# A Simple Procedure to Estimate Reference Evapotranspiration during the Irrigation Season in a Hot-Summer Mediterranean Climate

^{1}

^{2}

^{*}

## Abstract

**:**

_{Rs}) is calibrated for each site, acceptable ETo estimations (RMSE and R

^{2}equal to 0.79 for the entire region) can be achieved. Results also show that a procedure to estimate ETo based only on maximum temperature performs acceptably, when compared with ETo estimation using PM equation (RMSE = 0.83 mm day

^{−1}and R

^{2}= 0.77 for Alentejo). When comparing these results with the ones attained when adopting a monthly adjusted HS method, the MaxTET procedure proves to be an accurate ETo estimator. Results also show that both methods can be used to estimate ETo when weather data are scarce.

## 1. Introduction

_{max}) and minimum (T

_{min}) temperature data are commonly observed at most weather stations, windspeed (u

_{2}), relative humidity (RH) and solar radiation (R

_{s}) are not frequently available, and, if recorded, the data quality may not be adequate. To overcome this constraint, [1] proposed a set of methods that allow for the estimation of theses missing variables. When RH data are missing, [1] recommended the estimation of actual vapor pressure based on the assumption that minimum temperature could be an acceptable estimator of dew point temperature. For estimation of R

_{s}, [1] proposed the adoption of the Hargreaves–Samani method [5], which expresses R

_{s}as a linear function expressed as:

_{s}= k

_{Rs}× R

_{a}× (T

_{max}− T

_{min})

^{0.5}

_{Rs}is an empirical radiation adjustment coefficient (°C

^{−0.5}) and R

_{a}is the extraterrestrial radiation (MJ m

^{2}day

^{−1}). Allen et al. [1] also proposed the use of the world average wind speed value u

_{2}= 2 m s

^{−1}as the default estimator when wind speed data are missing. However, this estimation may lead to some accuracy error [6,7].

_{Rs}for a specific location, the Hargreaves–Samani (HS) method showed its appropriateness for the most of part for the locations, leading to acceptable ETo estimations (RMSE = 0.84 mm day

^{−1}). However, it would benefit from further calibration, where a monthly kRs could be obtained. Nonetheless, the calculation of extra-terrestrial radiation can be a limitation for some users, and the complexity of calculation of both PM and HS methods requires a computerized approach to ease ETo estimation.

^{−1}when estimating ETo for fourteen locations across the region.

_{Rs}) will be calibrated for each location in order to assess if it leads to improved ETo estimations. Finally, the performance of the new simple temperature-based procedure, in comparison with the PM or HS method, will be assessed.

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Evapotranspiration Estimation Methods

_{PM}is the grass reference evapotranspiration (mm day

^{−1}); Rn is the net radiation (MJ m

^{−2}day

^{−1}); G is the soil heat flux density (MJ m

^{−2}day

^{−1}), considered as null for daily estimates; T is the daily mean air temperature (°C) at 2 m, based on the average of maximum and minimum temperatures; u

_{2}is the average wind speed at 2 m height (m s

^{−1}); e

_{s}is the saturation vapor pressure (kPa); e

_{a}is the actual vapor pressure (kPa); (e

_{s}− e

_{a}) is the saturation vapor pressure deficit (Δe, kPa) at temperature T; Δ is the slope of the saturated vapor pressure curve (kPa °C

^{−1}); γ is the psychrometric constant (0.0677 kPa °C

^{−1}). As for this study, the computation of all data required for calculating ETo were performed following [1].

_{HS}= 0.0135 × k

_{Rs}× 0.408R

_{a}× (T

_{avg}+ 17.8) × (T

_{max}− T

_{min})

^{0.5}

_{HS}is the grass reference evapotranspiration (mm day

^{−1}); Ra is the extraterrestrial radiation (MJ m

^{−2}day

^{−1}), 0.0135 is a factor for conversion from American to the International system of units; T

_{avg}is the average air temperature (°C); T

_{max}is the maximum air temperature (°C); T

_{min}is the minimum air temperature (°C) and k

_{Rs}is the radiation adjustment coefficient (°C

^{−0.5}). The empirical coefficient k

_{Rs}was originally considered [5] as 0.17 °C

^{−0.5}. For this study, a monthly k

_{Rs}was locally calibrated.

_{o}. A standard equation is hereby proposed as a maximum temperature-based evapotranspiration (MaxTET) procedure to estimate ETo:

_{Tmax}is the reference crop evapotranspiration (mm day

^{−1}), k

_{Tmax}is the temperature adjustment coefficient (mm °C

^{−1}) and T

_{max}is the maximum air temperature (°C). For this purpose, a monthly k

_{Tmax}was locally calibrated.

#### 2.3. Evaluation Criteria

_{PMi}and ET

_{TBi}(i = 1, 2, …, n) represent pairs of values of ET

_{o}estimated using the PM method and another temperature-based model, respectively, for a given variable and $\overline{{\mathrm{ET}}_{\mathrm{PM}}}$ and $\overline{{\mathrm{ET}}_{\mathrm{TB}}}$ are the respective mean values:

- The coefficients of regression and determination relating observed and simulated data, b and R
^{2}, respectively, are defined as:$$\mathrm{b}=\frac{{\sum}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{ET}}_{\mathrm{PMi}}{\mathrm{ET}}_{\mathrm{TBi}}}{{\sum}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{ET}}_{\mathrm{PMi}}{}^{2}}$$$${\mathrm{R}}^{2}={\left\{\frac{{\sum}_{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{ET}}_{\mathrm{PMi}}-\overline{{\mathrm{ET}}_{\mathrm{PM}}}\right)\left({\mathrm{ET}}_{\mathrm{TBi}}-\overline{{\mathrm{ET}}_{\mathrm{TB}}}\right)}{{\left[{\sum}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{ET}}_{\mathrm{PMi}}-\overline{{\mathrm{ET}}_{\mathrm{PM}}}\right)}^{2}\right]}^{0.5}{\left[{\sum}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{ET}}_{\mathrm{TBi}}-\overline{{\mathrm{ET}}_{\mathrm{TB}}}\right)}^{2}\right]}^{0.5}}\right\}}^{2}$$ - The root mean square error, RMSE, which characterizes the variance of the estimation error:$$\mathrm{RMSE}={\left[\frac{{\sum}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{ET}}_{\mathrm{TBi}}-{\mathrm{ET}}_{\mathrm{PMi}}\right)}^{2}}{\mathrm{n}}\right]}^{0.5}$$

_{Rs}and k

_{Tmax}. The calibration of these coefficients was performed using a trial and error procedure for each month and location, was calibrated using 50% of the years, randomly chosen from the dataset, and validated for the remainder of the years. Results for both HS and MaxTET approaches were compared with the PM method to test its accuracy.

## 3. Results

#### 3.1. Estimating a Monthly Adjusted Radiation Adjustment Coefficient for Each Location

_{Rs}for each month and location, as well as the irrigation season calibrated factor as suggested by [14]. Results show that, for most locations, the monthly calibrated k

_{Rs}differ, both locally and monthly, from the seasonal coefficient as proposed by [14]. Locations with the same seasonal coefficient, such as Beja, Castro Verde, Odemira and Redondo (seasonal k

_{Rs}= 0.17), tend to have different validated monthly k

_{Rs}throughout the irrigation season. k

_{Rs}for Beja varies from 0.16 to 0.18, while for Castro Verde and Redondo the empirical coefficient varies from 0.16 to 0.19. Additionally, when comparing the validated k

_{Rs}between those locations for the same month, different values may be found. For the month of July, the empirical radiation coefficient equals 0.17, 0.18, 0.16 and 0.17 for Beja, Castro Verde, Odemira and Redondo, respectively; but, for the month of October, a k

_{Rs}of 0.18, 0.19, 0.17 and 0.19 was obtained the same locations. For the entire Alentejo region, the coefficient ranges 0.15–0.16. Results also show that there is no regularity in the variation of k

_{Rs}values throughout the season.

_{Rs}. Results demonstrate that, contrarily to what is proposed by [1], the k

_{Rs}does not decrease with further distance to the sea. From the analysis in Figure 2, it can be concluded that “coastal” locations (such as Odemira an Alvalade do Sado) tend to reveal a lower k

_{Rs}than some more “interior” sites. However, there is no clear trend; locations with similar distances to the sea (e.g., Moura and Redondo) show quite different values. For Moura, the k

_{Rs}ranges from 0.13 to 0.14, while for Redondo the adjustment coefficient varies from 0.17 to 0.19. Indeed, the validated values for the latter are even higher than the ones obtained for more “coastal” locations, contradicting the standard trend as proposed by [1]. These results show there is no clear relation with the distance to sea, suggesting that other factors such as latitude, altitude and closeness to irrigated fields may have a direct impact on the radiation adjustment coefficient.

^{2}, RMSE) of ETo estimates for each location, which resulted from adopting the monthly adjusted HS method for calibration, validation and all years. As a comparison, Table 3 also presents the accuracy of the ETo estimations when using a seasonal calibrated k

_{Rs}for each site, as proposed by [14]. Results show that, after monthly calibrating the k

_{Rs}factor, ETo estimations by the HS equation tend to improve the method’s accuracy. For 10 locations (Aljustrel, Beja, Castro Verde, Elvas, Estremoz, Ferreira do Alentejo, Moura, Odemira, Redondo and Viana do Alentejo) the RMSE decreased, on average, from 0.77 to 0.74 mm day

^{−1}, while the R

^{2}increased from 0.79 to 0.80. As for the remaining four locations (Alvalade do Sado, Évora, Serpa and Vidigueira), the statistical results remain similar. For the entire Alentejo region, results also demonstrate an improvement, with the RMSE decreasing from 0.84 to 0.79 mm day

^{−1}and the coefficient of determination increasing from 0.77 to 0.79, proving that a monthly calibrated coefficient leads to improved ETo estimations. This trend come into agreement with the results found by [17], where the accuracy of ETo estimations when moving from an annual to seasonal calibration tends to improve significantly (especially from spring and summer).

#### 3.2. Validation of a Maximum Temperature-Based ETo Estimation Procedure

_{Tmax}). Table 4 presents the validated k

_{Tmax}for each month and location.

^{2}, RMSE) of ETo estimates for each location, which resulted from adopting the MaxTET procedure, for calibration, validation and all years. Results show that this method predict ETo with acceptable accuracy, with R

^{2}higher than 0.75 for most locations; only Odemira shows a slightly lower coefficient of determination (R

^{2}= 0.65). Additionally, this method led to an RMSE lower than 0.91 mm day

^{−1}(as low as 0.65 mm day

^{−1}for Odemira), averaging 0.80 mm day

^{−1}, with slight to no under- or overestimation of the ETo for all locations (b varied from 0.98 to 1.01). These results agree with the ones found by [8] when estimating ETo from a modified HS equation, leading to an RMSE = 0.72 mm day

^{−1}. Even when upscaling the approach for the entire Alentejo region, the MaxTET method proved to be accurate for ETo estimations, with a slope of 0.98, an R

^{2}equal to 0.77 and an RMSE of 0.83 mm day

^{−1}. Results for calibration and validation datasets tend to be similar, with low variations for both R

^{2}and RMSE indicators.

#### 3.3. Comparing the Accuracy of MaxTET and Monthly Adjusted Hargreaves–Samani Methods

_{HS}/ET

_{Tmax}and ET

_{PM}regression lines were used (Figure 3). Generally, both methods performed well in the study area. Results demonstrate that, for all locations, both Hargreaves–Samani and MaxTET tend to overestimate low ETo values, while for high ETo values both methods tend to underestimate reference evapotranspiration. For Aljustrel, Castro Verde, Évora, Redondo and Vidigueira, both methods led to similar results for high ETo values. Globally, both methods seem to accurately estimate the ETo for all 14 locations and for the Alentejo region as a whole.

^{−1}(for Castro Verde), averaging an RMSE equal to 0.05 mm day

^{−1}. Similarly, when comparing to the seasonally adjusted HS method, the MaxTET procedure led to a higher RMSE by, on average, 0.03 mm day

^{−1}. Contrarily, for the entire Alentejo region, the MaxTET procedure proved to be more accurate than the seasonally adjusted HS method, resulting in a lower RMSE (0.83 and 0.84 mm day

^{−1}, respectively).

^{−1}), present higher RMSE values. Globally, for all locations, the RMSE represents around 17% and 16% of the average ETo for MaxTET and monthly adjusted HS methods, respectively. One can conclude that both models perform similarly across the region.

## 4. Discussion

_{Rs}ranges from 0.16 to 0.19 °C

^{−0.5}, respectively, for “interior” or “coastal” regions, diverging from the original coefficient proposed by [5], with k

_{Rs}= 0.17 °C

^{−0.5}. Nevertheless, k

_{Rs}is supposed to vary with altitude, reflecting the air pressure changes as for the volumetric heat capacity of the atmosphere [18], and should vary spatially, internalizing the effects of the site elevation and distance to sea [1]. Allen [18] also found that, for some specific locations, k

_{Rs}may vary seasonally. Thus, one can suggest that not only a local calibration but also a monthly adjustment should be performed to reflect the volumetric heat capacity of the atmosphere.

_{Rs}per location may lead to less accurate ETo estimations. Results also show that a trend can be found across the irrigation season. For some locations, such as for Redondo and Viana do Alentejo, the radiation adjustment coefficient tended to increase during the irrigation season. Contrarily, some regions, such as Évora and Ferreira do Alentejo, remain mostly the same during the same period. Results (Figure 2) also demonstrate that, contrarily to what is proposed by Allen et al. (1998), the k

_{Rs}does not decrease with further distance to the sea. For summer months, “interior” and “coastal” locations illustrate the same radiation adjustment coefficient, reinforcing the statement that one should not assume the standard values of 0.16 and 0.19 °C

^{−0.5}, respectively, for “interior” or “coastal” regions. This can be due to the fact that, during these peak months, most cropped fields are being irrigated, influencing the air moisture and impacting the volumetric heat capacity of the atmosphere. It can be concluded that a monthly calibration/validation is advisable since k

_{Rs}can vary, not only depending on the distance to the sea, but also according to the month for which ETo is being estimated.

^{2}equal to 0.77 and an RMSE of 0.83 mm day

^{−1}for the entire Alentejo region. Enku and Melesse [16] aimed to develop a temperature-based evapotranspiration method for Ethiopia and, although more complex than the one proposed here, led to similar accuracy results, with an average R

^{2}equal to 0.65 and an RMSE averaging 0.59 mm day

^{−1}. However, and according to [14], the accuracy of this method, when estimating ETo for Alentejo, does not support its adoption since it led to an RMSE higher than 2.20 m day

^{−1}; one can conclude that the MaxTET procedure outperforms the previous established method proposed by [16] since it led to more accurate estimation results.

## 5. Conclusions

_{Rs}) per location, if a monthly adjusted k

_{Rs}is calibrated for each site, it leads to improved ETo estimations. Results also showed that there is no clear effect of the distance to the sea over k

_{Rs}, reinforcing the statement that one should not assume the standard values available in the literature. Additionally, results show that a monthly calibration/validation is advisable since k

_{Rs}can vary not only depending on the distance to the sea, but also according to the month for which ETo is being estimated.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Validated Hargreaves–Samani radiation adjustment coefficient (k

_{Rs}) values for each month and location ordered according to the distance to the sea (km).

**Figure 3.**Comparison of monthly adjusted Hargreaves–Samani (HS) method and maximum temperature-based evapotranspiration (MaxTET) procedure with Penman–Monteith (PM) for all locations.

**Figure 4.**RMSE (mm day

^{−1}) of ETo estimations using the maximum temperature-based evapotranspiration (MaxTET) procedure, and monthly and seasonally adjusted Hargreaves–Samani (HS) methods.

**Figure 5.**Spatial distribution of RMSE (mm day

^{−1}) of ETo estimations using (

**a**) the maximum temperature-based evapotranspiration (MaxTET) procedure and (

**b**) monthly adjusted Hargreaves–Samani (HS) method for all 14 locations.

**Table 1.**Weather stations characterization, data range of the weather data series and annual means and standard deviations of maximum (T

_{max}) and minimum (T

_{min}) temperatures, reference evapotranspiration (ETo) and mean annual rainfall.

Weather Station | Code | Latitude (N) | Longitude (W) | Elevation (m) | Distance to the Sea (km) | Period | T_{max}(°C) | T_{min}(°C) | Eto (mm day ^{−1}) | Rainfall (mm year ^{−1}) |
---|---|---|---|---|---|---|---|---|---|---|

Aljustrel | Alj | 37°58′17″ | 08°11′25″ | 104 | 55 | 2001–2019 | 29.1 (±5.9) | 12.9 (±3.5) | 4.7 (±1.7) | 204 |

Alvalade do Sado | Alv | 37°55′44″ | 08°20′45″ | 79 | 40 | 2001–2019 | 29.2 (±5.9) | 13.3 (±3.3) | 4.8 (±1.7) | 183 |

Beja | Bej | 38°02′15″ | 07°53′06″ | 206 | 79 | 2001–2019 | 28.8 (±6.1) | 13.2 (±3.5) | 5.0 (±1.8) | 216 |

Castro Verde | CV | 37°45′20.5″ | 08°04′35.4″ | 200 | 64 | 2001–2019 | 29.0 (±6.1) | 12.8 (±3.5) | 5.3 (±2.0) | 151 |

Elvas | Elv | 38°54′56″ | 07°05′56″ | 202 | 160 | 2001–2019 | 29.9 (±6.5) | 13.0 (±4.0) | 4.9 (±1.8) | 218 |

Estremoz | Est | 38°52′20″ | 07°35′49″ | 404 | 120 | 2006–2019 | 27.5 (±6.4) | 12.2 (±3.7) | 4.2 (±1.5) | 256 |

Évora | Evo | 38°44′16″ | 07°56′10″ | 246 | 85 | 2002–2019 | 28.6 (±6.2) | 12.0 (±3.6) | 4.5 (±1.6) | 245 |

Ferreira do Alentejo | FdA | 38°02′42″ | 08°15′59″ | 74 | 47 | 2001–2019 | 29.3 (±5.8) | 12.8 (±3.5) | 4.5 (±1.6) | 210 |

Moura | Mou | 38°05′15″ | 07°16′39″ | 172 | 100 | 2001–2019 | 30.2 (±6.4) | 12.0 (±4.3) | 4.4 (±1.6) | 204 |

Odemira | Ode | 37°30′06″ | 08°45′12″ | 92 | 4 | 2002–2019 | 23.9 (±4.2) | 13.3 (±2.8) | 3.8 (±1.1) | 213 |

Redondo | Red | 38°31′41″ | 07°37′40″ | 236 | 105 | 2001–2019 | 29.3 (±6.4) | 13.6 (±3.7) | 5.1 (±1.9) | 210 |

Serpa | Ser | 37°58′06″ | 07°33′03″ | 190 | 90 | 2004–2019 | 30.3 (±6.4) | 13.6 (±3.6) | 4.8 (±1.7) | 197 |

Viana do Alentejo | Via | 38°21′39″ | 08°07′32″ | 138 | 57 | 2006–2019 | 28.4 (±6.1) | 12.6 (±3.4) | 4.8 (±1.7) | 247 |

Vidigueira | Vid | 38°10′36.8″ | 07°47′35.1″ | 155 | 86 | 2007–2019 | 29.9 (±6.3) | 13.2 (±3.6) | 4.8 (±1.7) | 178 |

**Table 2.**Validated Hargreaves–Samani radiation adjustment coefficient (k

_{Rs}) values for each month and location.

Station | Month | Irrigation Season ^{1} | ||||||
---|---|---|---|---|---|---|---|---|

April | May | June | July | August | September | October | ||

Aljustrel | 0.15 | 0.15 | 0.15 | 0.16 | 0.16 | 0.15 | 0.16 | 0.16 |

Alvalade do Sado | 0.15 | 0.16 | 0.16 | 0.16 | 0.16 | 0.15 | 0.16 | 0.16 |

Beja | 0.16 | 0.17 | 0.17 | 0.17 | 0.17 | 0.17 | 0.18 | 0.17 |

Castro Verde | 0.16 | 0.17 | 0.17 | 0.18 | 0.18 | 0.17 | 0.19 | 0.17 |

Elvas | 0.15 | 0.15 | 0.15 | 0.16 | 0.16 | 0.15 | 0.16 | 0.16 |

Estremoz | 0.15 | 0.15 | 0.14 | 0.15 | 0.14 | 0.14 | 0.15 | 0.14 |

Évora | 0.14 | 0.15 | 0.15 | 0.15 | 0.15 | 0.15 | 0.15 | 0.15 |

Ferreira do Alentejo | 0.14 | 0.15 | 0.15 | 0.15 | 0.15 | 0.15 | 0.15 | 0.15 |

Moura | 0.13 | 0.13 | 0.13 | 0.14 | 0.14 | 0.14 | 0.14 | 0.14 |

Odemira | 0.17 | 0.17 | 0.16 | 0.16 | 0.16 | 0.17 | 0.17 | 0.17 |

Redondo | 0.16 | 0.16 | 0.16 | 0.17 | 0.17 | 0.17 | 0.19 | 0.17 |

Serpa | 0.15 | 0.15 | 0.15 | 0.15 | 0.15 | 0.15 | 0.15 | 0.15 |

Viana do Alentejo | 0.15 | 0.15 | 0.15 | 0.16 | 0.16 | 0.16 | 0.18 | 0.16 |

Vidigueira | 0.15 | 0.16 | 0.15 | 0.15 | 0.15 | 0.14 | 0.16 | 0.15 |

Alentejo | 0.15 | 0.16 | 0.15 | 0.16 | 0.16 | 0.16 | 0.16 | 0.16 |

^{1}—as proposed by [14].

**Table 3.**Accuracy of ETo estimations using the Hargreaves–Samani (HS) method after a monthly radiation adjustment coefficient (k

_{Rs}) factor calibration/validation.

Station | Monthly Adjusted HS Method | Seasonal Adjusted HS Method | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Calibration | Validation | All | ||||||||||

b | R^{2} | RMSE | b | R^{2} | RMSE | b | R^{2} | RMSE | b | R^{2} | RMSE | |

Aljustrel | 0.99 | 0.80 | 0.74 | 0.97 | 0.80 | 0.76 | 0.98 | 0.80 | 0.75 | 1.01 | 0.80 | 0.78 |

Alvalade do Sado | 0.99 | 0.81 | 0.73 | 0.98 | 0.84 | 0.68 | 0.98 | 0.82 | 0.71 | 0.99 | 0.82 | 0.71 |

Beja | 1.00 | 0.82 | 0.78 | 1.02 | 0.85 | 0.73 | 1.01 | 0.83 | 0.76 | 1.01 | 0.83 | 0.77 |

Castro Verde | 0.99 | 0.84 | 0.80 | 0.98 | 0.86 | 0.75 | 0.99 | 0.85 | 0.78 | 0.96 | 0.83 | 0.82 |

Elvas | 0.99 | 0.79 | 0.80 | 0.97 | 0.78 | 0.85 | 0.98 | 0.79 | 0.83 | 1.01 | 0.78 | 0.86 |

Estremoz | 1.00 | 0.81 | 0.64 | 0.99 | 0.78 | 0.73 | 0.99 | 0.79 | 0.69 | 0.96 | 0.79 | 0.70 |

Évora | 0.98 | 0.78 | 0.79 | 0.98 | 0.75 | 0.82 | 0.98 | 0.76 | 0.80 | 0.99 | 0.76 | 0.80 |

Ferreira do Alentejo | 1.01 | 0.79 | 0.74 | 1.00 | 0.81 | 0.69 | 1.00 | 0.80 | 0.71 | 1.01 | 0.80 | 0.72 |

Moura | 1.00 | 0.80 | 0.68 | 0.97 | 0.81 | 0.70 | 0.98 | 0.81 | 0.69 | 1.01 | 0.81 | 0.71 |

Odemira | 0.99 | 0.64 | 0.66 | 0.97 | 0.72 | 0.59 | 0.98 | 0.68 | 0.63 | 1.01 | 0.69 | 0.64 |

Redondo | 0.98 | 0.80 | 0.84 | 0.98 | 0.79 | 0.88 | 0.98 | 0.79 | 0.86 | 1.00 | 0.79 | 0.88 |

Serpa | 1.00 | 0.78 | 0.79 | 0.96 | 0.79 | 0.79 | 0.98 | 0.78 | 0.79 | 0.98 | 0.78 | 0.79 |

Viana do Alentejo | 0.98 | 0.83 | 0.69 | 0.96 | 0.82 | 0.76 | 0.97 | 0.83 | 0.73 | 0.99 | 0.81 | 0.77 |

Vidigueira | 0.99 | 0.80 | 0.74 | 0.97 | 0.79 | 0.78 | 0.98 | 0.80 | 0.75 | 0.97 | 0.80 | 0.75 |

Alentejo | 0.99 | 0.79 | 0.79 | 0.98 | 0.79 | 0.79 | 0.98 | 0.79 | 0.79 | 1.01 | 0.77 | 0.84 |

**Table 4.**Validated temperature adjustment coefficient (k

_{Tmax}) values for each month and location.

Station | Month | ||||||
---|---|---|---|---|---|---|---|

April | May | June | July | August | September | October | |

Aljustrel | 0.160 | 0.185 | 0.190 | 0.195 | 0.170 | 0.140 | 0.110 |

Alvalade do Sado | 0.165 | 0.190 | 0.195 | 0.195 | 0.175 | 0.140 | 0.115 |

Beja | 0.175 | 0.200 | 0.205 | 0.210 | 0.185 | 0.150 | 0.125 |

Castro Verde | 0.175 | 0.205 | 0.215 | 0.220 | 0.195 | 0.160 | 0.135 |

Elvas | 0.160 | 0.185 | 0.190 | 0.195 | 0.170 | 0.140 | 0.110 |

Estremoz | 0.160 | 0.175 | 0.175 | 0.180 | 0.155 | 0.125 | 0.105 |

Évora | 0.160 | 0.180 | 0.185 | 0.190 | 0.170 | 0.140 | 0.110 |

Ferreira do Alentejo | 0.155 | 0.180 | 0.180 | 0.180 | 0.160 | 0.130 | 0.110 |

Moura | 0.145 | 0.165 | 0.170 | 0.170 | 0.150 | 0.125 | 0.105 |

Odemira | 0.170 | 0.185 | 0.185 | 0.180 | 0.160 | 0.140 | 0.115 |

Redondo | 0.175 | 0.200 | 0.200 | 0.210 | 0.185 | 0.150 | 0.125 |

Serpa | 0.155 | 0.180 | 0.185 | 0.185 | 0.160 | 0.130 | 0.105 |

Viana | 0.160 | 0.185 | 0.185 | 0.195 | 0.180 | 0.145 | 0.130 |

Vidigueira | 0.160 | 0.185 | 0.185 | 0.190 | 0.165 | 0.130 | 0.110 |

Alentejo | 0.160 | 0.185 | 0.190 | 0.195 | 0.170 | 0.140 | 0.115 |

**Table 5.**Accuracy of ETo estimations using the maximum temperature-based evapotranspiration (MaxTET) procedure after temperature adjustment coefficient (k

_{Tmax}) calibration/validation.

Station | Monthly Adjusted k_{Tmax} | ||||||||
---|---|---|---|---|---|---|---|---|---|

Calibration | Validation | All | |||||||

b | R^{2} | RMSE | b | R^{2} | RMSE | b | R^{2} | RMSE | |

Aljustrel | 1.00 | 0.78 | 0.79 | 0.98 | 0.78 | 0.81 | 0.99 | 0.78 | 0.80 |

Alvalade do Sado | 1.00 | 0.78 | 0.78 | 0.99 | 0.81 | 0.74 | 0.99 | 0.80 | 0.76 |

Beja | 1.00 | 0.79 | 0.85 | 1.02 | 0.82 | 0.80 | 1.01 | 0.81 | 0.82 |

Castro Verde | 1.00 | 0.80 | 0.92 | 0.99 | 0.82 | 0.84 | 0.99 | 0.81 | 0.88 |

Elvas | 1.00 | 0.78 | 0.84 | 0.98 | 0.76 | 0.88 | 0.99 | 0.77 | 0.86 |

Estremoz | 1.00 | 0.78 | 0.68 | 0.99 | 0.76 | 0.77 | 0.99 | 0.77 | 0.73 |

Évora | 1.00 | 0.76 | 0.82 | 1.00 | 0.73 | 0.85 | 1.00 | 0.75 | 0.84 |

Ferreira do Alentejo | 0.99 | 0.77 | 0.77 | 0.98 | 0.79 | 0.74 | 0.99 | 0.78 | 0.75 |

Moura | 1.00 | 0.79 | 0.69 | 0.97 | 0.80 | 0.72 | 0.98 | 0.79 | 0.71 |

Odemira | 1.00 | 0.63 | 0.67 | 0.97 | 0.68 | 0.63 | 0.99 | 0.65 | 0.65 |

Redondo | 1.00 | 0.78 | 0.89 | 0.99 | 0.77 | 0.93 | 1.00 | 0.78 | 0.91 |

Serpa | 1.00 | 0.76 | 0.82 | 0.96 | 0.77 | 0.84 | 0.98 | 0.76 | 0.83 |

Viana | 1.00 | 0.79 | 0.80 | 0.97 | 0.78 | 0.85 | 0.98 | 0.79 | 0.82 |

Vidigueira | 1.00 | 0.78 | 0.79 | 0.98 | 0.78 | 0.83 | 0.99 | 0.78 | 0.81 |

Alentejo | 0.99 | 0.77 | 0.83 | 0.97 | 0.77 | 0.83 | 0.98 | 0.77 | 0.83 |

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**MDPI and ACS Style**

Rodrigues, G.C.; Braga, R.P.
A Simple Procedure to Estimate Reference Evapotranspiration during the Irrigation Season in a Hot-Summer Mediterranean Climate. *Sustainability* **2021**, *13*, 349.
https://doi.org/10.3390/su13010349

**AMA Style**

Rodrigues GC, Braga RP.
A Simple Procedure to Estimate Reference Evapotranspiration during the Irrigation Season in a Hot-Summer Mediterranean Climate. *Sustainability*. 2021; 13(1):349.
https://doi.org/10.3390/su13010349

**Chicago/Turabian Style**

Rodrigues, Gonçalo C., and Ricardo P. Braga.
2021. "A Simple Procedure to Estimate Reference Evapotranspiration during the Irrigation Season in a Hot-Summer Mediterranean Climate" *Sustainability* 13, no. 1: 349.
https://doi.org/10.3390/su13010349