Necessary Equations for Using the Penman–Monteith Method Shown in Table S1

Supplementary Materials:

Necessary equations for using the Penman–Monteith method shown in Table S1.

Table S1. Required equations for computing ETo using the FAO PM method.

Variable Definition Equation Related variables

+ : daily maximum temperature (°C), (°C) Mean daily air temperature = 2 : daily minimum temperature (°C) Saturation vapor pressure at 17.27 T: air temperature (°C), () (kPa) () = 0.6108 air temperature T + 237.3 exp (...): 2.7183 raised to the power (.)

e°(T): saturation vapor pressure (kPa), Mean saturation vapor () + () (kPa) = : daily maximum temperature (°C), pressure 2 : daily minimum temperature (°C)

17.27 : dew point temperature (°C), (kPa) Actual vapor pressure = () = 0.6108 + 237.3 exp (...): 2.7183 raised to the power (...) 17.27 Slope of saturation vapor 4098 0.6108 exp T: mean air temperature (°C), −1 + 237.3 ∆ (kPa °C ) ∆= pressure curve ( + 237.3) exp (...): 2.7183 raised to the power (...) 293 − 0.0065 . : elevation above sea level (m) (kPa) Atmospheric pressure = 101.3 293 : atmospheric pressure (kPa) (kPa °C−1) Psychrometric constant = 0.665 × 10 ×

−2 −1 −2 24(60) : solar constant = 0.0820 (MJ m min ), (MJ m Daily extraterrestrial = [ sin() sin() : latitude (rad) day−1) radiation + cos() cos() sin()] Inverse relative Earth-Sun 2 is the number of the day of the year between 1 (1 January) (rad) = 1 + 0.033 cos distance 365 and 365 or 366 (31 December) 2 is the number of the day of the year between 1 (1 January) (rad) Solar declination = 0.409 sin − 1.39 365 and 365 or 366 (31 December) − tan() tan() = 1 − [tan()][tan()] (rad) The sunset hour angle = − 2 . = 0.00001 ≤ 0 (MJ m−2 : elevation above sea level (m) Clear-sky solar radiation = (0.75 + 2 10) −1 −2 −1 day ) : extraterrestrial radiation (MJ m day ) : albedo or canopy reflection coefficient (0.23 for the (MJ m−2 Net solar or net shortwave = (1 − ) hypothetical grass reference crop (dimensionless), : the day−1) radiation incoming solar radiation (MJ m−2 day−1) : Stefan-Boltzmann constant (4.903 10-9 MJ K−4 m−2 day−1), + , , : maximum absolute temperature during the 24-hour −2 = (0.34 , (MJ m 2 Net longwave radiation period (K = °C + 273.16), ,: minimum absolute day−1) − 0.14 1.35 − 0.35 temperature during the 24-hour period (K = °C + 273.16), : measured or calculated solar radiation (MJ m−2 day−1) (MJ m−2 : Net solar or net shortwave radiation, : Net longwave Net radiation = − day−1) radiation Wind speed at 2 m above 4.87 : measured wind speed at z m above ground surface (m s−1), (m s−1) = ground ln (67.8 − 5.42) : height of measurement above ground surface (m)

Table S2. Number and percentage of missing data from 1980 to 2017 for stations in SK and NK (total number of data: 13,880).

Latitude Longitude Number of Missing Data Percent of Missing Data Relative to the Total Data (%) Country Station Name Station Code (Degree) (Degree) Tmin Tmax Ws RH Tmin Tmax Ws RH Daegwalryeong 100 37.68 128.72 2 0 1 1 0.01 0.00 0.01 0.01 Chuncheon 101 37.90 127.74 0 0 0 1 0.00 0.00 0.00 0.01 Gangnung 105 37.75 128.89 0 0 2 0 0.00 0.00 0.01 0.00 Seoul 108 37.57 126.97 0 1 4 0 0.00 0.01 0.03 0.00 Incheon 112 37.48 126.62 1 1 2 1 0.01 0.01 0.01 0.01 Wonju 114 37.34 127.95 0 0 0 0 0.00 0.00 0.00 0.00 Seosan 129 36.78 126.49 0 1 0 2 0.00 0.01 0.00 0.01 Cheongju 131 36.64 127.44 0 0 0 0 0.00 0.00 0.00 0.00 Daejeon 133 36.37 127.37 0 0 0 0 0.00 0.00 0.00 0.00 Chupungyong 135 36.22 127.99 0 0 0 1 0.00 0.00 0.00 0.01 South Korea Andong 136 36.57 128.71 0 0 0 0 0.00 0.00 0.00 0.00 Pohang 138 36.03 129.38 0 0 3 3 0.00 0.00 0.02 0.02 Daegu 143 35.89 128.62 0 1 3 2 0.00 0.01 0.02 0.01 Jeonju 146 35.82 127.15 0 0 2 0 0.00 0.00 0.01 0.00 Gwangju 156 35.17 126.89 0 0 0 0 0.00 0.00 0.00 0.00 Busan 159 35.10 129.03 0 0 0 0 0.00 0.00 0.00 0.00 Mokpo 165 34.82 126.38 0 0 0 0 0.00 0.00 0.00 0.00 Heuksan 169 34.69 125.45 0 0 0 0 0.00 0.00 0.00 0.00 Jeju 184 33.51 126.53 0 0 1 0 0.00 0.00 0.01 0.00 Gosan 185 33.29 126.16 0 0 2 2 0.00 0.00 0.01 0.01 Jinju 192 35.16 128.04 0 0 9 0 0.00 0.00 0.06 0.00 Seonbong 3 42.32 130.40 3949 3881 3660 3654 28.45 27.96 26.37 26.33 Samjiyeon 5 41.82 128.30 1217 1213 512 511 8.77 8.74 3.69 3.68 North Korea Cheongjin 8 41.78 129.82 650 654 327 326 4.68 4.71 2.36 2.35 Jung-gang 14 41.78 126.88 1776 1978 1557 1559 12.80 14.25 11.22 11.23 Hyesan 16 41.40 128.17 716 768 332 333 5.16 5.53 2.39 2.40 Gang-gye 20 40.97 126.60 615 621 273 272 4.43 4.47 1.97 1.96 Pungsan 22 40.82 128.15 1409 1626 885 885 10.15 11.71 6.38 6.38 Gimchaeg 25 40.67 129.20 1400 1619 1242 1241 10.09 11.66 8.95 8.94 Supung 28 40.45 124.93 1262 1439 913 915 9.09 10.37 6.58 6.59 Cheongjin 31 40.37 127.25 1666 1728 1141 1141 12.00 12.45 8.22 8.22 Sin-uiju 35 40.10 124.38 661 628 313 308 4.76 4.52 2.26 2.22 Guseong 37 39.98 125.25 1286 1401 827 826 9.27 10.09 5.96 5.95 Huicheon 39 40.17 126.25 1333 1488 856 857 9.60 10.72 6.17 6.17 Hamheung 41 39.93 127.55 632 625 285 285 4.55 4.50 2.05 2.05 Sinpo 46 40.03 128.18 1087 1729 63 63 7.83 12.46 0.45 0.45 Anju 50 39.62 125.65 1109 1104 572 572 7.99 7.95 4.12 4.12 Yangdeog 52 39.22 126.65 1257 1486 936 937 9.06 10.71 6.74 6.75 Wonsan 55 39.18 127.43 625 627 276 274 4.50 4.52 1.99 1.97 Pyeong-yang 58 39.03 125.78 546 541 271 274 3.93 3.90 1.95 1.97 Nampo 60 38.72 125.38 793 720 261 266 5.71 5.19 1.88 1.92 Jangjeon 61 38.73 128.18 1166 1176 689 691 8.40 8.47 4.96 4.98 Saliwon 65 38.52 125.77 767 728 325 314 5.53 5.24 2.34 2.26 Singye 67 38.50 126.53 1456 1607 918 928 10.49 11.58 6.61 6.69 Yong-yeon 68 38.15 124.88 898 888 324 325 6.47 6.40 2.33 2.34 Haeju 69 38.03 125.70 676 666 301 303 4.87 4.80 2.17 2.18 Gaeseong 70 37.97 126.57 794 975 435 433 5.72 7.02 3.13 3.12 Pyeong-gang 75 38.42 127.28 1619 1919 1296 1299 11.66 13.83 9.34 9.36 Table S3. MK test results before and after prewhitening test for ET on an annual scale.

MK (before Prewhitening) MK (after Prewhitening) Station Country Confidence Confidence Code Z P-Value β Z P-Value β Level Level Commented [M1]: Please confirm whether the ‘P’ should 100 3.30 0.00 95 1.70 1.87 0.06 90 1.25 be lower case. 101 1.21 0.23 0 0.30 0.84 0.40 0 0.22 Please help correct in the whole paper. 105 1.84 0.07 90 0.72 1.79 0.07 90 0.72 108 2.67 0.01 95 0.98 1.77 0.08 90 0.62 Commented [MGA2R1]: P-value is correct. Thank you. 112 2.10 0.04 95 0.85 1.20 0.23 0 0.55 114 4.41 0.00 95 2.30 2.00 0.05 95 1.03 129 3.02 0.00 95 0.87 1.44 0.15 0 0.36 131 0.57 0.57 0 −0.04 0.10 0.92 0 −0.19 133 3.26 0.00 95 0.90 2.11 0.03 95 0.64 135 1.89 0.06 90 0.60 1.48 0.14 0 0.64 South 136 3.68 0.00 95 1.46 2.44 0.01 95 0.85 Korea 138 0.21 0.83 0 −0.25 −0.10 0.92 0 −0.20 143 −2.43 0.02 95 −1.42 −2.96 0.00 95 −1.43 146 4.30 0.00 95 2.58 1.64 0.10 0 1.00 156 3.16 0.00 95 1.01 2.80 0.01 95 0.89 159 0.24 0.81 0 −0.27 −0.39 0.69 0 −0.20 165 −3.54 0.00 95 −2.70 −1.90 0.06 90 −1.07 169 −1.27 0.20 0 −1.24 −1.05 0.29 0 −0.71 184 2.73 0.01 95 0.70 2.38 0.02 95 0.70 185 4.97 0.00 95 3.69 2.26 0.02 95 1.04 192 −1.39 0.17 0 −1.07 −1.93 0.05 90 −1.16 3 4.80 0.00 95 1.66 3.13 0.00 95 0.82 5 0.98 0.33 0 0.86 1.22 0.22 0 0.38 8 3.01 0.00 95 1.18 2.20 0.03 95 0.52 14 2.15 0.03 95 0.90 0.82 0.41 0 0.12 16 0.94 0.34 0 0.20 0.86 0.39 0 0.13 20 −0.34 0.73 0 −0.14 −0.85 0.39 0 −0.47 22 2.22 0.03 95 2.15 1.14 0.25 0 0.22 25 2.97 0.00 95 1.67 0.93 0.35 0 0.11 28 −0.65 0.51 0 −0.51 −0.83 0.41 0 −0.50 31 −0.16 0.87 0 0.07 −0.34 0.73 0 −0.58 35 0.81 0.42 0 −0.03 0.01 0.99 0 −0.30 37 1.86 0.06 90 0.78 0.52 0.60 0 −0.08 39 −1.73 0.08 90 −0.67 −1.07 0.28 0 −0.59 North 41 −0.08 0.94 0 −0.58 −0.48 0.63 0 −0.64 Korea 46 4.24 0.00 95 2.44 2.03 0.04 95 0.60 50 −1.89 0.06 90 −0.82 −1.83 0.07 90 −0.78 52 2.79 0.01 95 1.97 1.22 0.22 0 0.32 55 3.17 0.00 95 1.74 2.11 0.03 95 0.77 58 4.51 0.00 95 1.86 1.53 0.13 0 0.52 60 1.72 0.08 90 0.42 0.67 0.50 0 0.04 61 1.07 0.29 0 0.14 0.63 0.53 0 −0.04 65 4.24 0.00 95 2.01 1.45 0.15 0 0.58 67 −1.10 0.27 0 −0.50 −0.39 0.69 0 −0.31 68 5.30 0.00 95 2.83 2.79 0.01 95 1.12 69 1.95 0.05 90 0.56 1.57 0.12 0 0.39 70 4.48 0.00 95 1.95 2.16 0.03 95 0.99 75 1.36 0.17 0 0.90 1.38 0.17 0 0.63

Table S4. The results of the MK test before and after the prewhitening test for EN on an annual scale.

MK (before prewhitening) MK (after prewhitening) Station Country Confidence Confidence Code Z P-value β Z P-value β level level 100 4.14 0.00 95 2.88 1.44 0.15 0 0.65 101 4.92 0.00 95 1.28 2.85 0.00 95 0.64 105 2.24 0.03 95 0.42 1.95 0.05 90 0.33 108 3.68 0.00 95 0.90 2.06 0.04 95 0.40 112 3.46 0.00 95 1.64 1.03 0.30 0 0.41 114 5.03 0.00 95 1.42 2.20 0.03 95 0.67 129 0.53 0.60 0 -0.11 0.09 0.93 0 −0.10 131 4.76 0.00 95 2.03 2.66 0.01 95 0.97 133 2.57 0.01 95 0.73 1.74 0.08 90 0.51 135 1.59 0.11 0 0.44 1.17 0.24 0 0.27 South 136 5.07 0.00 95 1.63 2.00 0.05 95 0.73 Korea 138 5.20 0.00 95 2.44 2.50 0.01 95 1.14 143 6.07 0.00 95 2.76 2.23 0.03 95 0.92 146 1.78 0.08 90 0.25 1.36 0.17 0 0.21 156 4.24 0.00 95 1.32 2.28 0.02 95 0.82 159 5.48 0.00 95 1.88 2.40 0.02 95 0.85 165 4.71 0.00 95 1.52 2.10 0.04 95 0.84 169 −2.87 0.00 95 −1.71 −1.49 0.14 0 −0.85 184 5.61 0.00 95 2.37 2.34 0.02 95 0.98 185 −1.51 0.13 0 −1.26 −1.11 0.27 0 −0.39 192 5.15 0.00 95 2.09 2.29 0.02 95 0.54 3 1.94 0.05 90 1.27 0.41 0.68 0 0.02 5 2.81 0.01 95 3.01 2.37 0.02 95 1.25 8 2.37 0.02 95 1.07 1.46 0.15 0 0.63 14 2.60 0.01 95 0.68 0.34 0.73 0 0.03 16 3.42 0.00 95 1.67 1.45 0.15 0 0.46 20 4.62 0.00 95 1.55 1.58 0.11 0 0.50 22 2.19 0.03 95 1.62 2.76 0.01 95 1.45 25 3.73 0.00 95 1.59 1.91 0.06 90 0.40 28 5.79 0.00 95 1.94 1.92 0.06 90 0.61 31 3.09 0.00 95 2.68 2.97 0.00 95 0.98 35 5.38 0.00 95 2.08 1.77 0.08 90 0.49 37 3.48 0.00 95 1.04 1.09 0.28 0 0.42 39 6.66 0.00 95 2.41 2.39 0.02 95 0.77 North 41 5.66 0.00 95 3.14 1.78 0.07 90 0.59 Korea 46 4.76 0.00 95 1.77 1.85 0.06 90 0.55 50 5.29 0.00 95 2.47 2.29 0.02 95 0.51 52 4.16 0.00 95 0.97 1.61 0.11 0 0.60 55 3.57 0.00 95 1.58 2.49 0.01 95 0.93 58 3.76 0.00 95 1.05 2.66 0.01 95 0.67 60 4.46 0.00 95 2.38 1.98 0.05 95 0.62 61 4.77 0.00 95 2.36 2.02 0.04 95 0.73 65 1.94 0.05 90 0.54 1.60 0.11 0 0.32 67 5.33 0.00 95 2.16 2.07 0.04 95 0.62 68 4.53 0.00 95 2.53 0.93 0.35 0 0.09 69 4.24 0.00 95 1.54 1.93 0.05 90 0.48 70 3.78 0.00 95 1.06 2.28 0.02 95 0.61 75 2.37 0.02 95 1.56 2.21 0.03 95 0.62

Table S5. The results of the MK test before and after the prewhitening test for AE on an annual scale

MK (before Prewhitening) MK (after Prewhitening) Station Country Confidence Confidence Code Z P-Value β Z P-Value β Level Level 100 0.03 0.98 0 −0.08 −0.10 0.92 0 0.03 101 −1.35 0.18 0 −0.72 −0.33 0.74 0 −0.22 105 0.43 0.67 0 0.28 0.38 0.70 0 0.02 108 −0.13 0.90 0 0.03 0.46 0.65 0 0.27 112 −2.64 0.01 95 −0.94 −1.23 0.22 0 −0.48 114 0.72 0.47 0 0.61 0.45 0.66 0 0.38 129 2.74 0.01 95 1.32 0.41 0.68 0 0.07 131 −3.24 0.00 95 −2.05 −1.83 0.07 90 −0.92 133 0.40 0.69 0 0.03 −0.27 0.78 0 −0.11 135 1.02 0.31 0 0.21 1.07 0.28 0 0.34 South 136 −1.81 0.07 90 −0.62 0.00 1.00 0 0.07 Korea 138 −4.32 0.00 95 −2.42 −1.74 0.08 90 −0.70 143 −5.36 0.00 95 −4.12 −1.51 0.13 0 −0.53 146 4.03 0.00 95 2.44 0.96 0.34 0 0.39 156 −0.98 0.33 0 −0.27 −1.11 0.27 0 −0.48 159 −3.55 0.00 95 −2.08 −1.49 0.14 0 −0.48 165 −4.21 0.00 95 −4.21 −1.91 0.06 90 −0.99 169 2.00 0.05 95 0.48 1.60 0.11 0 0.50 184 −5.53 0.00 95 −1.66 −1.15 0.25 0 −0.41 185 3.93 0.00 95 4.83 1.18 0.24 0 0.22 192 −4.46 0.00 95 −3.10 −2.83 0.00 95 −0.90 3 1.46 0.14 0 0.43 0.20 0.84 0 −0.02 5 −2.76 0.01 95 −2.28 −1.13 0.26 0 −0.80 8 0.64 0.52 0 0.13 0.98 0.33 0 0.15 14 0.38 0.71 0 0.11 0.98 0.33 0 0.14 16 −2.81 0.01 95 −1.55 −1.94 0.05 90 −0.82 20 −3.57 0.00 95 −1.76 −2.19 0.03 95 −0.74 22 1.56 0.12 0 0.38 0.48 0.63 0 −0.03 25 −0.08 0.94 0 0.14 −0.20 0.84 0 −0.42 28 −4.04 0.00 95 −2.80 −1.82 0.07 90 −0.82 31 −3.88 0.00 95 −3.18 −1.95 0.05 90 −1.21 35 −1.51 0.13 0 −2.10 −0.92 0.36 0 −0.89 37 0.34 0.73 0 0.21 0.14 0.89 0 −0.27 39 −4.26 0.00 95 −3.12 −2.37 0.02 95 −1.59 North 41 −3.15 0.00 95 −3.74 −1.55 0.12 0 −1.50 Korea 46 1.52 0.13 0 0.63 0.09 0.93 0 −0.19 50 −3.83 0.00 95 −2.78 −2.67 0.01 95 −1.18 52 0.65 0.51 0 1.00 0.43 0.67 0 −0.02 55 −0.30 0.76 0 -0.40 −0.86 0.39 0 −0.30 58 2.24 0.03 95 0.93 0.60 0.55 0 0.30 60 −1.91 0.06 90 −2.10 −2.16 0.03 95 −1.16 61 −2.39 0.02 95 −1.92 −1.61 0.11 0 -0.95 65 2.04 0.04 95 1.32 0.14 0.89 0 0.45 67 −3.76 0.00 95 −2.56 −2.03 0.04 95 −0.84 68 1.60 0.11 0 0.63 0.81 0.42 0 0.37 69 −1.52 0.13 0 −0.67 −1.90 0.06 90 −0.62 70 2.01 0.04 95 0.99 1.61 0.11 0 0.88 75 −1.42 0.15 0 −1.11 −0.29 0.77 0 0.08