# Trend Analysis of Long-Term Reference Evapotranspiration and Its Components over the Korean Peninsula

^{1}

^{2}

^{*}

## Abstract

**:**

_{o}) and its components consisting of the energy term (EN

_{o}) and the aerodynamic term (AE

_{o}) were considered over the Korean Peninsula. The T-test and Mann–Kendall (MK) test were used to detect parameter trends after removing the effect of serial correlation from annual and seasonal time series between 1980 and 2017. Due to the lack of solar-radiation data for North Korea (NK), a regionally calibrated model based on South Korea (SK) weather data was developed to estimate daily solar radiation in NK. The results showed that spatial distribution of the ET

_{o}increased southward in the range from 705 mm/year in the northeast to 1195 mm/year in the southeast of the Korean Peninsula. The spatial patterns of the EN

_{o}and AE

_{o}varied from the minimum in the north and increased southward, reaching their maximum values in the southern parts of the Korean Peninsula. The mean annual ET

_{o}values of SK and NK were also compared. Over the 37-year period, mean annual evapotranspiration in SK was approximately 18% higher than that in NK. Moreover, mean areal EN

_{o}and AE

_{o}in SK were higher than in NK. The trend of the EN

_{o}on annual and seasonal scales was also upward. In contrast, the trend of the AE

_{o}decreased over the Korean Peninsula through all seasons and annual scales. These opposite trends in the EN

_{o}and AE

_{o}parameters mitigated the significant trends of the ET

_{o}. Finally, the stronger significant upward trend of the energy term led to significant increasing trends of ET

_{o}on the Korean Peninsula, with EN

_{o}being the dominant component in the increase of the ET

_{o}.

## 1. Introduction

## 2. Methods

#### 2.1. Estimation of $E{T}_{o}$

^{−1}, and that is actively growing and well-watered. The FAO PM method can be expressed as follows [6]:

^{−1}), Δ is the slope vapor pressure curve (KPa °C

^{−1}), R

_{n}is the net radiation (MJ m

^{−2}day

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

^{−2}day

^{−1}), $\gamma $ is the psychrometric constant (KPa °C

^{−1}), T is the average daily air temperature (°C), ${u}_{2}$ is the wind speed at 2 m above ground level (m s

^{−1}), ${e}_{s}$ is the saturation vapor pressure (KPa), and ${e}_{a}$ is the actual vapor pressure (KPa). Other relevant equations used in computing ${\mathrm{ET}}_{\mathrm{o}}$ via the FAO PM method are explained in FAO 56 [6] and summarized in Table S1.

^{−1}) and ${\mathrm{AE}}_{\mathrm{o}}$ is the aerodynamic component (mm day

^{−1}) of the FAO PM equation. The energy term represents the ${\mathrm{ET}}_{\mathrm{o}}$ when the heat-exchange budget of the surface is obtained based on solar radiation and temperature under the condition in which short and well-watered reference vegetation is exposed to bright sunshine and light wind speed. The aerodynamic term reveals the ${\mathrm{ET}}_{\mathrm{o}}$ when short and well-watered reference vegetation is exposed to high wind speed and a large vapor-pressure deficit.

_{o}was calculated for each station. Then, the mean seasonal and annual ET

_{o}values for each year were derived by adding the daily values during each season and the annual ET

_{o}was obtained by summing the seasonal values.

#### 2.2. Estimation of Solar Radiation

_{o}. However, when solar-radiation or sunshine-duration data are unavailable, FAO 56 recommends using Hargreaves’ radiation formula to estimate solar radiation. Hargreaves’ radiation formula is calibrated and validated for various stations in different climate conditions. This formula, proposed by Reference [21], is expressed as follows:

^{−2}day

^{−1}); TD is the diurnal temperature, which is the difference between the maximum temperature (${T}_{max}$) and the minimum temperature (${T}_{min}$) (°C); K

_{Rs}is the adjustment coefficient; and R

_{a}is the extraterrestrial radiation (MJ m

^{−2}day

^{−1}), which varies throughout the day of the year and latitude.

#### 2.3. Trend-Analysis Method

#### 2.3.1. Parametric T-Test

#### 2.3.2. Nonparametric Mann–Kendall test

_{j}and X

_{i}are sequential data (j > i), and Sgn (${X}_{j}-{X}_{i}$) is a sign function that extracts the sign of ${X}_{j}-{X}_{i}$. Statistic S has normal distribution with zero mean and variance and is computed as

_{o}that Z has no significant trend is accepted if $-{Z}_{1-\frac{\alpha}{2}}\le Z\le {Z}_{1-\frac{\alpha}{2}}$, where α is the significance level for the test (5% and 10% significance levels) and +${Z}_{1-\frac{\alpha}{2}}$ and $-{Z}_{1-\frac{\alpha}{2}}$ are the critical values for the two-sided hypothesis. The slope of the trends in the nonparametric MK test can be calculated as follows:

#### 2.4. Impact of Serial Correlation in a Time Series

## 3. Study Area and Data

**,**${T}_{max}$, ${T}_{min}$, dew-point temperature $({T}_{dew})$, and wind speed $\left({W}_{s}\right)$. Daily meteorological data from 21 meteorological stations in SK and 27 stations in NK were collected from the Korea Meteorological Administration (https://data.kma.go.kr) within a sufficient meteorological time period (1980–2017). Statistics for the observed daily ${R}_{s}$ are available for the 21 weather stations in SK but not for those in NK. The spatial distribution of the stations in SK and NK is shown in Figure 1.

_{S}to reach the computed ${R}_{so}$ (where a is the corrective factor). Additional explanation about the integrity of solar-radiation data using clear-sky comparisons can be found in FAO 56 [6,24,36]. There were differences between ${R}_{s}$and ${R}_{so}$ for some years at stations in SK. These mismatches were found and modified for all stations in SK. Figure 2 shows the time series of solar radiation before and after this prescreening for the Incheon station in 1980 and Seaosan station in 1982.

## 4. Results and Discussion.

#### 4.1. Regional Calibration of ${K}_{Rs}$ and Estimation of Solar Radiation

^{2}= 0.89) and small root-mean-square error (RMSE = 0.007). Using the ${K}_{Rs}$ values for all stations in SK and NK, ${R}_{s}$ was estimated using Hargreaves’ formula (Equation (3)) for all stations in SK and NK.

#### 4.2. Estimation of $E{T}_{o}$ Using the Penman–Monteith Method

#### 4.3. Spatial Distribution of Mean Annual and Seasonal $E{T}_{o}$, $E{N}_{o}$, and $A{E}_{o}$

#### 4.4. Differences in the Mean Annual and Seasonal $E{T}_{o}$, $E{N}_{o}$, and $A{E}_{o}$ between SK and NK

#### 4.5. Spatial Variation of Annual and Seasonal $E{T}_{o}$, $E{N}_{o}$, and $A{E}_{o}$ Trends

#### 4.6. Difference in Trends of Mean Annual and Seasonal $E{T}_{o}$, $E{N}_{o}$, and $A{E}_{o}$ in SK and NK

## 5. Conclusions

- The spatial distribution of the mean annual ${\mathrm{ET}}_{\mathrm{o}}$ exhibited increasing spatial variation in annual ${\mathrm{ET}}_{\mathrm{o}}$ from NK to SK. A lower ${\mathrm{ET}}_{\mathrm{o}}$ was evident for the northeastern Korean Peninsula, and higher values were found over the southeastern Korean Peninsula.
- The spatial distribution of the ${\mathrm{EN}}_{\mathrm{o}}$ and ${\mathrm{AE}}_{\mathrm{o}}$ revealed a clear distribution from the minimum in NK and reached the peak in SK for both energy and aerodynamic terms. The energy term is influenced by ${\mathrm{R}}_{\mathrm{s}}$ and T, and the aerodynamic term is affected by RH and WS. The lower latitude in NK causes a lower amount of ${\mathrm{R}}_{\mathrm{s}}$ than that in SK, and mean annual T in NK is lower than in SK because T in the northern area of the Korean Peninsula is mostly affected by the influx of cold air from the Siberian high. These superimposed effects cause the higher energy term in SK.
- A comparison of the mean annual ${\mathrm{ET}}_{\mathrm{o}}$ showed that the average annual ${\mathrm{ET}}_{\mathrm{o}}$ in SK was 18% higher than that in NK from 1980 to 2017. Additionally, the mean areal ${\mathrm{EN}}_{\mathrm{o}}$ and ${\mathrm{AE}}_{\mathrm{o}}$ is higher, at 9.3% and 49.7%, respectively, in SK than in NK.
- The results of the trends test indicate that the significant increasing trend of ${\mathrm{ET}}_{\mathrm{o}}$ is mainly caused by significant increasing trends in the ${\mathrm{EN}}_{\mathrm{o}}$ term in SK and NK. This finding indicates that ${\mathrm{EN}}_{\mathrm{o}}$ is the dominant component affecting the ${\mathrm{ET}}_{\mathrm{o}}$ over the Korean Peninsula. In addition, opposite trends exist for ${\mathrm{EN}}_{\mathrm{o}}$ and ${\mathrm{AE}}_{\mathrm{o}}$ on the Korean Peninsula (significant increasing trends for ${\mathrm{EN}}_{\mathrm{o}}$ and significant decreasing trends for ${\mathrm{AE}}_{\mathrm{o}}$ on seasonal and annual time scales). The different trends in the mentioned parameter mainly arise from the effect of meteorological variables on the energy and aerodynamic terms (${\mathrm{R}}_{\mathrm{s}}$ and T for ${\mathrm{EN}}_{\mathrm{o}}$ and WS and RH for ${\mathrm{AE}}_{\mathrm{o}}$).

## Supplementary Materials

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Spatial distribution of (

**a**) topographic characteristics and name of weather stations, and (

**b**) land cover and code of stations on the Korean Peninsula.

**Figure 2.**Adjustment of daily solar radiation using the clear-sky envelope for the Incheon station in 1980 ((

**a**) and (

**b**)), and the Seosan station in 1982 ((

**c**) and (

**d**)); results for before and after adjustment are shown.

**Figure 4.**Box-and-whisker plots of the variability of annual ${\mathrm{ET}}_{\mathrm{o}}$ for stations in (

**a**) North Korea and (

**b**) South Korea from 1980 to 2017. (Note: The line inside the boxes represents the median, and the upper and lower lines indicate 75% and 25%, respectively. The upper and lower portions of the whiskers represent the maximum and minimum annual ${\mathrm{ET}}_{\mathrm{o}}$, respectively).

**Figure 5.**Spatial distribution of mean annual ${\mathrm{ET}}_{\mathrm{o}}$, ${\mathrm{EN}}_{\mathrm{o}}$, and ${\mathrm{AE}}_{\mathrm{o}}$. on annual and seasonal scales.

**Figure 6.**Difference between the amount of mean annual and seasonal ${\mathrm{ET}}_{\mathrm{o}}$, ${\mathrm{EN}}_{\mathrm{o}}$, and ${\mathrm{AE}}_{\mathrm{o}}$ in SK and North Korea (NK).

**Figure 7.**Spatial distribution of stations with increasing and decreasing trends according to the Mann–Kendall (MK) test on annual and seasonal ${\mathrm{ET}}_{\mathrm{o}}$, ${\mathrm{EN}}_{\mathrm{o}}$, and ${\mathrm{AE}}_{\mathrm{o}}$ during the period 1980 to 2017. Upward- and downward-pointing triangles indicate increasing and decreasing trends, respectively. Blue and red colors show the 90% and 95% confidence levels, respectively. The white color shows no significant trends.

**Figure 8.**Spatial distribution of stations with increasing and decreasing trends according to the T-test on annual and seasonal ${\mathrm{ET}}_{\mathrm{o}}$, ${\mathrm{EN}}_{\mathrm{o}}$, and ${\mathrm{AE}}_{\mathrm{o}}$ during the period 1980 to 2017. Upward- and downward-pointing triangles indicate increasing and decreasing trends, respectively. Blue and red colors show the 90% and 95% confidence levels, respectively. The white color shows no significant trends.

**Table 1.**Statistical analysis for comparison of daily observed and calculated solar-radiation data for 21 stations of South Korea (SK).

Station Code | Station Name | R^{2} | Root-Mean-Square Error (RMSE) |
---|---|---|---|

100 | Daegwalryeong | 0.87 | 3.00 |

101 | Chuncheon | 0.85 | 3.07 |

105 | Gangnung | 0.86 | 3.10 |

108 | Seoul | 0.84 | 3.57 |

112 | Incheon | 0.82 | 3.73 |

114 | Wonju | 0.66 | 4.96 |

129 | Seosan | 0.85 | 4.11 |

131 | Cheongju | 0.83 | 3.49 |

133 | Daejeon | 0.86 | 2.68 |

135 | Chupungyong | 0.81 | 3.53 |

136 | Andong | 0.84 | 2.98 |

138 | Pohang | 0.85 | 3.18 |

143 | Daegu | 0.89 | 2.71 |

146 | Jeonju | 0.88 | 2.81 |

156 | Gwangju | 0.88 | 2.70 |

159 | Busan | 0.86 | 3.17 |

165 | Mokpo | 0.89 | 2.59 |

184 | Jeju | 0.92 | 2.67 |

185 | Gosan | 0.87 | 2.84 |

169 | Heuksando | 0.90 | 1.78 |

192 | Jinju | 0.88 | 2.56 |

**Table 2.**Mean seasonal and annual ${\mathrm{ET}}_{\mathrm{o}}$, ${\mathrm{EN}}_{\mathrm{o}}$, and ${\mathrm{AE}}_{\mathrm{o}}$ from 1980 to 2017 and ratios with ${\mathrm{ET}}_{\mathrm{o}}.$

Period | ET_{o} | Annual ET_{o} | EN_{o} | AE_{o} | EN_{o}/ET_{o} | AE_{o}/ET_{o} |
---|---|---|---|---|---|---|

(mm/year) | (%) | (mm/year) | (mm/year) | (%) | (%) | |

South Korea | ||||||

Spring | 267.6 | 27.6 | 180.5 | 87.1 | 67.4 | 32.6 |

Summer | 426.9 | 44.0 | 358.0 | 68.9 | 83.9 | 16.1 |

Autumn | 196.0 | 20.2 | 133.3 | 62.8 | 68.0 | 32.0 |

Winter | 80.6 | 8.3 | 36.6 | 43.9 | 45.5 | 54.5 |

Annual | 971.2 | 100.0 | 708.4 | 262.7 | 72.9 | 27.1 |

North Korea | ||||||

Spring | 224.9 | 27.3 | 164.4 | 60.5 | 73.1 | 26.9 |

Summer | 391.1 | 47.5 | 346.3 | 44.8 | 88.6 | 11.4 |

Autumn | 155.9 | 18.9 | 111.4 | 44.4 | 71.5 | 28.5 |

Winter | 51.7 | 6.3 | 25.9 | 25.8 | 50.1 | 49.9 |

Annual | 823.5 | 100.0 | 648.0 | 175.5 | 78.7 | 21.3 |

**Table 3.**Statistical trends in the seasonal and annual ${\mathrm{ET}}_{\mathrm{o}}$, ${\mathrm{EN}}_{\mathrm{o}}$, and ${\mathrm{AE}}_{\mathrm{o}}$ from 1980 to 2017.

Period | South Korea | North Korea | ||||||
---|---|---|---|---|---|---|---|---|

Parametric T-Test | Nonparametric MK Test | Parametric T-Test | Nonparametric MK Test | |||||

T | B | Z | β | T | B | Z | β | |

ET_{o} | ||||||||

Spring | $\underset{\_}{\underset{\_}{1.67}}$ | 0.26 | 2.03 | 0.28 | $\underset{\_}{\underset{\_}{1.94}}$ | 0.31 | $\underset{\_}{\underset{\_}{2.09}}$ | 0.35 |

Summer | 2.18 | 0.34 | 2.26 | 0.45 | 2.51 | 0.39 | $\underset{\_}{\underset{\_}{2.63}}$ | 0.40 |

Autumn | 0.59 | 0.09 | 0.04 | –0.03 | 0.66 | 0.10 | 0.16 | –0.03 |

Winter | –0.53 | –0.08 | –0.46 | –0.06 | –0.32 | –0.05 | –0.21 | –0.07 |

Annual | 2.42 | 0.38 | 2.69 | 0.60 | 1.30 | 0.21 | 0.98 | 0.08 |

EN_{o} | ||||||||

Spring | 2.23 | 0.35 | $\underset{\_}{\underset{\_}{2.33}}$ | 0.23 | 2.42 | 0.38 | $\underset{\_}{\underset{\_}{2.77}}$ | 0.33 |

Summer | 3.47 | 0.55 | $\underset{\_}{\underset{\_}{3.39}}$ | 0.65 | 2.90 | 0.46 | $\underset{\_}{\underset{\_}{2.64}}$ | 0.54 |

Autumn | 2.44 | 0.38 | $\underset{\_}{\underset{\_}{2.03}}$ | 0.15 | 2.54 | 0.40 | $\underset{\_}{\underset{\_}{2.08}}$ | 0.16 |

Winter | 1.97 | 0.31 | $\underset{\_}{\underset{\_}{2.15}}$ | 0.07 | $\underset{\_}{\underset{\_}{1.66}}$ | 0.26 | $\underset{\_}{\underset{\_}{1.96}}$ | 0.05 |

Annual | 2.63 | 0.42 | $\underset{\_}{\underset{\_}{2.86}}$ | 0.64 | 2.15 | 0.34 | $\underset{\_}{\underset{\_}{2.15}}$ | 0.43 |

AE_{o} | ||||||||

Spring | –2.73 | –0.43 | –2.34 | –0.18 | –0.82 | –0.14 | –0.64 | –0.17 |

Summer | –2.61 | –0.41 | –2.54 | –0.22 | –1.60 | –0.27 | –1.62 | –0.18 |

Autumn | –2.19 | –0.35 | –2.07 | –0.21 | –1.26 | –0.21 | –1.31 | –0.16 |

Winter | –1.56 | –0.25 | –1.54 | –0.10 | –0.70 | –0.12 | –0.90 | –0.09 |

Annual | –2.55 | –0.40 | –2.46 | –0.52 | –1.01 | –0.17 | –1.30 | –0.49 |

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**MDPI and ACS Style**

Ghafouri-Azar, M.; Bae, D.-H.; Kang, S.-U.
Trend Analysis of Long-Term Reference Evapotranspiration and Its Components over the Korean Peninsula. *Water* **2018**, *10*, 1373.
https://doi.org/10.3390/w10101373

**AMA Style**

Ghafouri-Azar M, Bae D-H, Kang S-U.
Trend Analysis of Long-Term Reference Evapotranspiration and Its Components over the Korean Peninsula. *Water*. 2018; 10(10):1373.
https://doi.org/10.3390/w10101373

**Chicago/Turabian Style**

Ghafouri-Azar, Mona, Deg-Hyo Bae, and Shin-Uk Kang.
2018. "Trend Analysis of Long-Term Reference Evapotranspiration and Its Components over the Korean Peninsula" *Water* 10, no. 10: 1373.
https://doi.org/10.3390/w10101373