Because of its nature, lake evaporation (E L ) is rarely measured directly. The most common method used is to apply a pan coefficient (K p ) to the measured pan evaporation (E p ). To reconstruct the long sequence dataset of E p , this study firstly determined the conversion coefficients of E p of two pans (φ20 and E601, each applied to a different range of years) measured synchronously at the nearest meteorological station during the unfrozen period through 1986 to 2001, and then E p was

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... ted by the PenPan model that developed to the Class A pan and applied to quantify the E L of the Juyan Lake, located in the hyper-arid area of northwest China. There was a significantly linear relationship between the E601 and φ20 with the conversion coefficients of 0.60 and 0.61 at daily and monthly time scales, respectively. The annual E p based on monthly conversion coefficients was estimated at 2240.5 mm and decreased by 6.5 mm per year, which was consistent with the declining wind speed (U) during the 60 years from 1957 to 2016. The E p simulated by the PenPan model with the modified net radiation (R n ) had better performance (compared to E p measured by E601) than the original PenPan model, which may be attributed to the overestimated R n under the surface of E601 that was embedded in the soil rather than above the ground similar to the Class A and φ20. The measured monthly E L and E p has a significantly linear relationship during the unfrozen period in 2014 and 2015, but the ratio of E p to E L , i.e., K p varied within the year, with an average of 0.79, and was logarithmically associated with U. The yearly mean E L with full lake area from 2005 to 2015 was 1638.5 mm and 1385.6 mm, calculated by the water budget and the PenPan model with the modified R n , respectively; the latter was comparable to the surface runoff with an average of 1462.9 mm. In conclusion, the PenPan model with the modified R n has good performance in simulating E p of the E601, and by applying varied K p to the model we can improve the estimates of lake evaporation. Water 2017, 9, 952 2 of 16 ecosystems [2, [4] [5] [6] . In order to protect and restore these degraded ecosystems, the Ecological Water Conveyance Project (EWCP) in the arid inland river basin was implemented by China's government in 2000 [7,8]. For the operability of management, the EWCP identified that maintaining a certain size of lake area is an important index of whether this project has succeeded or not [9] . Yet, there has been considerable debate as to whether it is the waste or utilization for the limited water resource [9] [10] [11] . Fundamentally, the question is how much water evaporated from those lakes. Because of the larger area of natural lakes, lake evaporation (E L ) is rarely measured directly. The most common indirect method is to multiply the measured pan evaporation (E p ) by a pan coefficient (K p ). There are many measurements of E p from all over the world. The World Meteorological Organization [12] recommended the reference equipment as follows: the United States Class A pan, the GGI-3000 pan, and the 20 m 2 evaporation tank of the Russian Federation. However, this equipment cannot be found in most meteorological and hydrological stations in China; instead, the φ20 and E601 pan are used during different times and in different districts [13] [14] [15] . The E601, a modified GGI-3000 pan, appears to have consistently good performance when compared to the 20-m 2 evaporation tanks [14] . However, E601 has been used for less time than φ20, which was applied at most meteorological and hydrological stations over the last century in China [13] . Thus, evaporation datasets collected at different times need to be transformed into uniform times in order to determine the long-term trend of E p [15] . Therefore, it is necessary to determine the conversion coefficients between the different types of evaporation pan. In addition to the direct measurement by evaporation pan, models have been widely used to estimate E P [16, 17] . Although the multiple factors affect evaporation at different time scales [16, 18] , it has been demonstrated that the combination methods have better performance than single-variable methods when applied to estimate E P [19] [20] [21] . However, E L is different from E p owing to the wall of the pan intercepts' additional radiation that enhances heat exchange, the pan edge effect that increases wind turbulence, and the oasis effect whereby the air mass of a surrounding area with lower relative humidity crosses a water body's surface and will take away more water vapor [22] . Therefore, in order to estimate the E p precisely, Rotstayn et al. [23] developed a physical model, i.e., the PenPan model, which coupled the radiative component of Linacre [22] and the aerodynamic component of Thom et al. [24]. The PenPan model was applied successfully to estimate monthly and annual E p of the Class A at sites across Australia [25-27] and the USA [28], and the φ20 at sites across China [29-31], but there are almost no studies reported for E601. Another alternative model to estimate E P is reference crop evapotranspiration (ET 0 ) divided by a coefficient (K c ), for which a value of 0.83 was recommended [32]. We undertook a study at Juyan Lake, a typical terminal lake that is located in the lower Heihe River Basin (HRB), in the arid northwest of China [9] . It comprises the East Juyan Lake (also referred to as Sogo Nur, where the study was focused) and West Juyan Lake (also referred to as Gaxun Nur, this dried up in 1961), respectively [33] . It was famous for the discovery of a large number of Juyan bamboo slips of the Han dynasty by Sven Hedin and his partner in 1930 while they mapped the lower HRB, including Juyan Lake. To estimate E L , the E p of the nearest meteorological station has frequently been used [10]; however, previous studies showed drastic differences in E p : some reported more than 3500 mm [7, 34, 35] , but others reported less than 2500 mm [36] [37] [38] . The cause of this discrepancy was the diversity of equipment used at different times. Recently, the measured E L by Liu et al. [10] showed that the yearly E L was 1183.3 mm during the unfrozen period in 2014 and 2015, which suggests an overestimation of E L using the directly measured E p . The objectives of our study were to (1) construct a long-term and good temporal dataset of E p by linking different types of pans through conversion coefficients; (2) identify the most appropriate model to estimate E p ; (3) quantify the magnitude of E L to improve the management of the lake's water resources in the hyper-arid climate, northwest China.