ETCALC - Evapotranspiration online calculator
1. About ETCalc
ETCalc is an online evapotranspiration calculator developed through a collaborative research effort between Canadian Rivers Institute (CRI), University of New Brunswick (UNB), Agriculture and Agri-Food Canada (AAFC) and Environment and Climate Change Canada (ECCC). ETCalc has been developed as part of the research effort aimed at evaluating the effects of agricultural production practices on groundwater and surface water quality and on the quality of downgradient aquatic ecosystems. This calculator is part of a suite of tools that can be used for analyzing streamflow (i.e. baseflow / hydrograph separation), soil water balance, soil water deficit, crop water stress (deficit or excess), crop irrigation requirements, impact of irrigation on aquifer storage, impact of climate change on soil water balance, etc.). The tools are available at https://www.hydrotools.tech.
ETCalc offers several customizable methods for calculating daily Potential Evapotranspiration (PET) / Reference Evapotranspiration (ETR) and Actual Evapotranspiration (ET) based on user provided meteorological data and crop coefficients. The empirical equations included in ETCalc have been already published and have been selected following extensive literature search. The web-based tool provides various output and data visualization options through a user-friendly interface and a streamlined process.
For detailed instructions on how to use this tool please refer to the User Guide section.
Citation:
Danielescu S (2021) ETCalc - a web-based tool for estimation of evapotranspiration. Reference Manual. Available at https://etcalc.hydrotools.tech.
2. Background
Although several definitions exist, evapotranspiration can be simply conceptualised as the sum of evaporation of water from soil or surface of the ground and the transpiration of plants. Evapotranspiration is a key component of the hydrological cycle from local to global scales. Therefore, knowledge of the amount of evapotranspiration is important for example for understanding or estimating local or watershed scale water balances, plant / crop water stress and irrigation requirements, subsurface water storage, impacts of climate change on water balance components, etc.
There are currently many equations available for calculating the various forms of evapotranspiration. ETCalc integrates several of these methods into a streamlined interface that allows for the calculation of daily Potential Evapotranspiration (PET) / Reference Evapotranspiration (ETR) and Actual Evapotranspiration (ET) (see table below). Of note, ETCalc will calculate the various evapotranspiration forms only for the methods for which data is included in the user input dataset (i.e. the methods for which required input data is not present in the input file are disabled).
ETCALC: available methods and data requirements*
MethodPPTmeanTmaxTminRHmeanRHmaxRHminSRTOASRSFCWND
Penman-Monteith (PM) xOpt.Opt.Opt.Opt.Opt. xx
Thornthwaite (TH) x
Blaney - Criddle (BC) x
Turc (TU) x x x
Priestley - Taylor (PT) x x
Hargreaves (HA) x x x x
Jensen - Haise (JH) x x
Abtew (AB) x
Notations: Opt. - optional data; PP - daily total precipitation (Note: PP is not currently used by any of the ETCalc methods; PP could be included in the user input data if comparison with ETCalc output is of interest); Tmax - daily maximum air temperature; Tmin - daily minimum air temperature; RHmean – daily mean air relative humidity; RHmax – daily maximum air relative humidity; RHmin – daily minimum air relative humidity; SRTOA - daily solar radiation @ top-of-atmosphere; SRSFC - daily solar radiation @ surface of the ground; WND - daily wind speed.
A diagram of ETCalc workflow is shown below. All methods integrated in ETCalc require daily weather data and depending on the method, the direct output consists in either Potential Evapotranspiration (PET) or Reference Evapotranspiration (ETR). Actual or crop evapotranspiration (ET) is obtained by multiplying the direct output of the method with the chosen crop coefficients, which can be fixed throughout the year or variable on a monthly basis.
ETCalc Workflow
For detailed instructions on how to use the evapotranspiration online calculator please refer to the User Guide section.
3. Methodology
Currently, the ETCalc online evapotranspiration calculator includes 8 methods for calculating the various evapotranspiration forms. Brief descriptions of the concepts and methods used are included below.
3.1. Definitions
The definitions for the most relevant terms used by the ETCalc online evapotranspiration calculator are included below. It should be noted, that in literature, there are slight variations in the definition of some of these terms, and hence, the user is encouraged to thoroughly review the various concepts and definitions used in calculation of the various forms of evapotranspiration.
Crop coefficients: these are coefficients that allow for accounting for the difference between potential evapotranspiration (PET) or reference evapotranspiration (ETR) and crop or actual evapotranspiration (ET). The crop coefficient has been introduced for accounting for the differences between the evapotranspiration for the actual crop (or “land cover”) and the evapotranspiration for the reference surface or reference crop (i.e. the land cover or the crop used for calculating PET or ETR). Of note, the definition (and values) of crop coefficients vary in accordance with the specifics of each evapotranspiration calculation method (i.e. the crop coefficient is method specific). In ETCalc, the crop coefficients are denoted with the letter K and can be fixed (Kfix, one value for the entire year) or variable (Kvar, the value can change on a monthly basis).
PET (Potential evapotranspiration): this is considered to be equivalent to the maximum evapotranspiration that would occur if the water supply is not limiting. Note that specific evapotranspiration methods might use a slightly different definition for PET. For example, PET could be considered to be equivalent of the evaporation from an open water surface (e.g. lake). In ETCalc output, ET0 notation is used for PET, and the user has to refer to the description of the method to identify if for a particular method either PET or ETR is calculated.
ETR (Reference evapotranspiration): this is typically considered to occur for example when a short crop (i.e. grass) fully covers the ground and always has a good supply of water. Note that specific evapotranspiration methods might use a slightly different definition for ETR. ETR is always lower than PET. In ETCalc output, ET0 notation is used for PET, and the user has to refer to the description of the method to identify if for a particular method either PET or ETR is calculated.
ET (Crop evapotranspiration or Actual evapotranspiration): this form of evapotranspiration accounts for both weather (i.e. integrated in PET and ETR formulas) and land cover or crop (i.e. via crop coefficients). ET is the product of ET0 (PET or ETR, depending of the method) and K (crop coefficient). Note that specific evapotranspiration methods might use a slightly different definition for the various evapotranspiration forms or crop coefficients. ET is always lower than PET, however it can be higher or lower than ETR. In ETCalc output, depending on the method of calculation, ETF or ETV notations are used for actual (crop) evapotranspiration, depending on the type of crop coefficient used for its calculation. ETF is used for the cases when a fixed crop coefficient has been used (Kfix) and ETV is used for the cases when a variable crop coefficient has been used (Kvar) respectively.
Input data: this is a dataset consisting of daily weather data and validation data. The input data has to be uploaded using a file with a fixed number of columns (i.e. 14 columns, with 1 column for date, 10 columns for weather data and 3 columns for validation data). The columns for which data is not available can be left blank. For example, if only daily mean air temperature data is available, then only the column Tmean should have values, with all other columns left blank. The methods for which required data is not present are disabled by ETCalc. Consult Load Input Data and Perform Evapotranspiration Calculations sections of the User Guide for more details regarding the data quality checks included in ETCalc. In the example above, only Blaney-Criddle (BC) and Thornthwaite (TH) methods will be available for calculating the evapotranspiration forms.
Validation data: this dataset is part of the Input data file (i.e. the last 3 columns in the input data file). The validation data provides means for directly comparing any of the data output from ETCalc with a dataset obtained using different methods or sources. The validation dataset can consist of evapotranspiration data, but could also consist of other data types such as soil moisture, soil temperature, groundwater table elevations, etc.
3.2. Crop Coefficients (K)
Depending on the method(s) selected, the direct output from each of the evapotranspiration methods included in the ETCalc online evapotranspiration calculator is either Potential Evapotranspiration (PET) or Reference Evapotranspiration (ETR). To obtain actual (crop) evapotranspiration (ET), the crop coefficients (K) need to be used. Crop coefficients can be interpreted as "land cover" coefficients when evapotranspiration is estimated in non-agricultural areas. ET is simply the product of the method's direct output (i.e. PET or ETR) and the crop coefficient (K). It should be noted the meaning of crop coefficients can be slightly different for each of the methods integrated in ETCalc. Hence, the best practice is to calibrate the crop coefficients separately for each method. The higher the crop coefficient is, the higher ET will be. ET is always lower than PET, however it can be either lower or higher than ETR.
ETCalc provides the option to use either fixed (Kfix) or monthly variable (Kvar) crop coefficients throughout the year, and these can be different for each of the methods used. In ETCalc, the resulting actual (crop) evapotranspiration (ET) is denoted either as ETF if a fixed crop coefficient has been used or as ETV, if a variable crop coefficient has been used. Generally, Kvar would be the better choice as it allows the crop coefficient to be adjusted in response to, for example, monthly weather and various growth stages of the plants. However, Kvar values might be more difficult to obtain and hence, Kfix option is provided if a simplified approach is deemed sufficient for the purpose of calculating evapotranspiration.
There are currently many sources of crop coefficients values readily available in literature. Typically, in literature either a single value (e.g. 0.3), a range of values (e.g. 0.2-0.5) or values for beginning, middle and end of the growing season (e.g. 0.2/0.65/0.2) are provided. In ETCalc initial values for both Kfix and Kvar are provided, however, the users are encouraged to adjust these values in accordance with their requirements and conditions of their study area (e.g. change Ks to reflect the crops for which evapotranspiration is calculated).
For Kfix a single value is provided for the entire year, while for Kvar, ETCalc uses an interpolation algorithm to calculate Kvar for each month of the year based on values provided by the user for three key periods: January - February, July-August and December. Once an initial set of values for Ks(Kfix and/or Kvar) is selected, this set becomes a “reference” set and the Ks for each of the methods can be obtained by applying a user specified multiplier (i.e. factor) to the Ks used for the “reference” set. For example if for a selected method the user wishes to use the same K values as the one used in the reference set, a value of “1” has to be specified for the K multiplier.
3.3. Penman-Monteith Method (PM)
Overview: Penman-Monteith method is a widely used method for estimation of ETR based on a combination of energy balance and aerodynamic components. This method has been developed by FAO and is recommended as the standard method for estimating ETR. One disadvantage of the method is that it requires extensive input data sets and hence, is calculation intensive. For example Penman-Monteith methods requires more than 20 steps for obtaining ETR compared to up to 4 steps required by other methods included in ETCalc. The Penman-Monteith formulation used in ETCalc is based on Allen et al. (1998), following the calculation steps outlined in Zotarrelli et al. (2010) and Cai et al. (2007). In addition, several calibration coefficients (i.e. ac, bc, al, bl) required for the calculation of the net longwave radiation were incorporated in ETCalc based on the methodology proposed in Carmona et al. (2017).
Data requirements: Mean air temperature (Tmean); Maximum air temperature (Tmax), Minimum air temperature (Tmin), Mean air relative humidity (RHmean), Maximum air relative humidity (RHmax), Minimun air relative humidity (RHmin), Solar Radiation at the surface of the ground (SRSFC) and Wind speed (WND). ETCalc, in accordance with the methodologies described in the references above, allows for i) use of Tmean instead of Tmax and Tmin for calculation of mean saturation vapor pressure (es) if Tmax and Tmin are absent or not reliable; ii) use of RHmean instead of RHmax and RH min for calculation of actual vapor pressure (ea) if RHmax and RHmin are absent or not reliable; and iii) use of Tmin instead of RHmean for calculation of actual vapor pressure (ea) if RH data is absent or not reliable.
Data output: Reference Evapotranspiration (ETF and/or ETV), Actual evapotranspiration (ET) (using crop coefficients).
Formula:
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Penman-Monteith Method
Where:
ETR - daily reference evapotranspiration (mm)
SRSFC - daily solar radiation incident on a horizontal surface at the surface of the earth (MJm-2 day-1)
RHmean - daily mean air relative humidity (%)
RHmax - daily maximum air relative humidity (%)
Rh mean - daily minimum air relative humidity (%)
Tmax - daily maximum air temperature (oC)
Tmean - daily mean air temperature (oC)
Tmin - daily minimum air temperature (oC)
WNDh - daily wind speed measured at h m above the ground (m s-1)

a - albedo or canopy reflection coefficient
ac - FAO calibration coefficient 3 (1.35)
al - FAO calibration coefficient 1 (0.34)
bc - FAO calibration coefficient 4 (-0.35)
bl - FAO calibration coefficient 2 (-0.14)
Cd - the denominator constant for the reference crop type and time step
Cn - numerator constant for the reference crop type and time step
dr - daily inverse relative distance Earth-Sun
DT - daily Delta Term (DT) (part of calculations for Radiation Term)
ea - daily mean actual vapour pressure (kPa)
ea1 - daily mean actual vapour pressure (kPa) [used as ea when RH max and RH min are available and reliable]
ea2 - daily mean actual vapour pressure (kPa) [used as ea when RH max and RH min are absent or not reliable]
ea3 - daily mean actual vapour pressure (kPa) [used as ea when RH data is absent or not reliable]
es - daily mean vapour pressure of the air at saturation (kPa)
eTmax - daily saturation vapour pressure at the mean daily maximum air temperature (kPa)
eTmean- daily saturation vapour pressure at the daily mean air temperature (kPa) [used as es if Tmax and Tmin are absent or not reliable)
eTmin - daily saturation vapor pressure at the mean daily minimum air temperature (kPa)
ETrad - daily radiation term (mm day-1)
ETwind - daily wind term (mm day-1)
G - daily soil heat flux density (MJ m-2 day-1) [G may be ignored for daily time step computation]
GSC - solar constant (0.082 MJ m-2 min-1)
h - height of wind speed measurement above the ground surface (m)
J - day-of-year number (i.e. day number of the day in the year; 1 to 365 or 366)
P - atmospheric pressure (kPa)
PT - daily Psi Term (PT) (part of calculations for Wind Term)
Ra - daily extraterrestrial radiation (MJ m-2 day-1)
Rn - daily net radiation flux (MJ m-2 day-1)
Rng - daily net radiation (Rn) in equivalent of evaporation (mm)
Rnl - daily net outgoing longwave radiation (MJ m-2 day-1)
Rns - daily net solar or shortwave radiation (MJ m-2 day-1)
Rso - daily clear sky solar radiation (MJ m-2 day-1)
TT - daily Temperature Term (TT) (part of calculations for Wind Term)
WND2 - daily wind speed 2 m above the ground surface (m s-1)
z - elevation above sea level at the location (m)
γ - psychrometric constant (kPa oC-1)
δ - daily solar declination (rad)
∆ - daily slope of the vapor pressure curve (kPa oC-1)
σ - Stefan-Boltzmann constant (4.903 x 10-9 MJ K-4 m-2 day-1)
ϕ - latitude of the location (rad)
ωs - daily sunset hour angle (rad)
References:
Allen RG, Pereira LS, Raes D, Smith M (1998) Crop Evapotranspiration: Guidelines for Computing Crop Water Requirements. FAO Irrigation and Drainage Paper 56, Rome, 300.
Cai J, Liu Y, Lei T, Pereira LS (2007) Estimating reference evapotranspiration with the FAO Penman-Monteith equation using daily weather forecast messages. Ag. For. Meteor. 145: 22-35
Carmona F, Rivas R, Kruse E (2017) Estimating daily net radiation in the FAO Penman-Monteith method. Theor. Appl. Climatol. 129:89-95
Zotarelli L, Dukes MD, Romero CC, Migliaccio KW, Morgan KT (2010) Step by Step Calculation of the Penman-Monteith Evapotranspiration (FAO-56 Method). AE459. Agricultural and Biological Engineering Department, Florida Cooperative Extension Service, IFAS, UF. URL: http://edis.ifas.ufl.edu/ae459, 12 pgs.
3.4. Thornthwaite Method (TH)
Overview: This is a simple method which requires only mean air temperature data. Previous research suggested that Thornthwaite method might underestimate evapotranspiration under arid conditions while overestimating it under equatorial humid regions. Hence, an adaptation of this method (i.e. Wilmott adaptation) has been developed for reducing this bias when air temperature is above 26 oC. Although the method has been initially used with monthly data, a correction factor for applying the method to daily data has been developed.
Data requirements: Mean air temperature (Tmean).
Data output: Reference Evapotranspiration (ETF and/or ETV), Actual evapotranspiration (ET) (using crop coefficients). (using crop coefficients).
Formula:
Thornthwaite Method
If Tmean ≤ 0 oC
Thornthwaite Method
If 0 oC ≤ Tmean ≤ 26 oC
Thornthwaite Method
Thornthwaite Method
Thornthwaite Method
If Tmean > 26 oC
Thornthwaite Method
Where:
C - correction factor from converting from monthly to daily time scale
N - duration of the photoperiod (h)
ETR - daily reference evapotranspiration (mm)
Tmean - daily mean air temperature (oC)
I - thermal index
a - exponent
Tnormal - local normal climatic temperature (oC)
References:
Pereira AR, Pruitt WO (2004) Adaptation of the Thornthwaite scheme for estimating daily reference evapotranspiration. Ag. Wat. Manag. 66: 251-257.
Thornthwaite CW (1948) An approach toward a rational classification of climate. Geogr. Rev. 38: 55-94.
Willmott CJ, Rowe C., Mintz Y (1985) Climatology of the terrestrial seasonal water cycle. J. Climatol. 5: 589-606.
3.5. Blaney-Criddle Method (BC)
Overview: This is a simple method, which uses only mean air temperature data. Because of the limited input data this method is not very accurate and can be used to provide a rough estimate of evapotranspiration. It was shown in the past that evapotranspiration obtained with Blaney-Criddle method could be underestimated in windy, dry, sunny conditions and overestimated in calm, humid, clouded areas.
Data requirements: Mean air temperature (Tmean);
Data output: Reference Evapotranspiration (ETF and/or ETV), Actual evapotranspiration (ET) (using crop coefficients).
Formula:
Blaney-Criddle Method
Where:
ETR - daily reference evapotranspiration (mm)
p - mean daily percentage of annual daytime hours
Tmean - daily mean air temperature (oC)
Mean daily percentage (p) of annual daytime hours for various latitudes
(based on Brouwer & Heibloem [1986])
LatitudeNorthJanFebMarAprMayJunJulAugSepOctNovDec
SouthJulAugSepOctNovDecJanFebMarAprMayJun
60°0.150.200.260.320.380.410.400.340.280.220.170.13
55°0.170.210.260.320.360.390.380.330.280.230.180.16
50°0.190.230.270.310.340.360.350.320.280.240.200.18
45°0.200.230.270.300.340.350.340.320.280.240.210.20
40°0.220.240.270.300.320.340.330.310.280.250.220.21
35°0.230.250.270.290.310.320.320.300.280.250.230.22
30°0.240.250.270.290.310.320.310.300.280.260.240.23
25°0.240.260.270.290.300.310.310.290.280.260.250.24
20°0.250.260.270.280.290.300.300.290.280.260.250.25
15°0.260.260.270.280.290.290.290.280.280.270.260.25
10°0.260.270.270.280.280.290.290.280.280.270.260.26
5°0.270.270.270.280.280.280.280.280.280.270.270.27
0°0.270.270.270.270.270.270.270.270.270.270.270.27
References:
Brouwer C, Heibloem M (1986) Irrigation Water Management: Irrigation Water Needs. Part II - Determination of Irrigation Water Needs. FAO Irrigation Water Management. Training manual No. 3, FAO, Land and Water Development Division, Rome, Italy.
Blaney HF, Criddle WD (1950) Determining water requirements in irrigated areas from climatological and irrigation data. United States Department of Agriculture, Soil Conservation Service.
3.6. Turc Method (TU)
Overview: This is an energy balance-based method which uses mean air relative temperature, solar radiation and air relative humidity. The method has been modified in ETCalc by introducing an additional condition (i.e., ET=0 if Tmean<0) to prevent the formula from yielding negative ET values at temperatures below 0 oC.
Data requirements: Mean air temperature (Tmean); Solar Radiation at the surface of the ground (SRSFC), Mean air relative humidity (RHmean).
Data output: Potential Evapotranspiration (PET), Actual evapotranspiration (ETF and/or ETV).
Formula:
If Tmean<0oC:
Turc Method
If Tmean>0oC and RH<50%:
Turc Method
If Tmean>0oC and RH>50%:
Turc Method
Where:
PET - daily Potential evapotranspiration (mm)
Tmean - daily mean air temperature (oC)
SRSFC - daily solar radiation incident on a horizontal surface at the surface of the earth (MJm−2 day−1)
RHmean - daily mean air relative humidity (%)
References:
Amatya DM, Harriso CA (2016) Grass and Forest Potential Evapotranspiration Comparison Using Five Methods in the Atlantic Coastal Plain. J. Hydrol. Eng. 05016007.
Turc L (1961) Estimation of irrigation water requirements, potential evapotranspiration: A simple climatic formula evolved up to date. J. Ann. Agron., 12: 13-14 (in French).
3.7. Priestley-Taylor Method (PT)
Overview: This is physically-based formulation, which could be interpreted as a simplified version of the Penman - Monteith formula for calculating evapotranspiration. This simplification has been achieved by removing the aerodynamic terms from the Penman-Monteith equation and by using a constant (i.e. α). This constant has been derived empirically and is considered to be higher for arid areas or areas with significant water stress. The Priestley-Taylor formula can be used for calculating daily evapotranspiration, but can also be used for smaller time-steps (i.e. hourly) provided the required data is available.
Data requirements: Mean air temperature (Tmean); Solar Radiation at the surface of the ground (SRSFC).
Data output: Potential Evapotranspiration (PET), Actual evapotranspiration (ETF and/or ETV).
Formula:
Priestley-Taylor Method
If Tmean<0oC
Priestley-Taylor Method
If Tmean>0oC
Priestley-Taylor Method
Where:
PET - daily potential evapotranspiration (m)
λv - latent heat of vaporization (2260 kJ kg-1)
ρw - density of water (1000 kg m-3)
Δ - slope of the saturation vapor density curve from the psychrometric chart (kg oC-1)
γ - psychrometric constant (4.95x10-4 kg m-3 oC-1)
Tmean - daily mean air temperature (oC)
SRSFC - daily solar radiation incident on a horizontal surface at the surface of the earth (kJ m−2)
References:
Priestley CHB, Taylor RJ (1972) On the assessment of the surface heat flux and evaporation using large-scale parameters. Mon. Weather Rev 100: 81-92.
Jensen ME, Burman RD, Allen RG (1990) Evapotranspiration and Irrigation Water Requirement. ASCE Manuals and Reports on Engineering Practices. Vol. 70. New York, NY: American Society of Civil Engineers. ISBN 978-0-87262-763-5.
3.8. Hargreaves Method (HA)
Overview: Hargreaves formula provides a simple method for calculating evapotranspiration based on an empirical relationship involving temperature and solar radiation.
Data requirements: Mean air temperature (Tmean); Maximum air temperature (Tmax), Minimum air temperature (Tmin), Solar Radiation at the top of atmosphere (SRTOA).
Data output: Reference Evapotranspiration (ETR), Actual evapotranspiration (ETF and/or ETV).
Formula:
Hargreaves Method (HA)
Where:
ETR - daily reference evapotranspiration (m)
Cf - conversion factor (0.0023)
Tmean - daily mean air temperature (oC)
Tmax - daily maximum air temperature (oC)
Tmin - daily minimum air temperature (oC)
SRTOA - daily solar radiation incident on the top-of-atmosphere (MJ m-2 day-1)
References:
Allen RG, Pereira LS, Raes D, Smith M (1998) Crop Evapotranspiration: Guidelines for Computing Crop Water Requirements. FAO Irrigation and Drainage Paper 56, Rome, 300.
Hargreaves GH, Allen RG (2003) History and evaluation of Hargreaves evapotranspiration equation. J Irring Drain Engine. 129: 53-63..
3.9. Jensen-Haise Method (JH)
Overview: Jensen-Haise (McGuiness model) formula provides a method for calculating evapotranspiration based on daily temperature and solar radiation. By including the solar radiation term, Jensen-Haise method represents an improvement over the methods based only on temperature.
Data requirements: Solar Radiation at the top of atmosphere (SRTOA), Mean air temperature (Tmean).
Data output: Potential Evapotranspiration (PET), Actual evapotranspiration (ETF and/or ETV).
Formula:
Jensen-Haise Method (JH)
Where:
PET - daily potential evapotranspiration (m)
SRTOA - daily solar radiation incident on the top-of-atmosphere (MJ m-2 day-1)
Tmean - daily mean air temperature (oC)
λ - latent heat of vaporization (2260 kJ kg-1)
ρ - density of water (1000 kg m-3)
References:
Tegos A, Efstratiadis A, Koutsoyiannis D. (2013) A Parametric Model for Potential Evapotranspiration Estimation Based on a Simplified Formulation of the Penman-Monteith Equation. In Evapotranspiration - an overview, Alexandris S (ed.), IntechOpen, eBook ISBN: 978-953-51-5369-6.
Jensen M, Haise H (1963) Estimating evapotranspiration from solar radiation. Journal of the Irrigation and Drainage Division. Proceedings of the ASCE 1963; 89: 15-41.
McGuinness JL, Bordne EF (1972) A comparison of lysimeter-derived potential evapotranspiration with computed values. Technical Bulletin 1452. Agricultural Research Service, US Department of Agriculture, Washington, DC.
3.10. Abtew Method (AB)
Overview: Abtew method for calculation of evapotranspiration is a simplified energy-based formulation that requires only solar radiation. Abtew method is the only method included in ETCalc that does not require temperature data. K1 coefficient has been derived empirically based on several land covers/vegetation types and hence can be adjusted accordingly.
Data requirements: Solar radiation incident on a horizontal surface at the surface of the earth (SRSFC).
Data output: Potential Evapotranspiration (PET), Actual evapotranspiration (ETF and/or ETV).
Formula:
Abtew Method (AB)
Where:
PET - daily potential evapotranspiration (m)
K1 - dimensionless coefficient (0.53)
SRSFC - daily solar radiation incident on a horizontal surface at the surface of the earth (MJ m-2 day-1)
λ - latent heat of vaporization (2.45 MJ kg-1)
Reference: Abtew W (1996) Evapotranspiration measurements and modeling for three wetland systems in south Florida. J. Am. Water Resour. Assoc. 32: 465-473.
For detailed instructions on how to use the evapotranspiration online calculator please refer to the User Guide section.
3.11. Input and Validation Data
Input data: this is a dataset consisting of daily weather data and validation data. The input data has to be uploaded using file with a fixed number of columns (i.e. 14 columns, with 1 column for date, 10 columns for weather data and 3 columns for validation data). The columns for which data is not available can be left blank. For example, if only daily mean air temperature data is available, then only the column Tmean should have values, with all other columns left blank. The methods for which required data is not present are disabled by ETCalc and the output for the respective methods will consist in zero values for all output parameters (i.e. ET0, ETF, ETV). In the example above, only Blaney-Criddle method will be available for calculating the evapotranspiration forms.
The table below shows the weather data required for each of the methods currently included in the ETCalc online evapotranspiration calculator.
ETCALC: available methods and data requirements*
MethodPPTmeanTmaxTminRHmeanRHmaxRHminSRTOASRSFCWND
Penman-Monteith (PM) xOpt.Opt.Opt.Opt.Opt. xx
Thornthwaite (TH) x
Blaney - Criddle (BC) x
Turc (TU) x x x
Priestley - Taylor (PT) x x
Hargreaves (HA) x x x x
Jensen - Haise (JH) x x
Abtew (AB) x
Notations: Opt. - optional data; PP - daily total precipitation (Note: PP is not currently used by any of the ETCalc methods; PP could be included in the user input data if comparison with ETCalc output is of interest); Tmax - daily maximum air temperature; Tmin - daily minimum air temperature; RHmean – daily mean air relative humidity; RHmax – daily maximum air relative humidity; RHmin – daily minimum air relative humidity; SRTOA - daily solar radiation @ top-of-atmosphere; SRSFC - daily solar radiation @ surface of the ground; WND - daily wind speed.
The methods for which required data is not present are disabled by ETCalc. In the example above (i.e. only Tmean available), only Blaney-Criddle (BC) and Thornthwaite (TH) methods will be available for calculating the evapotranspiration forms. Consult Load Input Data and Perform Evapotranspiration Calculations sections of the User Guide for more details regarding the data quality checks included in ETCalc.
Validation data: In addition to the weather data, the user can include validation data in the input dataset. The last three columns of the input file are reserved for the validation dataset. Validation data provides means for directly comparing any of the data output from ETCalc with a dataset obtained using different methods or sources. The validation data set can include evapotranspiration data, but could also include other data types such as soil moisture, soil temperature, groundwater table elevations, etc.
The number of columns, data format and the units of the various weather parameters required for the input file are shown in the next table:
(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)
DatePPTmeanTmaxTminRHmeanRHmaxRHminSRTOASRSFCWNDVAL1VAL2VAL3
dd-mmm-yymm°C°C°C%%%MJ/m²/dMJ/m²/dm/s???
Notes:
  • Columns have to be left blank for parameters for which data is not present
  • The first row in the input data file has to contain the column headings as specified in the table above
  • ETCalc will select the calculation methods that are available to the user based on the columns with available data
  • Data in columns Val1, Val2 and Val3 are used for comparison of ETCalc results with the data in the respective columns (i.e. if Val columns are not left blank). Measurement units for validation data are not required.
For detailed instructions on how to use the evapotranspiration online calculator please refer to the User Guide section.
4. User Guide
ETCalc is a web application that allows for the calculation of daily values of various evapotranspiration forms (Potential evapotranspiration - PET, Reference evapotranspiration - ETR, Actual (or crop) evapotranspiration - ET) based on user provided weather data and crop coefficients (Kfix, Kvar). Currently, ETCalc includes 8 methods already published and which have been selected following extensive literature research. The tool provides functionality for tabular and graphical representations of the input data (weather data and validation data), output data (PET, ETR, ET), comparison with validation data (included in the input data file), calculation of representative statistics and export of all data types (i.e. input data, output data, metadata).
On the left, a contextual menu provides access to the various components of the tool. At the top of the page, a progress bar displays the status of the analysis.
4.1. Quick Start
In order to run ETCalc the user has to complete the following steps:
  1. Load Input Data: provide required data [Source Data Menu];
  2. Perform Evapotranspiration Calculations: choose Crop Coefficients, Select ET methods and Run ETCalc [Analyze Menu];
  3. Investigate Results and Export Data: Review ETCalc output and export results [Output Data Menu].
The steps required for using this tool are described in more detail below.
4.2. Load Input Data
The first step in any analysis is to upload the Input Data file to be used by the online evapotranspiration calculator. The input data consists of a file containing 8 columns for daily weather data and 3 columns reserved for daily validation data. Not all the columns are required to be filled with data - ETCalc selects which methods for calculating evapotranspiration can be used based on the columns that contain data. The input data file can be uploaded using the Upload User Data menu entry under the SOURCE DATA menu section.
Alternatively, for a better understanding of ETCalc routines, the user can use the sample data set provided by using the Load Sample Data menu entry. The data set contains two years of daily weather and validation data.
The input dataset is a collection of daily weather data (i.e. total precipitation, mean air temperature, maximum air temperature, minimum air temperature, mean air relative humidity, maximum air relative humidity, minimum air relative humidity, solar radiation incident on the top-of-atmosphere, solar radiation incident on a horizontal surface at the surface of the earth and wind speed). The dataset has a fixed number of columns, with (i.e. 14 columns), with 1 column for date, 10 columns for weather data and 3 columns for validation data).
The tool accepts source data sets in MS Excel (xls, xslx) and Comma Separated File (csv) formats.
The table below shows the weather data required for each of the methods currently included in the ETCalc online evapotranspiration calculator. ETCalc selects which methods will be available for calculating the evapotranspiration forms based on the datasets that are uploaded (i.e. the user should leave the columns blank for the data that is not available). The methods for which required data is not present are disabled by ETCalc. Specifically, if an entire column in the input file is left blank ETCalc replaces the blank cells with zero values and disables the methods that require the respective data. However, if only some values are missing in the input file (i.e., the column with required input data contains both blank and non-blank values) ETCalc replaces the missing values with zeroes and allows for the calculations to proceed. Hence, it is recommended that the user verifies the integrity of the source data before uploading.
In addition to the daily weather data, the input file can also contain daily validation data (the last three columns of the input file) Validation data provides means for directly comparing any of the data output from ETCalc with a dataset obtained using different methods or sources. The validation data set can include evapotranspiration data, but could also include other data types such as soil moisture, soil temperature, groundwater table elevations, etc.
ETCALC: available methods and data requirements*
MethodPPTmeanTmaxTminRHmeanRHmaxRHminSRTOASRSFCWND
Penman-Monteith (PM) xOpt.Opt.Opt.Opt.Opt. xx
Thornthwaite (TH) x
Blaney - Criddle (BC) x
Turc (TU) x x x
Priestley - Taylor (PT) x x
Hargreaves (HA) x x x x
Jensen - Haise (JH) x x
Abtew (AB) x
Notations: Opt. - optional data; PP - daily total precipitation (Note: PP is not currently used by any of the ETCalc methods; PP could be included in the user input data if comparison with ETCalc output is of interest); Tmax - daily maximum air temperature; Tmin - daily minimum air temperature; RHmean - daily mean air relative humidity; RHmax - daily maximum air relative humidity; RHmin - daily minimum air relative humidity; SRTOA - daily solar radiation @ top-of-atmosphere; SRSFC - daily solar radiation @ surface of the ground; WND - daily wind speed.
The number of columns, data format and the units of the various weather parameters required for the input file are shown in the following table:
(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)
DatePPTmeanTmaxTminRHmeanRHmaxRHminSRTOASRSFCWNDVAL1VAL2VAL3
dd-mmm-yymm°C°C°C%%%MJ/m²/dMJ/m²/dm/s???
Notes:
  • Columns have to be left blank for parameters for which data is not present
  • The first row in the input data file has to contain the column headings as specified in the table above
  • ETCalc will select the calculation methods that are available to the user based on the columns with available data
  • Data in columns Val1, Val2 and Val3 are used for comparison of ETCalc results with the data in the respective columns (i.e. if Val columns are not left blank). Measurement units for validation data are not required.
Once the input dataset is loaded to ETCalc, a series of options become available in the SOURCE DATA menu section. These allow for investigation of the input data (i.e. weather and validation data) using a tabular format (Table View) as well as for visualization of the various time series (Graphical View). The Graphical View allows for inspection of the full data set or of a reduced subset by changing the beginning and the ending values of the time interval that is displayed. In the Graphical View, the user can select which parameters to be displayed, on which Y axis (i.e. left/primary or right/secondary), and what colors to be used for each of the datasets (i.e. parameters). Once the selections are completed the user can use the Update Graph button to display the data. Statistics for both the entire dataset and the selected subset are shown in Table View.
4.3. Perform Evapotranspiration Calculations
Evapotranspiration calculations can be performed once the input data is loaded and the Analyze menu entry becomes available. Once the user follows Analyze menu link, a page with two subsections becomes available: i) CROP COEFFCIENTS and II) METHOD SELECTION. The crop coefficients can be left unchanged if only the direct output of each of the available methods (i.e. Potential evapotranspiration or reference evapotranspiration, depending on the method) is of interest. Crop coefficients should be adjusted if the calculation of actual (crop) evapotranspiration (ET) is of interest. ETCalc can run all available methods at once (Run All button at the bottom of the page) or run only the methods selected by the user (Run Selected button at the bottom of the page). The methods for which required data is not present are disabled by ETCalc. Consult Load Input Data section for more details regarding the data quality checks included in ETCalc.
CROP COEFFICIENTS (K)
Crop coefficients are multiplied with the direct output (i.e. PET or ETR) from each of the methods for obtaining actual (crop) evapotranspiration (ET). Crop coefficients can be interpreted as "land cover" coefficients when evapotranspiration is estimated in non-agricultural areas. ETCalc provides the option to use either fixed (Kfix) or monthly variable (Kvar) crop coefficients throughout the year. The values of Kfix and Kvar can be different for each of the methods used, since these coefficients might have a slightly different definition for each of the methods. For Kfix a single value is provided for the entire year, while for Kvar, ETCalc uses an interpolation algorithm to calculate Kvar for each month based on values provided by the user for three periods of the year: January - February, July-August and December. Once an initial set of values for Ks (Kfix and/or Kvar) is selected, this set becomes a "reference" set and the Ks for all methods can be obtained by applying a user specified multiplier (i.e. factor) to the Ks used for the "reference" set. For example if for a selected method the user wishes to use the same K set as the one used in the reference set, a value of "1" has to be specified for the K multiplier. For more details regarding the definition of the crop coefficients, refer to section 3.2. Crop Coefficients.
METHOD SELECTION
Once the selection of the crop coefficients is complete, the user can proceed to adjusting the parameters required for each evapotranspiration calculation method. The default values for the constants associated with each method are identical with the ones used in the references provided for each of the methods, and hence it Is recommended that caution should be used if these values are to be changed. For some of the methods, the user is required to provide site-specific values (e.g. hemisphere and the latitude for Blaney-Criddle [BC], elevation of the location for Penman - Monteith [PM], etc.).
ETCalc can run all available methods at once (Run All button at the bottom of the page) or run only the methods selected by the user (Run Selected button at the bottom of the page). The methods for which required data is not present are disabled by ETCalc and the output for the respective methods will consist in zero values for all output parameters (i.e. ET0 - Potential Evapotranspiration or Reference Evapotranspiration, ETF - actual (crop) evapotranspiration using fixed crop coefficients, ETV - actual (crop) evapotranspiration using variable crop coefficients). The tool does not check for missing or erroneous data entries, hence it is recommended that the user verifies the integrity of the source data before uploading. ETCalc algorithm replaces each instance of a missing value in a non-blank column with a zero.
RANGES OF VALUES FOR COEFFICIENTS
ETCalc provides a default value for the coefficients used by each of the methods, however the user is allowed to change these values. Some of these coefficients (i.e., crop coefficients and crop coefficient multipliers, height of wind measurement, elevation of the site, albedo, geographical coordinates, normal climate temperature) and options (i.e., use of minimum and maximum temperature, use of mean or minimum and maximum air relative humidity, type of reference crop, duration of photoperiod) need to be adjusted by the user prior to performing evapotranspiration calculations. Changing of the values for the other coefficients is recommended only if further calibration and/or modification of the original formulation of the methods included in ETCalc is of interest. ETCalc checks for the values changed by the user to be within realistic limits (see table below). If the user-provided value of a coefficient is outside of these limits, then ETCalc reverts the respective value to the default value.
ETCALC: ranges of values for coefficients in the Analysis page
Input dataMin.Max.Units
Crop Coefficients
Fixed K0.002.00n.a.
Variable K0.002.00n.a.
K Multiplier0.005.00n.a.
Penman-Monteith (PM) Method
Height of wind measurement (h)0.0020.00m
Elevation of the site (z)-100.008000.00m
Albedo (a)0.001.00n.a.
Degrees latitude-4555deg.
Minutes latitude059min.
Numerator const. for ref. crop type (Cn)02000n.a.
Denominator const. for ref. crop type (Cd)0.001.00n.a.
FAO calib. coeff. 1 for Rnl (al)0.100.40n.a.
FAO calib. coeff. 2 for Rnl (bl)-0.50-0.10n.a.
FAO calib. coeff. 3 for Rnl (ac)-1.001.50n.a.
FAO calib. coeff. 4 for Rnl (bc)-1.00-0.25n.a.
Thornthwaite (TH) Method
Normal (average) temp. (Ta)2.0020.00oC
Duration of photoperiod (N)024hours
Temp. threshold for Willmott adapt.2428.00oC.
Blaney - Criddle (BC) Method
Degrees latitude-60.0060.00deg.
Turc (TU) Method
No additional coefficients required.
Priestley - Taylor (PT) Method
Empirically derived constant (α)0.102.00n.a.
Latent heat of vaporization (λv)15002000kJ kg-1
Density of water (ρw)900.01100.0kg m-3
Psychrometric constant (γ)1.00010.00010-4 kg m-3 oC
Hargreaves (HA) Method
Conversion factor (Cf)0.00100.0050n.a.
Jensen - Haise (JH) Method
Latent heat of vaporization (λv)15003000kJ kg-1
Density of water (ρw)900.01100.0kg m-3
Abtew (AB) Method
K (coefficient)0.101.00n.a.
Latent heat of vaporization (λv)1.503.00MJ kg-1
4.4. Investigate Results and Export Data
Following completion of the data analysis / evapotranspiration calculation, the tool redirects to the OUTPUT DATA (Table View) page, where the user can start to investigate the results using the method tabs located in the upper portion of this page. The user can browse the results for each method by clicking on each of the respective tabs. The Table View and Graphical View entries in the OUTPUT DATA menu section become visible only when either Run Selected or Run All has been used at least once). In a similar fashion as the Graphical View menu entry in SOURCE DATA, The Graphical View in OUTPUT DATA allows the user to inspect the full data set or only a reduced subset by changing the beginning and the ending values of the time interval that is displayed. In the Graphical View, the user can select which parameters are to be displayed, on which Y axis (i.e. left/primary or right/secondary), and what colors to be used for each of the datasets (i.e parameters). Once the selections are completed the user can use the Update Graph button to display the data.
The data set resulted from the analysis (i.e. output dataset and metadata), as well as the graphical representations and statistics relevant for the analysis, can be downloaded by using Export Output Data / Export Metadata / Download Image buttons in the Table View and Graphical View pages of OUTPUT DATA menu entries. It should be noted that Export Output Data, results in exporting all columns used by ETCalc (i.e. includes both input and output data). Export Metadata allows exporting the metadata associated with the dataset, including crop coefficients and parameters for all the methods used in the analysis.
5. Limitations
a) Large data sets (i.e. over 5000 rows) take longer to load. Please be patient until loading is completed. Once the loading is complete the user is redirected to the Source Data Table View page;
b) If the analysis cannot be conducted or takes too long even with only one method selected, it is recommended to split the input data set into smaller files. For example, running all methods simultaneously with a 2-year data set (730 rows x 11 columns = 8030 values) takes approximately 90 seconds. Running time for a single method with the above dataset ranges between 10 and 20 seconds;
c) ETCalc includes several data quality check routines (see Load Input Data and Perform Evapotranspiration Calculations sections of the User guide), however it is recommended that the user verifies the integrity of the source data before uploading for minimizing the risk for erroneous output;
d) In most cases the methods included in ETCalc have been developed for specific conditions and might not have been tested for all available situations (e.g. cold vs. warm climate; arid vs humid climate; extreme weather, etc.). Since the various methods include a wide range of input requirements and formulations and each method might be biased towards certain conditions, the user is advised to consult the references provided for determining if the application of the methods is appropriate.
6. Terms of Use
ETCalc can be used freely.
The authors do not assume any responsibility for the tool's operation, output, interpretation, or use of results. Please contact the author for additional information and feedback.
7. References (TBD)
Abtew W (1996) Evapotranspiration measurements and modeling for three wetland systems in south Florida. J. Am. Water Resour. Assoc. 32: 465–473.
Allen RG, Pereira LS, Raes D, Smith M (1998) Crop Evapotranspiration: Guidelines for Computing Crop Water Requirements. FAO Irrigation and Drainage Paper 56, Rome, 300.
Amatya DM, Harrison CA (2016) Grass and Forest Potential Evapotranspiration Comparison Using Five Methods in the Atlantic Coastal Plain. J. Hydrol. Eng. 05016007.
Blaney HF, Criddle WD (1950) Determining water requirements in irrigated areas from climatological and irrigation data. United States Department of Agriculture, Soil Conservation Service.
Brouwer C, Heibloem M (1986) Irrigation Water Management: Irrigation Water Needs. Part II – Determination of Irrigation Water Needs. FAO Irrigation Water Management. Training manual No. 3, FAO, Land and Water Development Division, Rome, Italy.
Cai J, Liu Y, Lei T, Pereira LS (2007) Estimating reference evapotranspiration with the FAO Penman–Monteith equation using daily weather forecast messages. Ag. For. Meteor. 145: 22–35.
Carmona F, Rivas R, Kruse E (2017) Estimating daily net radiation in the FAO Penman–Monteith method. Theor. Appl. Climatol. (2017) 129:89–95.
Hargreaves GH, Allen RG (2003) History and evaluation of Hargreaves evapotranspiration equation. J Irring Drain Engine. 129: 53–63.
Jensen ME, Burman RD, Allen RG (1990) Evapotranspiration and Irrigation Water Requirement. ASCE Manuals and Reports on Engineering Practices. Vol. 70. New York, NY: American Society of Civil Engineers. ISBN 978-0-87262-763-5.
Jensen ME, Haise H (1963) Estimating evapotranspiration from solar radiation. Journal of the Irrigation and Drainage Division. Proceedings of the ASCE 1963; 89: 15–41.
McGuinness JL, Bordne EF (1972) A comparison of lysimeter-derived potential evapotranspiration with computed values. Technical Bulletin 1452. Agricultural Research Service, US Department of Agriculture, Washington, DC.
Pereira AR, Pruitt WO (2004) Adaptation of the Thornthwaite scheme for estimating daily reference evapotranspiration. Ag. Wat. Manag. 66: 251–257.
Priestley CHB, Taylor RJ (1972) On the assessment of the surface heat flux and evaporation using large-scale parameters. Mon. Weather Rev 100: 81-92.
Tegos A, Efstratiadis A, Koutsoyiannis D. (2013) A Parametric Model for Potential Evapotranspiration Estimation Based on a Simplified Formulation of the Penman-Monteith Equation.In Evapotranspiration – an overview, Alexandris S (ed.), IntechOpen, eBook ISBN: 978-953-51-5369-6.
Thornthwaite CW (1948) An approach toward a rational classification of climate. Geogr. Rev. 38: 55–94.
Turc L (1961) Estimation of irrigation water requirements, potential evapotranspiration: A simple climatic formula evolved up to date. J. Ann. Agron., 12: 13–14 (in French).
Willmott CJ, Rowe C., Mintz Y (1985) Climatology of the terrestrial seasonal water cycle. J. Climatol. 5: 589–606.
Zotarelli L, Dukes MD, Romero CC, Migliaccio KW, Morgan KT (2010) Step by Step Calculation of the Penman-Monteith Evapotranspiration (FAO-56 Method). AE459. Agricultural and Biological Engineering Department, Florida Cooperative Extension Service, IFAS, UF. URL: http://edis.ifas.ufl.edu/ae459, 12 pgs.
8. Contact
Serban Danielescu, Ph.D.
Research Scientist | Chercheur scientifique
Environment and Climate Change Canada | Environnement et Changements Climatiques Canada Agriculture and Agri-Food Canada | Agriculture et Agroalimentaire Canada
Fredericton Research and Development Centre | Centre de recherche et développement de Fredericton
95 Innovation Rd., Fredericton, NB, E3B 4Z7
Telephone/Téléphone: 506-460-4468
Facsimile/Télécopieur: 506-460-4377
For detailed instructions on how to use evapotranspiration online calculator please refer to the User Guide section.