the corresponding ETo estimates computed by FAO-56 Penman–Monteith (FAO PM) in a previous study, via statistical indices of error and agreement. The MLR5 model with five input variables outperformed the other models (RMSE = 0.28 mm d−1, adj. R2 = 98.1%). Half of the tested models (two to six inputs) exhibited very satisfactory predictions. Models of one input (e.g., N, Rn) were also promising. However, the MLR with u2 as the sole input variable presented the worst performance, probably because its relationship with ETo cannot be linearly described. The results indicate that MLR has the potential to produce very good predictive models of ETo for the Peloponnese, based on the literature standards.
... The unavailability of input data is a global issue, due to the high cost of equipping and running meteorological stations, especially for developing countries. Thus, reducing the number of inputs for the predicting models to only trivial parameters is highly recommended [64]. Those parameters can be air temperature (minimum, maximum and mean values) plus parameters that can literature standards, and to indicate the most influential factors on ETo. ...
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The aim of the study was to investigate the utility of artificial neural networks (ANNs) for the estimation of reference evapotranspiration (ETo) on the Peloponnese Peninsula in Greece for two representative months of wintertime and summertime during 2016–2019 and to test if using fewer inputs could lead to satisfactory predictions. Datasets from sixty-two meteorological stations were employed. The available inputs were mean temperature (Tmean), sunshine (N), solar radiation (Rs), net radiation (Rn), vapour pressure deficit (es-ea), wind speed (u2) and altitude (Z). Nineteen Multi-layer Perceptron (MLP) and Radial Basis Function (RBF) models were tested and compared against the corresponding FAO-56 Penman Monteith (FAO PM) estimates of a previous study, via statistical indices. The MLP1 7-2 model with all the variables as inputs outperformed the rest of the models (RMSE = 0.290 mm d−1, R2 = 98%). The results indicate that even ANNs with simple architecture can be very good predictive models of ETo for the Peloponnese, based on the literature standards. The MLP1 model determined Tmean, followed by u2, as the two most influential factors for ETo. Moreover, when one input was used (Tmean, Rn), RBFs slightly outperformed MLPs (RMSE < 0.385 mm d−1, R2 ≥ 96%), which means that even a sole-input ANN resulted in satisfactory predictions of ETo.
... Zhao et al. (2019) [46] developed a method for post-processing seasonal GCM outputs to predict monthly and seasonal RET. Several models on heuristic and fuzzy-logic science for estimations of PE and RET and machine learning algorithms such as combined neural networks, genetic algorithm model, linear genetic programming, fuzzy genetic, adaptive neuro-fuzzy inference system, artificial neural networks, multilayer perceptron neural network, co-active neuro-fuzzy inference system, radial basis neural network and self-organizing map neural network showed high accuracy in different climate zones [15,[47][48][49][50][51]. ...
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Evapotranspiration (ET) is a parameter of major importance participating in both hydrological cycle and surface energy balance. Trends of ET are discussed along with the dependence of evaporation to key environmental variables. The evaporation paradox can be approached via natural phenomena aggravated by anthropogenic impact. ET appears as one of the most affected parameters by human activities. Complex hydrological processes are governed by local environmental conditions thus generalizations are difficult. However, in some settings, common hydrological interactions could be detected. Mediterranean climate regions (MCRs) appear vulnerability to the foreseen increase in ET, aggravated by precipitation shifting and air temperature warming, whereas in tropical forests its role is rather beneficial. ET determines groundwater level and quality. Groundwater level appeared to be a robust predictor of annual ET for peatlands in Southeast Asia. In semi-arid to arid areas, increases in ET have implications on water availability and soil salinization. ET-changes after a wildfire can be substantial for groundwater recharge if a canopy-loss threshold is surpassed. Those consequences are site-specific. Post-fire ET rebound seems climate and fire-severity-dependent. Overall, this qualitative structured review sets the foundations for interdisciplinary researchers and water managers to deploy ET as a means to address challenging environmental issues such as water availability.
... Since for each station, 17 model of MLP, GEP and RBF have formed and investigated, therefore, a total of 306 models for six climatic stations lie in various climatic zones of Pakistan were examined. As the previous studies indicate that the best practice frequently used to determine the best hydro-climatic model is to divide data set into training and testing phase ( [64], [71]). In this case, firstly model is trained with 70% of total data set while investigated its performance on predicted value for remaining 30% of total dataset. ...
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Estimation of reference evapotranspiration (ET o) is vibrantly required for estimating crop water requirement and budgeting irrigation scheduling. The beneficial use of water is of great importance due to shortage issues especially in developing countries like Pakistan. The Food and agricultural organization (FAO) developed a Peneman-Montieth (PM) method which can be globally considered as a standard method for estimation of ET o, but it requires numerous climatic data. Consequently, there is a need to find out the next best suitable method after PM method. The Multi-layer perceptron (MLP), Gene expression programing (GEP) and Radial basis function (RBF) were utilized to calculate ET o values. Monthly meteorological data of six different stations located in arid, semi-arid and humid regions of Paki-stan covered from 1980 to 2015. Seventeen input combinations comprise of various climatic variables were developed to evaluate the impact on ET o. Of the available meteorological data, 70% was employed in training while remaining 30% used in testing process. The yielded values of the developed models were compared with the ET o estimated by PM method. The outcome of the study was also applied on some other climatic regions located in USA, New Zealand and China for numerous duration only three climatic parameters, namely, maximum temperature, mean relative humidity and wind velocity had a large positive effect on increasing the accuracy of estimating ET o. By comparing the eight performing indices, MLP among all the powerful predictive modeling techniques can also be considered as the superior alternative to the conventional methods in estimation of ET o .
... The Penman method and its modifications [6,[14][15][16], Gorbunova and Mezentsev methods [2,3] and some other methods are most widely used to assess evaporation. Currently the development of methods for the evaluation of evapotranspiration from irrigated lands in arid regions is continued [7,10,17,19]. Modern models which describe the structure of the atmospheric boundary layer over the nonuniform complex land surface can be used as a base to specify and summarize methods for evapotranspiration assessment [4]. ...
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The applicability is analyzed of the modeling system consisting of the MGO regional climate model and multilevel atmospheric boundary layer model for the mesoscale climate change evaluation in the regions with irrigated land use. Based on these models, the Aral Sea evolution impact on the spatial distribution of temperature and humidity in the vicinity of irrigated land is assessed. Numerical experiments cover climate evolution during 1979-2011. It is shown that in the middle of the 20th century the Aral Sea impact was manifested in the temperature and humidity distributions up to the altitude of 200-300 m at the distance of about 40 km off the seashore. The effect of advection on the calculated values of evapotranspiration in irrigated areas located at different distances from the sea is also investigated. Different methods for the determination of evapotranspiration over the irrigated cotton fields are intercompared. The influence of different resolution of surface temperature distribution on total evapotranspiration estimates is analyzed.
Thesis
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The aim of the Ph.D thesis is the foundation of a new temperature-based model since simplified PET estimation proves very useful in absence of a complete data set. In this respect, the Parametric model is presented based on a simplified formulation of the well-established Penman-Monteith expression, which only requires mean daily or monthly temperature data. The model was applied at both global and local regions and the outcomes of this new approach are very encouraging, as indicated by the substantially high validation scores of the proposed approach across all examined data sets. In general, the parametric model outperforms well-established methods of the everyday practice. A second analysis which was examined as part of this thesis is related to which spatial techniques is the optimal in order to transform the point scale estimate in regional. A thorough analysis of different geostatistical model was carried out (Kriging, IDW, NN, BSS) and it can be concluded that the IDW even is the most simplify geostatistical model, it can be produce consistent spatial PET results. Another part of the thesis was the development of an R function for testing the trend significance of time series. The function calculates the trend significance using a modified Mann- Kendall test, which takes into account the well-known physical behavior of the Hurst-Kolmogorov dynamics. The function is tested in 10 stations in Greece, with approximately 50 years of PET data with the use of a recent parametric model. Finally, a number of hydrological, agronomist and climatologist applications are presented for lighting the robustness of the new Parametric approach in multidiscipline areas.
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This guide to estimating daily and monthly actual, potential, reference crop and pan evaporation covers topics that are of interest to researchers, consulting hydrologists and practicing engineers. Topics include estimating actual evaporation from deep lakes and from farm dams and for catchment water balance studies, estimating potential evaporation as input to rainfall-runoff models, and reference crop evapotranspiration for small irrigation areas, and for irrigation within large irrigation districts. Inspiration for this guide arose in response to the authors' experiences in reviewing research papers and consulting reports where estimation of the actual evaporation component in catchment and water balance studies was often inadequately handled. Practical guides using consistent terminology that cover both theory and practice are not readily available. Here we provide such a guide, which is divided into three parts. The first part provides background theory and an outline of the conceptual models of potential evaporation of Penman, Penman–Monteith and Priestley–Taylor, as well as discussions of reference crop evapotranspiration and Class-A pan evaporation. The last two sub-sections in this first part include techniques to estimate actual evaporation from (i) open-surface water and (ii) landscapes and catchments (Morton and the advection-aridity models). The second part addresses topics confronting a practicing hydrologist, e.g. estimating actual evaporation for deep lakes, shallow lakes and farm dams, lakes covered with vegetation, catchments, irrigation areas and bare soil. The third part addresses six related issues: (i) automatic (hard wired) calculation of evaporation estimates in commercial weather stations, (ii) evaporation estimates without wind data, (iii) at-site meteorological data, (iv) dealing with evaporation in a climate change environment, (v) 24 h versus day-light hour estimation of meteorological variables, and (vi) uncertainty in evaporation estimates. This paper is supported by a Supplement that includes 21 sections enhancing the material in the text, worked examples of many procedures discussed in the paper, a program listing (Fortran 90) of Morton's WREVAP evaporation models along with tables of monthly Class-A pan coefficients for 68 locations across Australia and other information.
Chapter
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Evaporation can be viewed both as energy (heat) exchange and an aerodynamic process. According to the energy balance approach, the net radiation at the Earth’s surface (Rn = Sn – Ln, where Sn and Ln are the shortwave—solar—and longwave—earth—radiation, respectively) is mainly transformed to latent heat flux, Λ, and sensible heat flux to the air, H. The evaporation rate, expressed in terms of mass per unit area and time (e.g. kg/m²/d), is given by the ratio E΄ := Λ / λ, where λ is the latent heat of vaporization, with typical value 2460 kJ/kg. By ignoring fluxes of lower importance, such as soil heat flux, the heat balance equation is solved for evaporation, yielding: where b := H / Λ is the co-called Bowen ratio. The estimation of b requires the measurement of temperature at two levels (surface and atmosphere), as well as the measurement of humidity at the atmosphere. On the other hand, the estimation of the net radiation Rn is based on a radiation balance approach to determine the components Sn and Ln. Typical input data required (in addition to latitude and time of the year), are solar radiation (direct and diffuse, or, in absence of them, sunshine duration data or cloud cover observations), temperature and relative humidity. The net radiation also depends of surface properties (i.e. albedo) and topographical characteristics, in terms of slope, aspect and shadowing. Recent studies proved that the impacts of topography are important at all spatial scales, although they are usually neglected in calculations [23]. where Δ is the slope of vapor pressure/temperature curve at equilibrium temperature (hPa/K), γ is a psychrometrcic coefficient, with typical value 0.67 hPa/K, and D is the vapor pressure deficit of the air (hPa), defined as the difference between the saturation vapor pressure ea and the actual vapor pressure es, which are functions of temperature and relative humidity. We remind that (2) estimates the evaporation rate (mass per unit area per day), which is expressed in terms of equivalent water depth by dividing by the water density ρ (1000 kg/m³). Next we will use symbols Ε΄ for evaporation rates, and E := Ε΄ / ρ for equivalent depths per unit time. In this context, FAO proposed the application of the Penman–Monteith method for the hypothetical reference crop, thus introducing the concept of reference evapotranspiration. With standardized height for wind speed, temperature and humidity measurements at 2.0 m and the crop height of 0.12 m, the aerodynamic and surface resistances become ra = 208 / u2 (where u2 is the wind velocity, in m/s) and rs = 70 s/m. The experts of FAO suggested using the Penman–Monteith method as the standard for reference evapotranspiration and advised on procedures for calculation of the various meteorological inputs and parameters [7].
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Evapotranspiration is a key hydrometeorological process and its estimation is important in many fields of hydrological and agricultural sciences. Simplified estimation proves very useful in absence of a complete data set. In this respect, a parametric model based on simplification of the Penman-Monteith formulation is presented. The basic idea of the parametric model is the replacement of some of the variables and constants that are used in the standard Penman-Monteith model by regionally varying parameters, which are estimated through calibration. The model is implemented in various climates on monthly time step (USA, Germany, Spain) and compared on the same basis with four radiation-based methods (Jensen-Haise, McGuiness and Bordne, Hargreaves and Oudin) and two temperature-based (Thornthwaite and Blaney-Criddle). The methodology yields very good results with high efficiency indexes, outperforming the other models. Finally, a spatial analysis including the correlation of parameters with latitude and elevation together with their regionalization through three common spatial interpolation techniques along with a recent approach (Bilinear Surface Smoothing), is performed. Also, the model is validated against Penman-Monteith estimates in eleven stations of the well-known CIMIS network. The total framework which includes the development, the implementation, the comparison and the mapping of parameters illustrates a new parsimonious and high efficiency methodology in the assessment of potential evapotranspiration field.
Article
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Eighteen radiation-based equations used to estimate reference evapotranspiration (ETref) were generalized into seven linear models. The general models were calibrated using the standard FAO-56 Penman-Monteith method. Model performance was evaluated under humid, sub-humid and semi-arid mediterranean climatic conditions in central Greece. Evaluation and comparison of the models was based on quantitative assessment of their ability to accurately estimate ETref values, generated by the FAO-56 Penman-Monteith equation. All models provided relatively accurate estimates of ETref. The Abtew model showed the best overall performance with respect to the data from all available climate stations of central Greece. The average error of the Abtew model in the monthly average daily ETref estimates was 0.24 mm, which corresponds to a relative error of 7.7 %. The Abtew method has not yet been tested under mediterranean climatic conditions. Based on our results, it seems to be a good choice for the estimation of monthly average daily ETref under different conditions in the mediterranean climate. An exception appears to be the mediterranean climate with relatively high humidity and low wind speed. Under these conditions the models of the Priestley-Taylor group, the Makkink group and the Jensen-Haise group performed better than the Abtew equation.
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This guide to estimating daily and monthly actual, potential, reference crop and pan evaporation covers topics that are of interest to researchers, consulting hydrologists and practicing engineers. Topics include estimating actual evaporation from deep lakes and from farm dams and for catchment water balance studies, estimating potential evaporation as input to rainfall-runoff models, and reference crop evapotranspiration for small irrigation areas, and for irrigation within large irrigation districts. Inspiration for this guide arose in response to the authors' experiences in reviewing research papers and consulting reports where estimation of the actual evaporation component in catchment and water balance studies was often inadequately handled. Practical guides using consistent terminology that cover both theory and practice are not readily available. Here we provide such a guide, which is divided into three parts. The first part provides background theory and an outline of the conceptual models of potential evaporation of Penman, Penman-Monteith and Priestley-Taylor, as well as discussions of reference crop evapotranspiration and Class-A pan evaporation. The last two sub-sections in this first part include techniques to estimate actual evaporation from (i) open-surface water and (ii) landscapes and catchments (Morton and the advection-aridity models). The second part addresses topics confronting a practicing hydrologist, e.g. estimating actual evaporation for deep lakes, shallow lakes and farm dams, lakes covered with vegetation, catchments, irrigation areas and bare soil. The third part addresses six related issues: (i) automatic (hard wired) calculation of evaporation estimates in commercial weather stations, (ii) evaporation estimates without wind data, (iii) at-site meteorological data, (iv) dealing with evaporation in a climate change environment, (v) 24 h versus day-light hour estimation of meteorological variables, and (vi) uncertainty in evaporation estimates. This paper is supported by a Supplement that includes 21 sections enhancing the material in the text, worked examples of many procedures discussed in the paper, a program listing (Fortran 90) of Morton's WREVAP evaporation models along with tables of monthly Class-A pan coefficients for 68 locations across Australia and other information.
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An analysis of water shortages for municipal and industrial, and (project type) irrigation uses is presented. The investigation was undertaken to compile data on water shortages for these uses and to establish general practical guides for use in planning studies by governmental agencies and consulting firms. It is concluded that shortages of any magnitude should not be permitted in studies in which water is to be supplied for municipal and industrial purposes. In regard to irrigation, no firm guides and limitations based entirely on water shortages are recommended. In determining the feasibility of irrigation, economic analyses will be made, on a project by project basis, that will consider reduced crop yields due to water shortages. Desirable limits on water shortages for irrigation in planning work are considered to be as follows: Maximum average annual for 50-yr period, 3% maximum for a single year, 50% maximum for two consecutive years (total), 70% and maximum shortage years, 27%.
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Increasing population and needs for an augmented food supply give greater importance to improved procedures for estimating agricultural water requirements both for irrigation and for rain- fed agriculture. Four methods for estimating potential evapotranspiration are compared and evaluated. These are the Class A evaporation pan located in an irrigated pasture area, the Hargreaves equation, the Jensen-Haise equation, and the Blaney-Criddle method. -from ASCE Publications Abstracts Dept of Agric & Irrig Eng, Utah State Univ, Logan, UT 84322, USA.
Article
New simple algebraic expressions equivalent in accuracy to the "standardized" FAO-56 Penman-Monteith daily reference crop evapotranspiration (ET0) computation procedure are derived. The suggested formulas are based on extensions made to a previously developed simple algebraic formula for the Penman evaporation equation. The derivation of the new formulas is based on simplifications made and the systematic analysis on the correspondence between the FAO-56 Penman-Monteith equation and the standardized Penman's equation. The ET0 calculated by the new formulas is easy to use for routine hydrologic applications requiring routine weather records usually available at standard weather stations: air temperature, T (degrees C), solar radiation R-s (MJ/m(2)/d), relative humidity, RH (%), and wind velocity, u (m/s). For places where not all these data are available (or reliable), new expressions which does not require wind speed and/or solar radiation data are proposed. A simplified formula for estimating reference crop evapotranspiration requiring T-max and T-min (the maximum and minimum air temperatures), and T-dew (the dew point temperature) or RH data alone is derived. The performance of the new derived formulas was tested under various climatic conditions using a global climatic data set including monthly data as well as daily data obtained from weather stations.