Simulation of Actual Evapotranspiration and Evaluation of Three Complementary Relationships in the Upper Regions of the Mekong River and the Salween River

: Based on observed precipitation and runoff data, monthly actual evapotranspiration ( ET a ) was calculated by the 41 hydrological budget balance method in the Nu River Basin (NRB) and Lancang River Basin (LCRB). The performance 42 of three developed complementary relationship methods, the nonlinear advection-aridity (nonlinear AA) method, 43 generalized complementary relationship method (B2015), and sigmoid generalized complementary function (H2018), on 44 simulating ET a were evaluated. The evaluation results showed that three methods were able to accurately simulate ET a series. The NSE between the monthly ET a simulated by the nonlinear AA, B2015, and H2018 methods 46 and the water-balance-derived ET a were 0.89, 0.83, and 0.91, respectively. The R-square were 0.90, 0.84, and 0.93, 47 respectively. Overall, the H2018 method showed the best performance. The parameter 𝛼 had a negative correlation with 48 regional aridity index. Annual ET a and precipitation showed significant increasing trends during 1956-2018 in the basins 49 at all temporal scales (dry and wet seasons and annual series). Runoff also exhibited an increasing trend in each sub-basin, 50 except for the downstream region of the LCRB. The increasing magnitudes of wet reason precipitation and runoff in the 51 mid-stream region was the highest, with the value of 73.7 mm/10a and 44.9 mm/10a, respectively. The ET a increased 52 dramatically in the downstream region, the magnitude reached 25.9 mm/10a. Precipitation was the main factor leasing to ET a change. The increasing magnitude of ET a accounted for 42.4% of the precipitation increment. Research on the influence mechanism between meteorological factors and a showed that the contribution rate of air temperature to ET a was the highest, reaching 23.5%, which showed a significant positive correlation. The second was wind speed, whose 56 contribution rate was -10.2% on average, and even reached -14.1% in the upstream region of the NRB. The correlation 57 coefficient between and wind speed was highest in mid-stream region of the NRB, which was greater than 0.80. The contribution rates of increasing humidity to ET a were -12.5% and -9.2% in the NRB and LCRB, respectively. ET a was negatively correlated with humidity. The negative correlation was especially strong in the mid-stream region, with 60 coefficients were greater than -0.65. The sunshine hours had the least effect on ET a , and the contribution rates were -6.5% 61 and -4.1%, respectively.


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The manuscript has not been published before and is not being considered for publication elsewhere. We declare that we

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A wide range of studies have investigated the spatiotemporal pattern of ET a at regional scales (Gao et  Because the drop is more than 4,600 m within the channel length about 2,000 km. Therefore, the time of runoff 122 concentration of the basin is short and the velocity of streamflow is high. This would have a great impact on regional ET a .

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The climate in the basins varied significantly from northwest to the southeast due to impacts of topography and latitude.

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The upstream region belongs to a plateau climate. The climate is cold with little precipitation. The runoff in the upper 125 reaches of the river is mainly recharge by groundwater, accounting for more than 50% of the annual runoff, followed by     Kahler and Brutsaert (2006) pointed out that the assumed symmetric nature of the CR becomes asymmetric when used 172 with evaporation pan data. This meant that the change in the apparent potential evaporation, as the environment dries from 173 an initially wet condition, will be larger than the corresponding change in ET a . Therefore, the AA method had since

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Normalized by , the nonlinear AA method can be expressed as a linear function (Han et al. 2008): where and are the radiation and aerodynamic terms for the Penman equation, respectively (mm/day); is psychrometric constant (hPa/°C); is the net radiation near the surface (mm/day); is the soil heat flux; ( ) is the pressure at air temperature (hPa). All these variables are calculated by the method recommended by the Food and where is thought to be zero under usual situations (Brutsaert, 2015). Thus, a fixed = 0 and calibrated parameter of  The performance of the nonlinear AA, B2015 and H2018 methods in simulating monthly ET a in the NRB and LCRB 208 was evaluated by water-balance-derived ET a , in which the optimal model parameters , and −1 are also calibrated.

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The evaluation criteria included the Nash efficiency coefficient (NSE), the square-R (R 2 ), the normalized root mean square 210 error (NRMSE), and the relative error between the modeled ET a and the observed ET a .  of meteorological factors to ET a was the sensitivity coefficient of a single meteorological factor multiplied by the multi-

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year relative change rate of this factor. It could be expressed as follows, where is meteorological factor such as temperature, wind speed, relative humidity, and sunshine hours; is the 220 contribution rate of to the change in ; is the sensitivity coefficient of ; (%) is the multi-year relative 221 change rate of .

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The dimensionless relative sensitivity coefficient proposed by McCuen (1974) where and ∆ are the daily and daily variation, respectively; and and ∆ are the daily meteorological 226 factor values and daily variation, respectively. Under the condition that the variable of a single meteorological factor varies 227 by ± 10%, the sensitivity coefficient of ET a to each meteorological factor was calculated in turn.

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The multi-year relative change rate of meteorological factor was calculated by the following formula, where is the multi-year average value of ; is the annual climate tendency rate of .

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and 0.28 mm, respectively. Overall, the H2018 performed better than the B2015 and nonlinear AA methods.

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The performance of three developed CR methods in simulating wet season ET a was generally similar with that of annual 242 ET a . It showed a relatively poor performance in simulating dry season ET a , with the NSE lower than 0.6 except for 243 nonlinear AA method in LCRB. However, the relative errors were less than 10%, indicating that the methods were able 244 to accurately simulate the average value.

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In general, the developed CR methods were able to simulate ET a with a high accuracy at the annual and wet season scales 246 in the LCRB and NRB. The simulation accuracy of the LCRB was slightly higher than that of the NRB in terms of 247 evaluation criteria. and dry seasons ET a were shown in Fig.2. In general, the frequency of the relative error of developed CR methods 251 exhibited a normal distribution. In term of the frequency distribution of the H2018 method, more than 95.2% of the errors 252 were between -25% and 25%. Among them, the error frequency between -5% and 5% was the highest, with the value of 253 30.1%. The frequency distribution of wet season was consistent with that of annual series. An 85.7% margin of error was 254 between -25% and 25%. The error frequency was the highest between -5% and 5%, with the value of 30.6%.

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The frequency distribution of the relative error of dry season ET a was not consistent with that of wet season. More than

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The error frequency of 19.4% was greater than 50%, which was much higher than that of 2.4% in annual and rainy seasons.

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The relative error was slightly higher in dry season in terms of frequency distribution.

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The frequency distribution of the relative error for nonlinear AA and B2015 were basically the same as those of H2018.

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For example, more than 90% of the errors were between -25% and 25%, and the error frequency was the highest between

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-5% and 5% with the value of 33.3%. However, there were some inconsistencies. For example, the B2015 method had a 262 better simulation effect in dry season. More than 71.4% of the errors distributed between -25% and 25%. The error 263 frequency was the highest between -10% and -5% with the value of 14.3%.   Table 2 showed the trends of precipitation, runoff and ET a in the NRB and LCRB. In terms of precipitation, the increasing

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The increasing magnitude of wet season ET a was 7.1 times that of dry season. This is because dry season ET a accounted 287 for only 13% of the annual ET a . Dry season ET a accounted for the highest proportion of annual increasing magnitude in

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The spatial distribution of ET a was highly consistent with precipitation. The ET a in NRB and LCRB were downstream 318 region > upstream region > mid-stream region. In the LCRB, for example, the annual ET a in the downstream region

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Sunshine hours in the LCRB exhibited significant decreasing trends at all temporal scales (7/9). It only showed an 344 increasing trend at two stations located at the boundary of the downstream region. However, there was a seasonal and 345 regional differences in the NRB. The decreasing sunshine hours were detected at the upstream and mid-stream regions.

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While downstream sites increased slightly. Compared with the dry season sunshine hours, the wet season hours showed 347 an increasing trend with four more observed stations in the upstream and mid-stream regions. The spatial and temporal

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The contribution rate of meteorological factors to ET a was shown in Fig.5

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The correlation coefficients between meteorological factors and ET a in the NRB and LCRB were shown in Fig.6. There  on the complementary relationship of ET a . In this study, the value of the parameter α was negatively correlated with the regional aridity index (AI= /P) in the basins (Fig.7), which was consistent with Liu et al.

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which provides more references and possibilities for the study of regional ET a .

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ET a is directly sourced from soil water, open water, and indirectly from water by vegetation (Balugani et al. 2016

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B2015 and H2018 were evaluated by monthly water-balance-derived values. Impacts of major meteorological factors on 415 ET a were also assessed. The conclusions were as follows,

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(1) All three developed CR methods were able to accurately simulate monthly ET a series. The NSE between the 417 monthly ET a simulated by the nonlinear AA, B2015, and H2018 methods and the water-balance-derived values 418 were 0.89, 0.83, and 0.91, respectively. The R-square were 0.90, 0.84, and 0.93, respectively. The difference between 419 NSE and R-square was highest in dry season ET a , with an average of 0.55 and 0.67, respectively. Overall, the H2018 420 method showed the relatively best performance. The parameter had a negative correlation with the regional 421 aridity index.

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(2) Annual ET a and precipitation showed significant increasing trends during 1956-2018 in the basins at all temporal