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Water 2017, 9(12), 952; doi:10.3390/w9120952
Simulation of Pan Evaporation and Application to Estimate the Evaporation of Juyan Lake, Northwest China under a Hyper-Arid Climate
Alxa Desert Eco-hydrology Experimental Research Station, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou 730000, China
Key Laboratory of Eco-hydrology of Inland River Basin, Chinese Academy of Sciences, Lanzhou 730000, China
Gansu Hydrology and Water Resources Engineering Research Center, Lanzhou 730000, China
Heihe Water Resources and Ecological Protection Research Center, Lanzhou 730000, China
Correspondence: Tel.: +86-931-496-7089
Received: 30 October 2017 / Accepted: 5 December 2017 / Published: 7 December 2017
Because of its nature, lake evaporation (EL) is rarely measured directly. The most common method used is to apply a pan coefficient (Kp) to the measured pan evaporation (Ep). To reconstruct the long sequence dataset of Ep, this study firstly determined the conversion coefficients of Ep 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 Ep was estimated by the PenPan model that developed to the Class A pan and applied to quantify the EL 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 Ep 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 Ep simulated by the PenPan model with the modified net radiation (Rn) had better performance (compared to Ep measured by E601) than the original PenPan model, which may be attributed to the overestimated Rn 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 EL and Ep has a significantly linear relationship during the unfrozen period in 2014 and 2015, but the ratio of Ep to EL, i.e., Kp varied within the year, with an average of 0.79, and was logarithmically associated with U. The yearly mean EL 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 Rn, respectively; the latter was comparable to the surface runoff with an average of 1462.9 mm. In conclusion, the PenPan model with the modified Rn has good performance in simulating Ep of the E601, and by applying varied Kp to the model we can improve the estimates of lake evaporation.
Keywords:pan evaporation; pan coefficient; water budget; lake evaporation; arid area
Lakes are sentinels of climate change and/or human activities [1,2,3]. Over the past several decades, serious environmental degradation has occurred in arid northwest of China, in which the most remarkable event was a vast number of inland lakes drying up and the disappearance of aquatic 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 . 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 (EL) is rarely measured directly. The most common indirect method is to multiply the measured pan evaporation (Ep) by a pan coefficient (Kp). There are many measurements of Ep from all over the world. The World Meteorological Organization  recommended the reference equipment as follows: the United States Class A pan, the GGI-3000 pan, and the 20 m2 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-m2 evaporation tanks . 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 . Thus, evaporation datasets collected at different times need to be transformed into uniform times in order to determine the long-term trend of Ep . 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 EP [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 EP [19,20,21]. However, EL is different from Ep 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 . Therefore, in order to estimate the Ep precisely, Rotstayn et al.  developed a physical model, i.e., the PenPan model, which coupled the radiative component of Linacre  and the aerodynamic component of Thom et al. . The PenPan model was applied successfully to estimate monthly and annual Ep of the Class A at sites across Australia [25,26,27] and the USA , and the φ20 at sites across China [29,30,31], but there are almost no studies reported for E601. Another alternative model to estimate EP is reference crop evapotranspiration (ET0) divided by a coefficient (Kc), for which a value of 0.83 was recommended .
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 . 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 . 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 EL, the Ep of the nearest meteorological station has frequently been used ; however, previous studies showed drastic differences in Ep: 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 EL by Liu et al.  showed that the yearly EL was 1183.3 mm during the unfrozen period in 2014 and 2015, which suggests an overestimation of EL using the directly measured Ep. The objectives of our study were to (1) construct a long-term and good temporal dataset of Ep by linking different types of pans through conversion coefficients; (2) identify the most appropriate model to estimate Ep; (3) quantify the magnitude of EL to improve the management of the lake’s water resources in the hyper-arid climate, northwest China.
2. Study Area
The study area was located at the lower HRB (39°30′–42°30′ N; 99°00′–102°00′ E, 890–1200 m a.s.l.), normally referred to as the Ejin Oasis/Delta owing to the surrounding extensive Badain Jaran and Gobi Deserts, in northwest China (Figure 1). The lower HRB starts at Zhengyixia (ZYX) hydrological station, passes through Ejin Delta, and ends at the Juyan Lake, having a length of 190 km and an area of 30,000 km2 . Geologically, it belongs to the Mongolian Plateau. The southwestern and northern parts of the basin are mainly formed of an alluvial plain and aggraded flood area, while the central basin consists of an alluvial plain and a lake plain. The southeastern part of the basis borders the Badain Jaran Desert . The land type in the basin is similar to that of the Gobi desert except for adjacent rivers and an oasis, distributed along the Heihe River on the alluvial fan (Figure 1).
3.1. Meteorological Data Collection
The Ejin County National Reference Meteorological Station (41°57′ N, 101°04′ E, 940.5 m a.s.l., hereafter referred to the Ejin station) is situated in Dalain Hob, Ejin county, Inner Mongolia, about 40 km from East Juyan Lake (Figure 1). It was established in December 1956. Air temperature (Ta, °C), precipitation (P, mm), relative humidity (RH, %), wind speed (U, m·s−1), actual sunshine duration (Sd, h), and atmospheric pressure (Pa, kPa) have been collected here since 1957. Before 2002, the Ep (mm) was measured by the φ20 (20 cm diameter and 10 cm depth) in the whole year, and after 2002 by the E601 (61 cm diameter and 60 cm depth cylinder plus 8.7 cm depth circular cone) during the unfrozen period between April and October and by the φ20 during the frozen period between November and March of the next year, with a freeze–thaw transition period similar to that of the lake.
To determine the relationship between φ20 and E601, the Ep of two pans was measured synchronously during the unfrozen period from 1986 to 2001. Based on these observations, the daily and monthly φ20 and E601 datasets were used to estimate the conversion coefficient of two pans using the linear regression model following Xiong et al. . After that, the Ep measured by the φ20 before 2002 was recalculated using the conversion coefficient to obtain the long-term Ep of the E601 from 1957 to 2016. The monthly variation of annual averaged P, Ep, Ta, RH and U, collected from the Ejin station, is shown in Figure S1.
3.2. PenPan Model
To estimate the Ep, the PenPan model following Rotstayn et al.  was used:where EPenPan is the calculated Ep (Ep,cal, mm·day−1) for the Class A (unscreened), Δ is the slope of the vapor pressure curve at Ta (kPa·°C−1), γ is the psychrometric constant (kPa·°C−1), ap is a constant adopted as 2.4 , which accounts for the additional energy exchange due to the walls of the pan, and Rn,Pan is the daily net radiation (Rn) at the pan (MJ·m−2·day−1), λ is the latent heat of vaporization (MJ·kg−1), (es − ea) is vapor pressure deficit (kPa), f(u) is the function of U at 2 m height (u2, m·s−1) :
To estimate Rn,Pan, we refer to Rotstayn et al. ; the calculation is also provided in the Supplementary Material 6 of McMahon et al. :where αA is the albedo for a Class A pan given as 0.14 , Rs,Pan is the total shortwave radiation received by the pan (MJ·m−2·day−1), Rs and Rnl are incoming solar radiation and net outgoing long-wave radiation, MJ·m−2·day−1, respectively . fdir is the fraction of Rs that is direct, and was defined as:where Ra is the extra-terrestrial radiation (MJ·m−2·day−1). Prad is a pan radiation factor defined as:where lat is the absolute value of latitude in degrees. The equations to estimate the Δ, γ, λ, (es − ea), Rs, Ra and Rnl was following FAO .
3.3. FAO Penman–Monteith Model
To compare with the PenPan model, the FAO Penman–Monteith model  was applied to calculate the ET0:where G (MJ·m−2·day−1) acted as the heat storage term of water bodies that can be negligible at a daily time scale. The Rn can be calculated aswhere α is the albedo or canopy reflection coefficient, fixed at 0.23 for the standardized reference surface (dimensionless). To compare, the relationship between Rn and Rn,pan is shown in Figure S2. ET0 is an alternative method that applies a Kc (a value of 0.83 was recommended) to estimate Ep following the FAO :
Rn = (1 − α)Rs − Rnl,
ET0 = Kc × Ep.
3.4. Pan Coefficient and Lake Evaporation
Despite the short distance between Juyan Lake and Ejin station (Figure 1), distinct differences between their meteorological variables have been documented previously . To calculate EL, the meteorological variables Ta, RH, and U measured at the Ejin station were first recalculated according to the relationship between the two sites  and Ep was estimated by the selected models. Secondly, the monthly Ep was related to the measured EL (mm·month−1) at the surface of the lake approximately 150 m from the bank during the unfrozen period of 2014 to 2015 by Liu et al. , and a coefficient (Kp) was calculated following Abtew :
Kp = EL/Ep.
Finally, the long-term EL was calculated by applying the Kp to the estimated Ep.
3.5. Water Budget of Lake
In addition to the pan method, a water budget approach can be applied as a simple method to estimate EL [40,41]. Because Juyan Lake is a closed lake and there is no outlet, the water budget for the lake can be written as follows:where ΔS is the change in lake storage (S, m3) and Qs and Qg (m3·day−1) are the surface and ground runoff flow into the lake, respectively. The water budget was applied on an annual time scale to estimate EL.
ΔS = P + Qs + Qg − EL,
The Qs inflow into Juyan Lake was measured by the weir and water level sensor that has been located at the lake inlet since August 2003 (Figure 1). To convert the unit of Qs, m3·day−1 to mm and calculate the ΔS, the lake area (AL, km2) and S was acquired using the relationship between lake elevation and AL and S developed by the Wuhai Hydrographic and Water Resources Survey Bureau in 2003 (Figure S3). The lake elevation has been measured at 10-day intervals since 2002 at the northeast of Juyan Lake. The maximum lake elevation was about 903.5 m and the maximum area was 42.7 km2 in 2011. The temporal variation of 10-day measurements of S, AL, ΔS, and Qs was used to calculate EL for Juyan Lake from 2002 to 2015, as shown in Figure S4.
3.6. Assessments of Model Performance
Many statistical methods, including adjusted coefficient of determination (Radj2) and root mean square error (RMSE), are used to assess Ep model performance.where Xi is measured daily or monthly Ep, Yi is estimated daily or monthly Ep, and are mean of measured and estimated Ep, respectively. The RMSE was computed as follows:
Regardless of the method used to compute the standard errors, the confidence intervals are computed using the following formula:where is the best-fit value for parameter b, n is the number of observations, p is the number of parameters, is the standard error of , and ta,n−p is the 100(1 − a/2)th percentile of the t-distribution with n − p degrees of freedom. The value a is chosen so the confidence level is 100(1 − a)%. One can actually compute these statistical methods and confidence intervals in SigmaPlot (Systat Software, Inc., San Jose, CA, USA).
4.1. Pan Evaporation of Two Types of Evaporator
During the unfrozen period from 1986 to 2001, the daily Ep measured synchronously by E601 and φ20 was ranged from 0.4 to 20.1 mm·day−1 and 0.6 to 31.0 mm·day−1 (Figure 2a), with an average of 9.0 mm·day−1 and 13.9 mm·day−1, respectively. The monthly Ep ranged from 27.9 to 361.2 mm·month−1 and 41.8 to 625.9 mm·month−1(Figure 2b), with an average of 266.7 mm·month−1 and 413.8 mm·month−1, respectively. Whether at a daily or monthly time scale, there was a significant linear relationship between E601 and φ20 with a slope of 0.60 and 0.61 (referring to the conversion coefficients, Cp), respectively; there was less scatter at the monthly than the daily time scale within the 95% prediction band (Figure 2), which suggested that the monthly Cp may be better for reconstructing the long-term series of Ep.
Based on the estimated monthly Cp (E601/φ20 = 0.61), the Ep from 1957 to 2001 measured by φ20 was converted to the E601 during the unfrozen period by multiplied by the Cp and adding the φ20 during the frozen period, and, along with the Ep measured by E601 from 2002 to 2016, the long-term Ep dataset by E601 over the past 60 years from 1957 to 2016 was established. The monthly variation of Ep and other climatic variables at Ejin station from 1957 to 2016 is summarized in Table 1. Based on the records, the annual Ep (E601) is 2240.5 mm, a figure that is greater than P (37.5 mm) by a factor of 60 (i.e., the aridity index equal to 0.02). The mean, maximum, and minimum annual Ta are 8.9 °C, 17.0 °C and −9.5 °C, respectively. The mean annual U is 3.2 m·s−1 with a relatively high value in the spring. The lowest RH occurred in May with an average of 33.9%, which is the opposite of the variation of U (Figure S1). The mean annual Sd ranged from 3000 h to 3600 h, with an average of 3382 h.
4.2. Pan Evaporation Calculated by the Two Models
The relationship between the Ep observed by the evaporation pan (E601 and φ20) and calculated by the original PenPan model and modified PenPan model with the Rn recomputed following the FAO at daily and monthly time scale is shown in Figure 3 and Figure 4, respectively. Whether at a daily or monthly scale, the Ep calculated by the original PenPan model was overestimated compared to the E601 (Figure 3a and Figure 4a), but underestimated compared to the φ20 (Figure 3c and Figure 4c). The calculated Ep by the modified PenPan model showed very good consistency with the Ep measured by the E601 for both of daily (Figure 3b) and monthly time scales (Figure 4b), but underestimated the Ep by the φ20 (Figure 3d and Figure 4d). In addition, whether for the original or modified PenPan model, the calculated Ep was closer to the fitting line for the φ20 (Figure 3b,d and Figure 4b,d) than for the E601 (Figure 3a,c and Figure 4a,c), which was also supported by the higher Radj2 and lower RMSE for the former than the later. The scattered points were identified, focusing on the transition between the frozen and unfrozen periods, i.e., April and October (Figure 4). Similarly, Ep calculated by the FAO Penman–Monteith model was also consistent with the Ep measured by the E601 (Figure 5a), but obviously underestimated the Ep measured by the φ20 (Figure 5b). Compared to the two models, the Rn calculated by the original PenPan model was higher than by the Penman–Monteith model (Figure S2). In summary, the results suggested that the Ep calculated by the modified PenPan model has a better performance than the original PenPan and Penman–Monteith model.
Based on the above, the reconstructed dataset of Ep measured by the E601 and calculated by the modified PenPan model, its radiative and aerodynamic components, and associated meteorological variables VPD and U from 1957 to 2016 are shown in Figure 6. There is an obvious declining trend of Ep, with a rate of −6.5 mm·year−1. There are four distinct phases (highlighted by the vertical dotted lines in Figure 6): (1) increase in Ep from 1957 to 1972, at a rate of 19.0 mm·year−1; (2) decline from 1973 to 1991, at a rate of −27.5 mm·year−1; (3) another increase from 1992 to 2009, at a rate of 24.4 mm year−1; and (4) decrease in Ep at a rate of −46.4 mm·year−1 during recent years. The oscillation period is roughly 18 to 20 years (Figure 6a). The yearly variations of Ep were more closely associated with the aerodynamic rather than the radiative component (Figure 6b). Specifically, the variation in Ep was consistent with U (with a linear relationship (Radj2 = 0.63, p < 0.001)) rather than with VPD (Figure 6c). On the whole, the U, VPD, calculated Ep, and its two components lagged behind the Ep of the E601.
4.3. Lake Water Budget and Evaporation
The monthly water budget of Juyan Lake during the unfrozen period between 2014 and 2015 is shown in Table 2. Because the water allocation to the lower HRB was mainly focused in the summer (July) and autumn (September), Qs and ΔS increased at the same time; inversely, ΔS decreased when there was no surface flow. The EL of the two assessment years was approximately equivalent owing to the same lake (e.g., AL) and meteorological (e.g., Ta, RH, and U) conditions, but the ratio of EL to Qs for 2015 (1.6) was twice as high as for 2014 (0.8). The Kp initially decreased and then increased with an average of 0.79 for both years, which was opposite to the variation of Ep. The calculated Qg was associated with Qs, i.e., discharge from the groundwater with surface flow and recharged into the groundwater without surface flow, and it was positive in 2014 but almost balanced in 2015, which suggests that Qg can be neglected in the water budget at a yearly time scale.
There is a significant linear relationship (t-test, p < 0.001) between the measured monthly EL and Ep during the unfrozen period, but the slope was less than 1 and the intercept was non-zero (Figure 7a), suggesting that Kp cannot be directly applied to calculate EL by multiplying Ep. In fact, Kp varied within the year (Table 2), and was associated with U (Figure 7b). The yearly EL from 2005 to 2015 with full lake area calculated by the water budget and the modified PenPan model ranged from 1380.5 mm to 2135.7 mm and 1206.5 mm to 1462.1 mm with an average of 1638.5 mm and 1385.6 mm, respectively (Table 3). The Qs ranged from 309.0 mm to 2364.5 mm with an average of 1462.9 mm, which was comparable to the EL estimated by the modified PenPan model. In addition, the EL calculated by the modified PenPan model was consistent with the measured EL in 2014 and 2015. The yearly EL calculated by the water budget varied more drastically than that calculated by the modified PenPan model, especially when high surface runoff was observed (Figure 8).
5.1. Pan Evaporation
For a long time, Ep has been used to gauge the evaporative demand of the atmosphere for various practical applications [27,32]. Fu et al.  compared Ep from numerous evaporation tanks and pans and concluded that the yearly Ep from a 100-m2 evaporation tank has a distinct relationship to that of a 20-m2 tank, which was about 0.99, 0.87, and 0.60 times that of the E601, Class A, and φ20, respectively. The results suggested that Ep measured by the E601 was a better approach to measuring potential evaporation than φ20. Given that, we thought the potential evaporation might be overestimated by the φ20, in which a conversion coefficient, Cp, is needed for long-term trend estimation. The monthly Cp between the E601 and φ20 (0.61, Figure 2) was comparable with that in the central region of Northern China (0.61) , where the study site was located for the short-term dataset. Based on the monthly Cp, the annual mean Ep (E601) was 2240.5 mm from 1957 to 2016, which was far less than the 3500 mm from 1957 to 2001 measured by the φ20 [7,34,35]. In addition, Ep estimated by the modified PenPan model (Figure 3 and Figure 4) and Penman–Monteith model (Figure 5) has a closer fit to the E601 than to the φ20, which suggests that the Ep measured by the E601 better represents the potential evaporation.
Because lake evaporation is different from the Ep , models developed for the lake evaporation are not always applicable [16,20,21]. Thus, some researchers are devoted to developing special Ep models, among which the PenPan model [22,23] was confirmed as providing better performance across Australia and the USA for Class A [25,26,28] and China for the φ20 [29,30,31]. Our results show that the PenPan model developed for Class A [22,23] overestimated the E601, but underestimated the φ20 (Figure 3 and Figure 4). We thought this inconsistency was caused by the difference in estimation of Rn (Figure S2), which is the driving force of lake evaporation and a key input variable to Penman-type combination equations . The consistent performance of Ep calculated by the FAO Penman–Monteith model further confirms that the Rn following the FAO was better (Figure 5). In contrast to the Class A and φ20, the E601 was embedded into the soil with its rim 30 cm above the ground and surrounded by four arc water troughs 20 cm in width that reduce the edge effects of turbulence generated by the rim of the pan [14,43]. Thus we thought the Rn above the surface of the E601 was overestimated. Irmak et al.  evaluated the performance of Rn estimation methods for ET0 and reported that the FAO Penman–Monteith model (similar to Model 6) performed well against the ASCE-EWRI Rn estimating method. Therefore, we thought the better performance at estimating the Ep of the E601 by the modified PenPan model than the original PenPan and Penman–Monteith models could be attributed to the appropriate estimation of Rn above the surface of the E601.
Despite variable trends in Ep all over the world over the past 50 years , a decline in Ep from the 1950s to the early 1990s has been acknowledged in the arid northwest of China [13,29,45]; however, the decreased rate of Ep measured by the E601 (−11.7 mm·year−1, 1958–1991) was higher than the mean of the northwest (−6.0 mm·year−1) measured by the φ20 . Similarly, the increased rate of Ep (24.4 mm·year−1, 1992–2009) was higher than the mean for the northwest (10.7 mm·year−1) . While potential explanations for the decreased trends in Ep are diverse , our results support the conclusion that the decreased Ep was mainly induced by the weakening U [26,29,30]. This site-specific decrease in U was also confirmed at the larger spatial scale across China [46,47].
5.2. Lake Evaporation
Because of its nature, EL is rarely measured directly, except at relatively small spatial and temporal scales . Hence, the most common approach used by hydrologists or meteorologists is to apply a Kp to the measured Ep [27,40,49]. Although numerous values of Kp have been reported in the literature [32,40], most apply to Class A [20,41]. Because of the similarity of conversion coefficients of the E601 and Class A to the 20-m2 evaporation tank , our Kp value (0.79) of the E601 (Table 2) was comparable with Class A. For example, for the second-largest completely contained freshwater lake, Lake Okeechobee in Florida, USA, Abtew  report monthly Kp values from 0.64 to 0.91, with an average of 0.76. For a semi-arid region like India, Ali et al.  reported yearly Kp values ranged from 0.65 to 0.73 with an average of 0.69. However, the fact that Kp varied seasonally (Table 2) suggests that applying a constant Kp to estimate EL will induce large errors. It is interesting that the Kp was related to the U (Figure 7). Even though it had poor performance with a Radj2 of 0.42, it provided a way to calculate the KP for the long term without assuming it is constant.
The yearly EL from 2005 to 2015 with the full lake area was 1638.5 mm and 1385.6 mm, calculated by the water budget and the modified PenPan model with the variable Kp estimated by the U, respectively, i.e., the lake evaporation calculated by the modified PenPan model with the variable Kp was less than that calculated by the water budget without considering the ground runoff. The reasons for this inconsistency are: (1) the KP can vary depending on the local environment of the pan, including pan operations or management , suggesting that a simple empirical relationship (Figure 7b) was insufficient to estimate EL; (2) the dynamic change of discharge and recharge to the groundwater may be enormous and non-ignorable, and has a large influence on the water budget of a small lake in arid and semi-arid land. Both of these reasons require further exploration.
Our study has confirmed that the PenPan model, which was developed for Class A, overestimated the Ep measured by the E601, which attribute to the overestimation of Rn. The modified PenPan model with the Rn calculated following the FAO has a better performance compared to the Ep measured by the E601. The EL calculated by the modified PenPan model with the variable Kp was less than that calculated by the water budget method without considering the ground runoff, but consistent with the EL measured in the short term. In summary, the linking of best pan evaporation and the best model can improve the estimation of lake evaporation and therefore water management.
The following are available online at www.mdpi.com/2073-4441/9/12/952/s1, Figure S1: The monthly variation in mean annual meteorological variables included precipitation (P, mm), pan evaporation (Ep, mm), air temperature (Ta, °C), relative humidity (RH, %) and wind speed (U, m·s−1), Figure S2: The relationship between net radiation (Rn, MJ·m−2·day−1) calculated by the Penman–Monteith model (Equation (8)) and Rn of pan (Rn, Pan, MJ·m−2·day−1) calculated by the original PenPan model (Equations (3)–(6)) from 1957 to 2016, Figure S3: The relationship between lake elevation (m) and area (AL, km2) and storage (S, million m3) of Juyan Lake, as surveyed by the Wuhai Hydrographic and Water Resources Survey Bureau, Inner Mongolia, China, in 2003, Figure S4: The time series of ten-days measured (a) lake storage (S, mm) and area (AL, km2), (b) change of S (mm) and surface runoff (Qs, mm) for Juyan Lake, and (c) observed pan evaporation (Ep, mm) by the E601 (Obs) and calculated by the modified PenPan model (Cal) from 2002 to 2015.
This study was supported by the Key Research Program of Frontier Sciences, CAS (QYZDJ-SSW-DQC031), National Key R&D Program of China (2017YFC0404305), Youth Foundation of the National Natural Science Foundation of China (41401033) and the Chinese Postdoctoral Science Foundation (2014M560819). Thanks to Elizabeth A. Pinkard for her review of the paper. The authors would also like to thank the two anonymous reviewers for their constructive and valuable comments, which helped to improve this article.
Teng-Fei Yu, Jian-Hua Si, Qi Feng, and Yong-Wei Chu conceived and designed the experiments; Teng-Fei Yu, Hai-Yang Xi, and Kai Li analyzed the data; Teng-Fei Yu wrote the paper.
Conflicts of Interest
The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.
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Figure 1. The schematic diagram of the Heihe River Basin, hydrological (Zhengyixia, ZYX; Shaomaying, SMY; Langxinshan, LXS; East Juyan, EJY) and meteorological station (Ejin station that located at Dalain Hob, Ejin County), the Juyan Lake and land coverage surrounding the lake.
Figure 2. Relationship between pan evaporation of φ20 (Ep_φ20) and E601 (Ep_E601): (a) Daily (mm·day−1); (b) Monthly (mm·month−1) time scale for Ejin station during the unfrozen period from 1986 to 2001. The linear fitting, 95% confidence band, prediction band line, and value of regression analysis are shown.
Figure 3. Relationship between daily observed pan evaporation (Ep,obs) by the E601 (a,b) and φ20 (c,d) and calculated pan evaporation by the original (a,c) and modified (b,d) PenPan model (Ep,cal) for Ejin station during the unfrozen period from 1986 to 2001. The linear fitting, 95% confidence band, prediction band line, and value of regression analysis are shown.
Figure 4. Relationship between monthly observed pan evaporation (Ep,obs) by the E601 (a,b) and φ20 (c,d) and calculated pan evaporation by the original (a,c) and modified (b,d) PenPan model (Ep,cal) for Ejin station during the unfrozen period from 1986 to 2001. The symbol size represents the different month: maximum for October, minimum for April, and middle for the other months. The linear fitting, 95% confidence band, prediction band line, and value of regression analysis are shown.
Figure 5. Relationship between daily pan evaporation of (a) E601 (Ep_E601) and (b) φ20 (Ep_φ20) and calculated reference crop evapotranspiration (ET0) by the FAO Penman–Monteith equation for the Ejin station during the unfrozen period from 1986 to 2001. The linear fitting, 95% confidence band, prediction band line, and value of regression analysis are shown.
Figure 6. The reconstructed time series of (a) the observed pan evaporation (Ep, mm) by the E601 and calculated Ep by the modified PenPan model, and (b) its two components: radiative (Ep,Radi) and aerodynamic (Ep,Aero), and (c) associated meteorological variables include the vapor pressure deficit (VPD, kPa) and wind speed (U, m·s−1) for the Ejin station from 1957 to 2016. The trend line (solid) of the observed Ep by the E601 with distinctively different periods is shown in (a). The vertical (dotted) lines are the transition period of the observed Ep.
Figure 7. Relationship between (a) measured monthly lake evaporation (EL, mm·month−1) and observed pan evaporation (Ep, mm·month−1) and (b) pan coefficient (Kp = Ep/EL) and wind speed (U, m·s−1) during the unfrozen period in 2014 and 2015. The data can be found in Table 2. The linear fitting, 95% confidence band, prediction band line, and value of regression analysis are shown.
Figure 8. The yearly change of lake evaporation (EL, mm) calculated by the water budget method (Wb) without considering the ground runoff and by the modified PenPan model (Cal) and observed EL (Obs, 2014 and 2015) and surface runoff (Qs, mm). The mean of EL (straight line) calculated by the modified PenPan model is also shown.
Table 1. Monthly change of climatic variables included the mean (Tmean, °C), maximum (Tmax, °C), minimum (Tmin, °C) of air temperature, precipitation (P, mm), relative humidity (RH, %), sunshine duration (Sd, h), wind speed (U, m s−1), and pan evaporation (Ep, mm) at Ejin station over the past 60 years (1957–2016).
Table 2. The water budget of Juyan Lake and corresponding lake and meteorological conditions during the unfrozen period in 2014 and 2015. The surface runoff (Qs, mm), precipitation (P, mm), lake evaporation (EL, mm), and water storage change (ΔS, mm) were directly measured and ground runoff (Qg, mm) was calculated as a residue of the water budget. Mean of lake area (AL, km2), air temperature (Ta, °C), relative humidity (RH, %), wind speed (U, m·s−1), pan evaporation (Ep, mm), and the coefficient (Kp) of Ep to EL are also given.
Note: 1 Data are cited from Liu and Yu , and the value for April 2014 was calculated as the product of evaporation in May and the proportion of April to May in 2015.
Table 3. The yearly water budget of Lake Juyan with full water area from 2005 to 2015. The surface runoff (Qs, mm), precipitation (P, mm), change of storage (ΔS, mm), and estimated lake evaporation by water budget (Eb, mm, equal to Qs + P − ΔS), pan evaporation (Ep, mm), coefficient (KL) of Eb to Ep, and calculated lake evaporation (EL, mm) by the variable Kp are shown.
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