Package 'ET0RadModels'

Description

The ET0RadModels package provides functions for estimating daily reference evapotranspiration (ET0) using 10 radiation-based empirical models, with the FAO Penman-Monteith method included as the standard reference for model comparison. The package also includes statistical evaluation metrics and visualization tools.

Radiation-Based Models (10)

Jensen-Haise (1963)

Solar radiation and mean temperature.

McGuinness-Bordne (1972)

Extraterrestrial radiation and mean temperature.

Irmak (2003)

Solar radiation-based regression equation.

Makkink (1957)

Solar radiation and slope of SVP curve.

Turc (1961)

Solar radiation and mean temperature (humid conditions).

Caprio (1974)

Linear function of solar radiation and temperature.

Abtew (1996)

Simple solar radiation-based approach (coefficient 0.53).

Priestley-Taylor (1972)

Net radiation with empirical coefficient alpha = 1.26.

Jones-Ritchie (1990)

Simplified Priestley-Taylor with alpha = 1.1.

Hargreaves (1975)

Radiation-based method using solar radiation.

Key Functions

et0_rad_all

Compute ET0 using all 10 radiation-based models + FAO PM.

et0_fao_pm

FAO Penman-Monteith reference method.

evaluate_models

Compute all 9 statistical metrics.

plot_taylor

Generate Taylor diagrams.

plot_scatter

Generate scatter plots.

Data

The package includes a sample meteorological dataset (jhansi_weather) from a semi-arid region in central India for demonstrating package functionality.

Author(s)

Maintainer: Samir Barman [email protected] (ORCID)

Authors:

• Ajay N. Satpute

• Amit Kumar Singh

• Avijit Ghosh

• Gaurendra Gupta

References

Satpute, A.N., Barman, S., Singh, A.K., Ghosh, A., & Gupta, G. (2026). A multi-scale evaluation of 30 empirical models for reference evapotranspiration estimation in a data-scarce semi-arid region: A case study of Jhansi, India. Journal of Hydrology: Regional Studies. doi:10.1016/j.ejrh.2026.103925

Allen, R.G., Pereira, L.S., Raes, D., & Smith, M. (1998). Crop evapotranspiration: Guidelines for computing crop water requirements. FAO Irrigation and Drainage Paper No. 56.

See Also

Useful links:

• https://github.com/samirigfri/ET0RadModels

• Report bugs at https://github.com/samirigfri/ET0RadModels/issues

Description

Computes actual vapor pressure from relative humidity and temperature.

Usage

actual_vapor_pressure(Tmin, Tmax, RH_morning, RH_evening)

Arguments

Value

Actual vapor pressure (kPa).

References

Allen et al. (1998), FAO-56, Eq. 17.

Examples

actual_vapor_pressure(15, 30, 90, 40)

Description

Computes Willmott's index of agreement. Values range from 0 to 1, with 1 indicating perfect agreement.

Usage

calc_d(observed, predicted)

Arguments

Value

Index of agreement (numeric scalar between 0 and 1).

References

Willmott, C.J. (1981). On the validation of models. Physical Geography, 2(2), 184-194.

Examples

obs <- c(3.5, 4.2, 5.1, 2.8, 6.0)
pred <- c(3.3, 4.5, 4.9, 3.0, 5.8)
calc_d(obs, pred)

Description

Mean Absolute Error (MAE)

Usage

calc_mae(observed, predicted)

Arguments

Value

MAE value (numeric scalar).

Examples

calc_mae(c(3.5, 4.2, 5.1), c(3.3, 4.5, 4.9))

Description

Computes the mean bias error as mean percentage absolute error. Positive values indicate overall overestimation by the model.

Usage

calc_mbe(observed, predicted)

Arguments

Value

MBE value (numeric scalar, as percentage).

Examples

calc_mbe(c(3.5, 4.2, 5.1), c(3.3, 4.5, 4.9))

Description

Mean Squared Error (MSE)

Usage

calc_mse(observed, predicted)

Arguments

Value

MSE value (numeric scalar).

Examples

calc_mse(c(3.5, 4.2, 5.1), c(3.3, 4.5, 4.9))

Description

RMSE normalized by the mean of observed values.

Usage

calc_nrmse(observed, predicted)

Arguments

Value

NRMSE value (numeric scalar).

Examples

calc_nrmse(c(3.5, 4.2, 5.1), c(3.3, 4.5, 4.9))

Description

Computes the Nash-Sutcliffe efficiency coefficient. A value of 1 indicates perfect agreement; values below 0 indicate the model is worse than the mean.

Usage

calc_nse(observed, predicted)

Arguments

Value

NSE value (numeric scalar).

References

Nash, J.E. & Sutcliffe, J.V. (1970). River flow forecasting through conceptual models. Journal of Hydrology, 10(3), 282-290.

Examples

obs <- c(3.5, 4.2, 5.1, 2.8, 6.0)
pred <- c(3.3, 4.5, 4.9, 3.0, 5.8)
calc_nse(obs, pred)

Description

Pearson Correlation Coefficient (r)

Usage

calc_r(observed, predicted)

Arguments

Value

Pearson correlation coefficient (numeric scalar).

Examples

calc_r(c(3.5, 4.2, 5.1), c(3.3, 4.5, 4.9))

Description

Computes R-squared as the square of the Pearson correlation coefficient.

Usage

calc_r2(observed, predicted)

Arguments

Value

R-squared value (numeric scalar between 0 and 1).

Examples

calc_r2(c(3.5, 4.2, 5.1), c(3.3, 4.5, 4.9))

Description

Root Mean Squared Error (RMSE)

Usage

calc_rmse(observed, predicted)

Arguments

Value

RMSE value (numeric scalar).

Examples

calc_rmse(c(3.5, 4.2, 5.1), c(3.3, 4.5, 4.9))

Description

Computes the maximum possible daylight hours for a given day and latitude.

Usage

daylight_hours(J, lat)

Arguments

Value

Maximum daylight hours.

References

Allen et al. (1998), FAO-56, Eq. 34.

Examples

daylight_hours(172, 25.43)

Description

Estimates dew point temperature from actual vapor pressure.

Usage

dew_point_temperature(ea)

Arguments

Value

Dew point temperature (degrees Celsius).

Examples

ea <- actual_vapor_pressure(15, 30, 90, 40)
dew_point_temperature(ea)

Description

Estimates daily ET0 using the Abtew (1996) method, a simple solar radiation-based approach developed for subtropical wetland conditions.

Usage

et0_abtew(Tmean, J, lat, n)

Arguments

Value

Daily ET0 (mm/day).

References

Abtew, W. (1996). Evapotranspiration measurements and modelling for three wetland systems in south Florida. JAWRA, 32(3), 465-473.

See Also

Other radiation models: et0_caprio(), et0_hargreaves(), et0_irmak(), et0_jensen_haise(), et0_jones_ritchie(), et0_makkink(), et0_mcguinness_bordne(), et0_priestley_taylor(), et0_turc()

Examples

et0_abtew(25, 172, 25.43, 9)

Description

Estimates daily ET0 using the Caprio (1974) method, a linear function of solar radiation and mean temperature.

Usage

et0_caprio(Tmean, J, lat, n)

Arguments

Value

Daily ET0 (mm/day).

References

Caprio, J.M. (1974). The solar thermal unit concept in problems related to plant development and potential evapotranspiration. In: Phenology and Seasonality Modeling. Springer, Berlin, 353-364.

See Also

Other radiation models: et0_abtew(), et0_hargreaves(), et0_irmak(), et0_jensen_haise(), et0_jones_ritchie(), et0_makkink(), et0_mcguinness_bordne(), et0_priestley_taylor(), et0_turc()

Examples

et0_caprio(25, 172, 25.43, 9)

Description

Computes daily reference evapotranspiration (ET0) using the FAO Penman-Monteith equation (Allen et al., 1998). This is the standard reference method recommended by FAO.

Usage

et0_fao_pm(Tmin, Tmax, RH_morning, RH_evening, u2, n, J, lat, z = 0)

Arguments

Value

Daily ET0 (mm/day).

References

Allen, R.G., Pereira, L.S., Raes, D., & Smith, M. (1998). Crop evapotranspiration: Guidelines for computing crop water requirements. FAO Irrigation and Drainage Paper No. 56.

Examples

et0_fao_pm(Tmin = 15, Tmax = 30, RH_morning = 90, RH_evening = 40,
           u2 = 1.5, n = 8, J = 172, lat = 25.43, z = 216)

Description

Estimates daily ET0 using the Hargreaves (1975) radiation-based method, distinct from the Hargreaves-Samani (1985) temperature-range method.

Usage

et0_hargreaves(Tmean, J, lat, n)

Arguments

Value

Daily ET0 (mm/day).

References

Hargreaves, G.H. (1975). Moisture availability and crop production. Transactions of the ASAE, 18(5), 980-984.

See Also

Other radiation models: et0_abtew(), et0_caprio(), et0_irmak(), et0_jensen_haise(), et0_jones_ritchie(), et0_makkink(), et0_mcguinness_bordne(), et0_priestley_taylor(), et0_turc()

Examples

et0_hargreaves(25, 172, 25.43, 9)

Description

Estimates daily ET0 using the Irmak et al. (2003) solar radiation-based regression equation.

Usage

et0_irmak(Tmean, J, lat, n)

Arguments

Value

Daily ET0 (mm/day).

References

Irmak, S., Irmak, A., Allen, R.G., & Jones, J.W. (2003). Solar and net radiation-based equations to estimate reference evapotranspiration in humid climates. Journal of Irrigation and Drainage Engineering, 129(5), 336-347.

See Also

Other radiation models: et0_abtew(), et0_caprio(), et0_hargreaves(), et0_jensen_haise(), et0_jones_ritchie(), et0_makkink(), et0_mcguinness_bordne(), et0_priestley_taylor(), et0_turc()

Examples

et0_irmak(25, 172, 25.43, 9)

Description

Estimates daily ET0 using the Jensen and Haise (1963) method based on solar radiation and mean air temperature.

Usage

et0_jensen_haise(Tmean, J, lat, n)

Arguments

Value

Daily ET0 (mm/day).

References

Jensen, M.E. & Haise, H.R. (1963). Estimating evapotranspiration from solar radiation. Journal of Irrigation and Drainage Division, ASCE, 89(4), 15-41.

See Also

Other radiation models: et0_abtew(), et0_caprio(), et0_hargreaves(), et0_irmak(), et0_jones_ritchie(), et0_makkink(), et0_mcguinness_bordne(), et0_priestley_taylor(), et0_turc()

Examples

et0_jensen_haise(25, 172, 25.43, 9)

Description

Estimates daily ET0 using the Jones and Ritchie (1990) radiation-based approach, a simplified Priestley-Taylor variant with alpha = 1.1.

Usage

et0_jones_ritchie(Tmin, Tmax, J, lat, n)

Arguments

Value

Daily ET0 (mm/day).

References

Jones, C.A. & Ritchie, J.T. (1990). Chapter 4: crop growth models. In: Jones, J.W. & Kiniry, J.R. (Eds.), CERES-Maize: A Simulation Model of Maize Growth and Development. Texas A&M University Press, 49-75.

See Also

Other radiation models: et0_abtew(), et0_caprio(), et0_hargreaves(), et0_irmak(), et0_jensen_haise(), et0_makkink(), et0_mcguinness_bordne(), et0_priestley_taylor(), et0_turc()

Examples

et0_jones_ritchie(15, 35, 172, 25.43, 9)

Description

Estimates daily ET0 using the Makkink (1957) method based on solar radiation and the slope of the saturation vapor pressure curve.

Usage

et0_makkink(Tmean, J, lat, n, z = 0)

Arguments

Value

Daily ET0 (mm/day).

References

Makkink, G.F. (1957). Testing the Penman formula by means of lysimeters. Journal of the Institution of Water Engineers, 11(3), 277-288.

See Also

Other radiation models: et0_abtew(), et0_caprio(), et0_hargreaves(), et0_irmak(), et0_jensen_haise(), et0_jones_ritchie(), et0_mcguinness_bordne(), et0_priestley_taylor(), et0_turc()

Examples

et0_makkink(25, 172, 25.43, 9, 216)

Description

Estimates daily ET0 using the McGuinness and Bordne (1972) method based on extraterrestrial radiation and mean air temperature.

Usage

et0_mcguinness_bordne(Tmean, J, lat, n)

Arguments

Value

Daily ET0 (mm/day).

References

McGuinness, J.L. & Bordne, E.F. (1972). A comparison of lysimeter-derived potential evapotranspiration with computed values. USDA Technical Bulletin No. 1452.

See Also

Other radiation models: et0_abtew(), et0_caprio(), et0_hargreaves(), et0_irmak(), et0_jensen_haise(), et0_jones_ritchie(), et0_makkink(), et0_priestley_taylor(), et0_turc()

Examples

et0_mcguinness_bordne(25, 172, 25.43, 9)

Description

Estimates daily ET0 using the Priestley and Taylor (1972) method, an equilibrium evaporation approach using net radiation with an empirical coefficient (alpha = 1.26).

Usage

et0_priestley_taylor(Tmin, Tmax, RH_morning, RH_evening, n, J, lat, z = 0)

Arguments

Value

Daily ET0 (mm/day).

References

Priestley, C.H.B. & Taylor, R.J. (1972). On the assessment of surface heat flux and evaporation using large-scale parameters. Monthly Weather Review, 100(2), 81-92.

See Also

Other radiation models: et0_abtew(), et0_caprio(), et0_hargreaves(), et0_irmak(), et0_jensen_haise(), et0_jones_ritchie(), et0_makkink(), et0_mcguinness_bordne(), et0_turc()

Examples

et0_priestley_taylor(15, 35, 90, 40, 9, 172, 25.43, 216)

Description

A convenience wrapper that computes daily reference evapotranspiration using all 10 radiation-based empirical models plus the FAO Penman-Monteith standard method as the reference/base for comparison.

Usage

et0_rad_all(Tmin, Tmax, RH_morning, RH_evening, u2, n, J, lat, z = 0)

Arguments

Details

The 10 radiation-based models included are:

• Jensen-Haise (1963)

• McGuinness-Bordne (1972)

• Irmak (2003)

• Makkink (1957)

• Turc (1961)

• Caprio (1974)

• Abtew (1996)

• Priestley-Taylor (1972)

• Jones-Ritchie (1990)

• Hargreaves (1975)

The FAO Penman-Monteith column serves as the standard reference against which models can be evaluated using evaluate_models.

Value

A data.frame with 11 columns: FAO_PM (reference) plus one column per radiation-based model. The number of rows equals the length of the input vectors.

Examples

result <- et0_rad_all(Tmin = 15, Tmax = 35, RH_morning = 90,
                      RH_evening = 40, u2 = 1.5, n = 9,
                      J = 172, lat = 25.43, z = 216)
print(result)

Description

Estimates daily ET0 using the Turc (1961) method based on solar radiation and mean air temperature. Assumes humid conditions (RH >= 50

Usage

et0_turc(Tmean, J, lat, n)

Arguments

Value

Daily ET0 (mm/day).

References

Turc, L. (1961). Estimation of irrigation water requirements, potential evapotranspiration: a simple climatic formula evolved up to date. Annals of Agronomy, 12, 13-49.

See Also

Other radiation models: et0_abtew(), et0_caprio(), et0_hargreaves(), et0_irmak(), et0_jensen_haise(), et0_jones_ritchie(), et0_makkink(), et0_mcguinness_bordne(), et0_priestley_taylor()

Examples

et0_turc(25, 172, 25.43, 9)

Description

Computes all 9 statistical evaluation metrics for one or more ET0 models compared against a reference method (typically FAO Penman-Monteith).

Usage

evaluate_models(observed, predicted)

Arguments

Value

A data.frame with one row per model and columns for each metric: NSE, d, MSE, RMSE, NRMSE, MAE, MBE, r, R2.

Examples

obs <- c(3.5, 4.2, 5.1, 2.8, 6.0)
preds <- data.frame(
  Model_A = c(3.3, 4.5, 4.9, 3.0, 5.8),
  Model_B = c(4.0, 4.0, 5.5, 2.5, 6.5)
)
evaluate_models(obs, preds)

Description

Computes the extraterrestrial radiation (Ra) for a given day and latitude following Allen et al. (1998).

Usage

extraterrestrial_radiation(J, lat)

Arguments

Value

Extraterrestrial radiation (MJ/m2/day).

References

Allen et al. (1998), FAO-56, Eq. 21.

Examples

extraterrestrial_radiation(172, 25.43)

Description

A dataset containing daily meteorological observations from the Central Research Farm of ICAR-Indian Grassland and Fodder Research Institute (IGFRI), Jhansi, Uttar Pradesh, India (25 deg 26' N, 78 deg 30' E, 216 m above sea level). The data covers one year (2010) and is representative of semi-arid climate conditions.

Usage

jhansi_weather

Format

A data frame with 365 rows and 8 columns:

Date

Date of observation (Date class).

J

Day of the year (1-365).

Tmax

Maximum air temperature (degrees Celsius).

Tmin

Minimum air temperature (degrees Celsius).

RH_morning

Morning relative humidity (percent).

RH_evening

Evening relative humidity (percent).

SSH

Bright sunshine hours.

WS

Wind speed at 2 m height (m/s).

Details

The study area has a semi-arid climate with extreme summers (average 32.7 degrees C) and mild winters (average 25.1 degrees C). The average annual precipitation is 840 mm, with 90 percent contributed by southwest monsoons between July and September. This dataset is suitable for demonstrating the package functions and comparing ET0 model performance in data-scarce semi-arid conditions.

The latitude for this station is 25.43 degrees N and the elevation is 216 m above sea level.

Source

ICAR-Indian Grassland and Fodder Research Institute (IGFRI), Jhansi, India.

Examples

data(jhansi_weather)
head(jhansi_weather)

# Compute FAO-PM ET0 for the first day
with(jhansi_weather[1, ],
  et0_fao_pm(Tmin, Tmax, RH_morning, RH_evening, WS, SSH, J,
             lat = 25.43, z = 216))

Description

Computes the latent heat of vaporization as a function of air temperature following Allen et al. (1998).

Usage

latent_heat(Tmean)

Arguments

Value

Latent heat of vaporization (MJ/kg).

References

Allen, R.G., Pereira, L.S., Raes, D., & Smith, M. (1998). FAO Irrigation and Drainage Paper No. 56.

Examples

latent_heat(25)

Description

Functions to compute statistical performance metrics for comparing ET0 model estimates against a reference (e.g., FAO Penman-Monteith).

Description

Computes net radiation (Rn) following the FAO-56 approach.

Usage

net_radiation(J, lat, n, Tmin, Tmax, ea, albedo = 0.23, a_s = 0.25, b_s = 0.5)

Arguments

Value

Net radiation (MJ/m2/day).

References

Allen et al. (1998), FAO-56.

Examples

ea <- actual_vapor_pressure(15, 30, 90, 40)
net_radiation(172, 25.43, 8, 15, 30, ea)

Description

Creates a bar chart comparing total annual ET0 estimated by each model against the FAO-PM reference.

Usage

plot_annual_bar(annual_et0, main = "Annual ET0 by Model", colors = NULL)

Arguments

Value

Invisible NULL.

Examples

annual <- c(FAO_PM = 1571, Blaney_Criddle = 1933, Schendel = 2593,
            Hargreaves_Samani = 1393)
plot_annual_bar(annual)

Description

Creates a line plot comparing the average monthly ET0 from multiple models against the FAO-PM reference.

Usage

plot_monthly_comparison(
  monthly_data,
  model_names = NULL,
  main = "Monthly ET0 Comparison",
  colors = NULL
)

Arguments

Value

Invisible NULL.

Examples

monthly <- data.frame(
  Month = 1:12,
  FAO_PM = c(2.0, 2.5, 3.5, 5.0, 6.5, 7.0, 6.0, 5.5, 4.5, 3.5, 2.5, 2.0),
  Model_A = c(2.2, 2.8, 3.8, 5.3, 6.8, 7.3, 6.3, 5.8, 4.8, 3.8, 2.8, 2.2)
)
plot_monthly_comparison(monthly)

Description

Creates a scatter plot comparing predicted ET0 values from one or more models against observed (reference) values, with 1:1 line and regression lines.

Usage

plot_scatter(
  observed,
  predicted,
  model_names = NULL,
  main = "Predicted vs Observed ET0",
  colors = NULL,
  ...
)

Arguments

Value

Invisible NULL. Called for its side effect of producing a plot.

Examples

obs <- c(3.5, 4.2, 5.1, 2.8, 6.0, 3.1, 4.8)
preds <- data.frame(
  Model_A = c(3.3, 4.5, 4.9, 3.0, 5.8, 3.4, 4.6),
  Model_B = c(4.0, 4.0, 5.5, 2.5, 6.5, 3.8, 5.0)
)
plot_scatter(obs, preds)

Description

Creates a Taylor diagram showing the correlation coefficient, standard deviation, and centered RMSE of multiple models relative to the observed reference.

Usage

plot_taylor(
  observed,
  predicted,
  model_names = NULL,
  main = "Taylor Diagram",
  colors = NULL,
  normalize = FALSE
)

Arguments

Value

Invisible NULL. Called for its side effect of producing a plot.

Examples

set.seed(42)
obs <- rnorm(100, mean = 5, sd = 2)
preds <- list(
  Model_A = obs + rnorm(100, 0, 0.5),
  Model_B = obs * 1.1 + rnorm(100, 0, 1)
)
plot_taylor(obs, preds)

Description

Functions for graphical evaluation of ET0 model performance including scatter plots, Taylor diagrams, monthly comparison plots, and annual bar charts.

Description

Computes the psychrometric constant as a function of atmospheric pressure.

Usage

psychrometric_constant(P = NULL, z = 0)

Arguments

Value

Psychrometric constant (kPa/degrees C).

References

Allen et al. (1998), FAO-56, Eq. 8.

Examples

psychrometric_constant(z = 216)

Description

Functions implementing 10 radiation-based empirical models for reference evapotranspiration (ET0) estimation.

Description

Computes the saturation vapor pressure at a given temperature using the Tetens formula (Allen et al., 1998).

Usage

saturation_vapor_pressure(Temp)

Arguments

Value

Saturation vapor pressure (kPa).

References

Allen et al. (1998), FAO-56, Eq. 11.

Examples

saturation_vapor_pressure(25)

Description

Computes the slope of the saturation vapor pressure-temperature curve.

Usage

slope_vapor_pressure(Tmean)

Arguments

Value

Slope of saturation vapor pressure curve (kPa/degrees C).

References

Allen et al. (1998), FAO-56, Eq. 13.

Examples

slope_vapor_pressure(25)

Description

Estimates incoming solar radiation (Rs) using the Angstrom formula with sunshine hours.

Usage

solar_radiation(J, lat, n, a_s = 0.25, b_s = 0.5)

Arguments

Value

Solar radiation (MJ/m2/day).

References

Allen et al. (1998), FAO-56, Eq. 35.

Examples

solar_radiation(172, 25.43, 8)