# Trend Analysis and Identification of the Meteorological Factors Influencing Reference Evapotranspiration

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^{2}

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## Abstract

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## 1. Introduction

^{−1,}and an albedo of 0.23. ETo enables one to calculate the energy and water exchanges in vegetation [2,3], soil surface [4], land surface [5,6], and atmosphere [7,8,9]. Estimation and measurements of ETo contribute greatly to our understanding of earth’s energy budget, agricultural water management, water resource management, and climate change studies [6,10,11,12,13,14,15,16]. There are different methods and approaches for measuring and estimating ETo. These methods can be divided into two main groups: direct methods (field water balance approach and soil moisture depletion approach) and indirect methods (empirical/statistical methods, micrometeorological methods, and remote sensing methods [1,8,17,18,19,20,21,22]).

## 2. Data and Methods

#### 2.1. The FAO-Penman-Monteith Method

^{−1,}and an albedo value (i.e., portion of light reflected by the leaf surface) of 0.23.

^{−1}),(R

_{n}) is the net radiation at the crop surface [MJ m

^{−2}day

^{−1}], G is the soil heat flux density [MJ m

^{−2}day

^{−1}], T is the air temperature at 2 m height [°C], ${U}_{2}$ is the wind speed at 2 m height [m s

^{−1}], e

_{s}is saturation vapor pressure [kPa], e

_{a}is actual vapor pressure [kPa], e

_{s}−e

_{a}is the saturation vapor pressure deficit [kPa], $\Delta $ is the vapor pressure curve slope [kPa °C

^{−1}], and $\gamma $ is the psychrometric constant [kPa °C

^{−1}].

#### 2.2. Mann-Kendall Test

_{j}are the values of the variable at time k and j, respectively, n is the length of the series and Sgn() is the sign function, defined as follows:

^{th}group.

_{0}, meaning that no significant trend is present, is accepted if the test statistic (Z) is not statistically significant, i.e., −Z

_{α/2}< Z < Z

_{α/2}, where Z

_{α/2}is the standard normal deviate.

_{t}to obtain a new sequence without an autocorrelation effect:

#### 2.3. Sen’s Slope Estimator

#### 2.4. Sensitivity Analysis

_{d}the dew point in °C, p the surface pressure in mbar, and q the specific humidity in kg/kg.

_{s}is saturation vapor pressure in mbar, e is vapor pressure in mbar, and RH is relative humidity in percent.

_{max}and T

_{min}contribute differently to the ETo trend. The FAO PM equation (Equation (1)) includes the e

_{s}saturation vapor pressure [kPa], e

_{a}actual vapor pressure [kPa], and their difference (e

_{s}−e

_{a}saturation vapor pressure deficit [kPa]). These terms are computed using the T

_{max}and T

_{min}.

#### 2.5. Contribution Rate

#### 2.6. Study Area and Data

_{max}) and minimum temperature (T

_{min}), relative humidity (RH), wind speed (WS), and solar radiation (SR) data were obtained from Piazza Armerina meteorological station installed and managed by the Sicilian Agro-meteorological informative service (Servizio Informativo Agrometeorologico Siciliano—SIAS, http://www.sias.regione.sicilia.it/, accessed on 20 July 2022). The astronomical location of the meteorological site is 37.382171° N and 14.3666704° E, and its elevation is 697 m a.s.l. (Figure 1). The dataset consisted of 17.25 years of daily data covering the period from 1 December 2003 to 28 February 2021, for all variables.

## 3. Results

#### 3.1. MK-Test Trends of Meteorological Factors and ETo

_{max}exhibits positive trends for March and September and spring and summer, while no significant trends were obtained for other time series. The T

_{min}presents positive monthly trends in August and September, and no other significant trends were observed. For Tmean, there was no significant trend except for September and spring and summer. Conversely, SR presents a negative trend in November and in Autumn. As regards WS, positive trends were observed on both seasonal and monthly scales. On the monthly scale, January, May, June, July, November, and December showed positive trends; for the remaining months no trend is evidenced. The HU also has a positive significant trend in March, April, May, June, July, August, September, October, and December, as well as in spring and summer. Rainfall showed a negative trend only in Autumn. The trend of ETo is negative only in November, and non-significant in the other cases.

#### 3.2. Sen’s Slope (Magnitude of the Trend)

_{max}increased in March (0.10 °C) and September (0.14 °C) (monthly trend analysis), and spring (0.10 °C) and summer (0.09 °C) (seasonal trend analysis). The T

_{min}also increased in August (0.09 °C) and September (0.07 °C). The T

_{mean}trend also increased in September (0.10 °C) in monthly analysis and in spring (0.07 °C), and summer (0.06 °C) in the seasonal analysis. The SR showed a downward trend in November (0.09 MJ/m

^{2}), at the monthly scale, and in Autumn (0.076 MJ/m

^{2}), at the seasonal scale. The WS also showed an upward trend in January (0.054 m/s), May (0.038 m/s), June (0.021 m/s), July (0.043 m/s), November (0.040 m/s), and December (0.042 m/s), as well as in winter (0.037 m/s) and spring (0.029 m/s). The HU trend also increased in March (0.711%), April (0.543%), May (1.169%), June (0.741%), July (1.012%), August (0.824%), September (0.816%), October (0.614%), and December (0.412%), as well as in spring (0.840%) and summer (0.942%). The RF also decreased in Autumn by 14.019 mm in the seasonal trend analysis.

#### 3.3. Sensitivity of ETo to Climatic Factors

_{max}, T

_{mean}, T

_{min}, SR, WS, and SHU were used as input climatological variables. ETo showed different levels of sensitivity to these climatological variables. In particular, the result showed that SHU, T

_{mean,}and T

_{max}have a very high sensitivity level, with sensitivity coefficients of 2.68, 1.46, and 1.35 respectively. The RS and T

_{min}also showed a high sensitivity level, with the sensitivity coefficient of 0.53 and 0.28 respectively. In contrast, the sensitivity level of wind speed was negligible, with a value of 0.02 for the sensitivity coefficient (Table 3).

#### 3.4. Contribution Rate of Climatic Factors for the Variation of ETo

_{min}are negative, with values of 91.73, 2.48, and 1.06, respectively. On the other hand, T

_{max}, T

_{mean,}and WS contribute positively with an 11.2, 9.74, and 0.9 contribution rate. This result shows that SHU has the highest contribution to the decrease of ETo and maximum temperature has the highest contribution to the increase of ETo in the study area.

## 4. Discussion

#### 4.1. Trend of Climatic Factors and ETo

#### 4.2. Sensitivity of ETo and Contribution Rate of Climatological Elements

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Daily ETo (

**A**), Annual ETo and Monthly ETo (

**B**), Seasonal ETo (

**C**), and Monthly Climatology (

**D**).

**Figure 4.**Daily timeseries of climate variables from December 1, 2003–December 28, 2021: (

**A**–

**E**) are Solar radiation, Air temperature (maximum, minimum, and mean temperature), Relative humidity, Specific humidity, and Wind speed, respectively.

Sensitivity Coefficient | Sensitivity Level |
---|---|

0.00 ≤ |$\mathit{S}{\mathit{v}}_{\mathit{i}}$| < 0.05 | Negligible |

0.05 ≤ |$\mathit{S}{\mathit{v}}_{\mathit{i}}$| < 0.2 | Moderate |

0.2 ≤ |$\mathit{S}{\mathit{v}}_{\mathit{i}}$| < 1 | High |

1.00 ≤ |$\mathit{S}{\mathit{v}}_{\mathit{i}}$| | Very high |

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | Win | Spr | Sum | Aut | Annual | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

T_{max} | 1.1 | 1.19 | 2.27 | 1.44 | 0.91 | 1.77 | 1.61 | 1.69 | 2.43 | 0.78 | 1.69 | 1.86 | 1.77 | 2.14 | 1.98 | 1.49 | 1.31 |

T_{min} | 0.08 | 0.95 | 0.99 | 0.62 | −0.49 | −0.21 | 1.19 | 2.18 | 2.14 | 0.01 | 1.36 | −0.37 | 0.12 | 0.33 | 1.03 | 1.4 | 1.19 |

T_{mean} | 0.12 | 1.03 | 1.94 | 1.36 | 0.29 | 0.45 | 1.69 | 1.77 | 2.35 | 0.29 | 1.77 | 0.62 | 0.95 | 2.51 | 2.18 | 1.49 | 1.58 |

SR | −0.95 | −0.54 | −0.7 | 0.62 | −1.65 | −0.33 | −0.78 | −1.2 | −1.07 | −1.44 | −2.02 | 0.95 | −0.12 | −0.87 | −0.91 | −2.6 | −1.44 |

WS | 2.68 | 0.99 | 1.03 | 1.28 | 2.76 | 2.18 | 2.97 | 1.73 | 0.77 | 0.95 | 2.39 | 2.23 | 2.76 | 2.02 | 0.95 | 0.86 | 0.95 |

HU | 0.41 | 0.5 | 2.27 | 2.27 | 2.12 | 2.84 | 3.17 | 2.39 | 2.12 | 2.02 | 1.22 | 2.02 | 0.86 | 2.21 | 2.03 | 1.31 | 1.31 |

ETo | −1.85 | −0.95 | −1.11 | 0.45 | −1.28 | −0.62 | 0.54 | 0.21 | 0.45 | 0.04 | −2.51 | −0.95 | −0.54 | −0.78 | −0.21 | −0.54 | −0.78 |

RF | −0.04 | 0.45 | −0.62 | −1.19 | 0.29 | −0.49 | 0.46 | 0.64 | −0.21 | 0.33 | 0.95 | 0.5 | −1.28 | −0.29 | −0.04 | −2.6 | −1.61 |

Climatological Element | Sensitivity Coefficient |x| | Sensitivity Level |
---|---|---|

Net solar radiation | |0.53| | High |

Maximum temperature | |1.35| | Very high |

Minimum temperature | |−0.28| | High |

Mean temperature | |1.46| | Very high |

Specific humidity | |−2.68| | Very high |

Wind speed | |0.02| | Negligible |

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**MDPI and ACS Style**

Aschale, T.M.; Peres, D.J.; Gullotta, A.; Sciuto, G.; Cancelliere, A.
Trend Analysis and Identification of the Meteorological Factors Influencing Reference Evapotranspiration. *Water* **2023**, *15*, 470.
https://doi.org/10.3390/w15030470

**AMA Style**

Aschale TM, Peres DJ, Gullotta A, Sciuto G, Cancelliere A.
Trend Analysis and Identification of the Meteorological Factors Influencing Reference Evapotranspiration. *Water*. 2023; 15(3):470.
https://doi.org/10.3390/w15030470

**Chicago/Turabian Style**

Aschale, Tagele Mossie, David J. Peres, Aurora Gullotta, Guido Sciuto, and Antonino Cancelliere.
2023. "Trend Analysis and Identification of the Meteorological Factors Influencing Reference Evapotranspiration" *Water* 15, no. 3: 470.
https://doi.org/10.3390/w15030470