Factors controlling the latent and sensible heat fluxes over Erhai Lake under different atmospheric surface layer stability conditions

MENG Xioni, LIU Huizhi, DU Qun, LIU Yng nd XU Lujun

aState Key Laboratory of Atmospheric Boundary Layer Physics and Atmospheric Chemistry, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China; bCollege of Earth and Planetary Science, University of Chinese Academy of Science, Beijing, China

ABSTRACT The stratification of the atmospheric surface layer (ASL) plays an important role in regulating the water vapor and heat exchange across the lake–air interface. Based on one year of data measured by the eddy covariance technique over Erhai Lake in 2015, the ASL stability (ζ) was divided into six ranges, including unstable (- 1 ≤ ζ ＜- 0.1), weakly unstable (- 0.1 ≤ ζ ＜- 0.01), near-neutral1(- 0.01 ≤ ζ ＜0), near-neutral2 (0 ≤ ζ ＜0.01), weakly stable (0.01 ≤ ζ ＜0.1), and stable(0.1 ≤ ζ ＜1). The characteristics of ASL stability conditions and factors controlling the latent (LE)and sensible heat (H) fluxes under different stability conditions were analyzed in this study. The stability conditions of Erhai Lake have noticeably seasonal and diurnal variation, with the nearneutral and (weakly) stable stratification usually occurring before July, with frequencies of 51.7%and 23.3%, respectively, but most of the (weakly) unstable stratification was observed after July,with a frequency of 59.8%. Large evaporation occurred even in stable atmospheric conditions, due to the coupled effects of the relatively larger lake–air vapor pressure difference and wind speed.The relative controls of LE and H by different atmospheric variables are largely dependent on the stability conditions. In stable and unstable ranges, LE is closely correlated with the vapor pressure difference, whereas in weakly unstable to weakly stable ranges, it is primarily controlled by wind speed. H is related to wind speed and the lake–air temperature difference under stable conditions,but shows no obvious relationship under unstable conditions.

KEYWORDS Atmospheric surface layer stability; eddy covariance;Erhai Lake; latent and sensible heat fluxes

1. Introduction

Lakes and reservoirs cover more than 4% of the global land surface area, and even more in the Northern Hemisphere (Downing et al. 2006), and play an important role in affecting the local and regional climate through turbulent exchange of heat and water vapor between the water and the overlying atmosphere(Rouse et al. 2005; Long et al. 2007). In recent times,the surface fluxes of latent (LE) and sensible (H) heat and their controlling factors have attracted more attention on inland water bodies owing to the development of direct measurements by the eddy covariance (EC)technique (Blanken et al. 2000; Liu et al. 2009; Lee et al.2014). However, the dynamics and drivers of surface exchange processes at the water–air interface vary on temporal and spatial scales, due to the difference in lake morphology, geographic condition, and weather and climatic background (Du et al. 2018a; Woolway et al.2018). More understanding on the dynamics and physical control factors of turbulent exchange processes between the lake and the atmosphere under climate change is much needed, which will help improve the parameterization of lake–atmosphere interaction in numerical models (Dutra et al. 2010).

Many researchers have pointed out that wind speed and the vertical gradient of temperature and humidity are critical factors for diurnal variations of LE and H at the water–air interface (Liu et al. 2009; Nordbo et al. 2011;Shao et al. 2015). A positive temperature gradient (lake surface temperature exceeds air temperature) is typically related to unstable stratification in the atmospheric surface layer (ASL), which can promote heat and water vapor transfer from the lake surface to the atmosphere (Verburg and Antenucci 2010). The stability condition of the ASL is closely related to the thermodynamic processes between the lake surface and the atmosphere, and thereby affects the surface energy exchange (Woolway et al. 2017). These drivers mentioned above can be parameterized by the bulk transfer relation, which is commonly used in numerical models for predicting LE and H.

The different properties of the overlying air mass under different ASL stratification play an important role in the water–air turbulent energy exchange process. The contribution of the entrainment process induced by downward cold and dry air to heat and water vapor fluxes is enhanced as the atmospheric condition changes from unstable to neutral (Gao et al. 2018). High wind speeds contribute to an increase in LE and H at the air–sea interface under unstable but very-close-to-neutral stratification, due to the downdrafts of cold and dry air caused by detached eddies (Andersson et al. 2019). Similar results have also been observed in lake studies insofar as large LE and H tend to be concentrated in weakly unstable to neutral stratification (Li et al. 2015; Yusup and Liu 2016).However, increased lake evaporation has been observed even under stable atmospheric conditions due to the mixing of downward warm and dry air, although turbulent mixing was depressed in this situation (Blanken, Rouse,and Schertzer 2003). As the stability represents the mixed contributions of mechanical and thermal convection to turbulence in the ASL, the role of other atmospheric variables (wind speed, vapor pressure difference, and temperature difference) in controlling the water vapor and heat exchange across the lake–atmosphere interface under different stability conditions needs further analysis.

Since the stability condition of lakes is dependent on lake size, latitude, and weather patterns (Woolway et al. 2017), the effects of stability on LE and H need to be investigated at site scale to provide a more comprehensive understanding of the parameterization of turbulent exchange over lake surfaces in numerical models. Erhai Lake is a highland open freshwater lake(25.46°N, 100.10°E) located at the southeastern margin of the Tibetan Plateau, with an altitude of 1978 m.Due to the low latitude and the associated small temperature difference between the lake surface and the atmosphere, the stability condition of Erhai Lake may be different from those lakes in mid- to highlatitude areas. The variability and driving force of surface energy exchange under different ASL stratification in low-latitude highland lakes remains unclear. On the basis of one year of EC measurement data at Erhai Lake in 2015, this study aims to (1) discuss the characteristics of ASL stratification over Erhai Lake; (2)analyze the variations of LE and H with ASL stability;and (3) investigate the factors controlling LE and H under different ASL stability conditions.

2. Measurements and data processing

2.1 Site description and instruments

The measurement site was located on the west side of Erhai Lake (Figure 1). The lake lies in a narrow valley stretching from north to south, with the Cangshan Mountains on the west and Yu’an Mountains to the east. It covers an area of 256.5 km2, with a south-tonorth length of about 40.5 km and an east-to-west length of about 3–9 km. The average and maximum water depth are 10 m and 20.7 m, respectively. The western shore of Erhai Lake is surrounded by villages and cropland. This region has a subtropical plateau monsoon climate, with a warm–wet season from May to October and a cold–dry season from November to April of the next year. The average annual temperature and precipitation in this region are 15.06°C and 1055 mm, respectively. The lake water is ice-free throughout the year. There are 117 rivers and streams flowing into the lake, but only one natural outlet (Xi’er River). The lake water is usually mixed most of the time,with no obvious thermal stratification (Feng et al. 2015).The EC system was installed on a concrete measurement platform approximately 70 m away from the western lake shore. The EC instruments were mounted at 2 m above the platform, including a three-dimensional sonic anemometer (CSAT3, Campbell Scientific) and an openpath infrared gas analyzer (IRGA, LI-7500, LI-COR). The sampling frequency of the EC instruments was 10 Hz.Sensors measured radiation, air temperature, relative humidity, wind speed/direction, and the water temperature profile every minute, recorded as 30-min-averaged values. More information about the measurement site and instruments can be found in our previous study (Liu et al. 2015).

2.2 Data processing and quality control

One year of EC measurement data at Erhai Lake in 2015 were analyzed in this study. The raw high-frequency(10 Hz) data were processed into 30-min mean fluxes using the EddyPro software, V.6.1 (LI-COR, Inc. 2015).Latent and sensible heat fluxes were calculated from 30-min mean covariances between the scalars and the vertical wind speed component. Since detailed information on the data post-processing procedures used in this study have already been documented in our previous study (Liu et al. 2015), only the quality control procedures are introduced here. The 0-1-2 flag system suggested by Foken et al. (2004) was applied to control the quality of the 30-min fluxes. The data points with flag = 2 were removed in this study. According to the footprint analysis described in Du et al. (2018a), the 90% cumulative footprint distances in the western direction are 177 m and 230 m under unstable and stable conditions, respectively. As the measurement site was close to the western shore of the lake(with a distance of 70 m), the fluxes from the western direction (225°– 315°) were also removed to eliminate the influence of the surrounding land areas.

The ASL stability (ζ) is quantified by a dimensionless parameter ζ = z/L, where z is the measurement height and L is the Monin–Obukhov length calculated as

Here, u*is the frictional velocity (m s-1); k is the von Karman constant (0.4), g is gravitational acceleration(9.8 m s-2), θ is the potential temperature (K), andis the vertical kinematic heat flux (K m s-1). The u*andcan be measured directly by the EC system. Other meteorological variables, including wind speed (U), temperature difference (ΔT, ΔT = Ts- Ta,°C), and vapor pressure difference (Δe, Δe = es- ea, kPa) were also analyzed. Tsand Taare the water surface temperature and air temperature, respectively. Tsis derived from longwave radiation. esand eaare the saturated vapor pressure at Tsand the vapor pressure at Ta, respectively.

In order to investigate the driving factors of LE and H under different stability conditions, we divided the stability (ζ) into six stability ranges. Data points with ζ ＞1 and ζ ＜- 1 were removed because there were not enough data (fewer than 20) in these two stability ranges. After the filtering processes mentioned above, about 62.5% of LE and 69.8% of H were available for further analysis. The six stability ranges were set as follows: unstable(- 1 ≤ ζ ＜- 0.1, n1= 1044, n2= 1078), weakly unstable(- 0.1 ≤ ζ ＜- 0.01, n1= 4059, n2= 4591), near-neutral1(- 0.01 ≤ ζ ＜0, n1= 1642, n2= 2068), near-neutral2(0 ≤ ζ ＜0.01, n1= 2177, n2= 2446), weakly stable(0.01 ≤ ζ ＜0.1, n1= 1864, n2= 1875), and stable(0.1 ≤ ζ ＜1, n1= 168, n2= 179), where n1and n2are the numbers of valid data points for LE and H, respectively.

3. Results and discussion

3.1 Characteristics of ASL stability conditions

The ASL stability conditions over Erhai Lake have obvious seasonal and diurnal variations. In terms of seasonal variation (Figure 2(a)), weakly stable (0.01 ≤ ζ ＜0.1) and stable(0.1 ≤ ζ ＜1) stratification usually occurred before July,with a total frequency of 23.3%, but rarely occurred after July (9.8%). Conversely, most of the weakly unstable(- 0.1 ≤ ζ ＜- 0.01) and unstable (- 1 ≤ ζ ＜- 0.1)stratification occurred after July, with a total frequency of 59.8%, while it was less common from March to June,especially for unstable ranges, with a frequency of ＜4%.Such seasonal variations of ASL stability over Erhai Lake are mainly caused by the variation of ΔT, where positive ΔT(water surface temperature Tsexceeds air temperature Ta)is usually related to unstable atmospheric conditions. The ΔT was mostly negative during January to June and became positive after June (not shown), which contributed to the occurrence of (weakly) stable stratification during January to June and (weakly) unstable stratification after June. The near-neutral (- 0.01 ≤ ζ ＜0.01) stratification mostly appeared during January to June, with a frequency of 51.7%. A high frequency of near-neutral stratification is related to the large cloud amount in this area and the relatively small temperature difference between the lake surface and the atmosphere (Du et al. 2018b). The diurnal variations of stability over Erhai Lake show two different patterns by month. As shown in Figure 2(b), ASL stratifications were stable in the afternoon during 1300 BJT (Beijing Time, one hour sssearlier than local time) to 1600 BJT and near-neutral during the rest of the day from March to June.The stratifications became unstable in daytime and nearneutral at nighttime after July, and the strongest unstable condition occurred during morning hours to midday. Such diurnal variation of stable stratification in late-afternoon and strong unstable stratification in the early morning was also found in a temperate reservoir, but seasonal variation of the ASL stability was not observed (Liu, Zhang, and Dowler 2012). In a tropical great lake (Lake Tanganyika) and a large high-altitude lake (Lake Ngoring), a persistent unstable ASL existed during the observation period (Li et al. 2016; Verburg and Antenucci 2010). This persistent unstable ASL was also found in a small lake on the Tibetan Plateau (Wang et al. 2017).

Figure 2.(a) Frequency percentage of six stability ranges in each month during 2015, and (b) monthly average diurnal patterns of the stability parameter (ζ) in 2015 according to the half-hourly measurement data.

3.2 Variations of latent and sensible heat fluxes with stability conditions

Figure 3 shows the variations of LE, H, and meteorological variables with atmospheric stability conditions.Under unstable conditions, U and frictional velocity (u*)increased from the unstable ( - 1 ≤ ζ ＜- 0.1) to nearneutral1 (- 0.01 ≤ ζ ＜0) range, leading to an increase in UΔe and LE with the weakening instability, although Δe decreased at the same time. The increase in LE can be mainly attributed to the enhanced wind speed and mechanical turbulent mixing (described by u*) when the stratification shifts towards near-neutral. Thus, Δe and stability seem to have a minor influence on the variation of LE under unstable conditions. Such an increasing trend of LE with weakening instability under unstable conditions has also been observed in other lakes of different size and latitude (Li et al. 2015; Wang et al. 2017; Yusup and Liu 2016). The maximum LE usually occurred under weakly unstable to near-neutral stratification, rather than under strong unstable stratification. Under stable conditions, U dropped from the near-neutral2 (0 ≤ ζ ＜0.01) to stable (0.1 ≤ ζ ＜1)range; and conversely, Δe started to increase, causing a slight decrease in UΔe but a slight increase in LE. Large evaporation still occurred under stable stratification.Meanwhile, the average value of LE was observed to be greater under stable conditions (ζ ＞0, 94.8 W m-2) than under unstable conditions (ζ ＜0, 82.4 W m-2), as was also the case for U and Δe (stable: 3.1 m s-1, 1.1 kPa;unstable: 2.5 m s-1, 0.8 kPa). The combination of a relatively larger lake–air vapor pressure difference and wind speed resulted in large evaporation under stable atmospheric conditions. A similar result was also found in a small boreal lake in Sweden (Heikinheimo et al. 1999).

The variation of H with stability conditions was closely related to ΔT. H decreased with weakening instability under unstable conditions, due to the depressed thermal convection by a decline in ΔT. When the atmospheric condition turned stable, H became negative such that energy was transferred from the atmosphere to the lake surface. Under stable conditions, decreased U and - ΔT contributed to the slightly reduced heat transfer as the ASL changed from near-neutral2 (0 ≤ ζ ＜0.01) to stable(0.1 ≤ ζ ＜1). The mean values of H, U, and ΔT were 10.8(- 11.4) W m-2, 2.5 (3.1) m s-1, and 2.4 (- 1.3) °C under unstable (stable) conditions. The heat exchange over Erhai Lake seems to be smaller than for low-altitude lakes in North America, such as Ross Barnett Reservoir (Liu, Zhang,and Dowler 2012), Lake Superior (Blanken et al. 2011), and Great Slave Lake (Blanken, Rouse, and Schertzer 2003). This might be related to the high frequency of near-neutral conditions caused by the large low-cloud amount in the plateau region and thereby relatively small temperature difference. Low cloud has a cooling effect on the surface energy budget in the southeastern plateau region (Cai, Xu,and Sun 2012) and might lead to smaller H over Erhai Lake.

Figure 3. Variations of LE/H and other meteorological variables (U, u*, Δe/ΔT, and UΔe/UΔT) with stability conditions. The black squares and error bars are the average values and the corresponding standard deviations in each stability range, respectively.

3.3 Driving factors of LE and H under different stability conditions

The coefficient of determination (R2, P ＜0.05) between the 30-min LE/H and the meteorological variables(U,Δe/ΔT, and UΔe/UΔT) was calculated to illustrate the driving factors of LE and H under different stability ranges(Table 1). The correlation between LE and U ranged from 0.38 to 0.69 under unstable conditions and from 0.21 to 0.50 under stable conditions. The Δe had a relatively stronger influence on LE under unstable (- 1 ≤ ζ ＜- 0.1)and stable (0.1 ≤ ζ ＜1) conditions when Δe was large and wind speed was small, which supports the importance of a large Δe magnitude on the water vapor exchange across the lake–air interface (Zhang and Liu 2014). U had a larger correlation with LE than Δe from weakly unstable (- 0.1 ≤ ζ ＜- 0.01) to weakly stable(0.01 ≤ ζ ＜0.1) conditions. The correlation between LE and UΔe was largest under all the stability ranges, with mean R2values of 0.65 under unstable conditions and 0.56 under stable conditions. However, the correlation coefficients between LE and UΔe were not obviously enhanced compared to the correlation between LE and U under near-neutral conditions (- 0.01 ≤ ζ ＜0.01), indicating a strong impact of U in near-neutral stratification associated with high wind speed and strong mechanical turbulent mixing.

U was correlated to H only under stable (0.1 ≤ ζ ＜1)conditions, with R2= 0.37, while its R2values were smaller than 0.1 in other stability ranges. ΔT had a stronger relationship with H under stable conditions,with R2varying from 0.23 to 0.40, but no significant relationship with H under unstable conditions(R2＜0.2). UΔT had the largest correlation with H under all the stability ranges. The correlations between H and meteorological variables (U, ΔT, and UΔT) were obviously stronger under stable conditions than underunstable conditions, reflecting the stability conditions having a significant influence on controlling the relative contributions of U, ΔT, and UΔT to transfer heat at the lake–air interface. The mean R2value between LE and UΔe was 0.60 under all stability ranges, while that between H and UΔT was 0.30. The smaller correlation between H and UΔT suggests that the atmospheric stability condition has a stronger influence on H than LE in terms of the bulk transfer relationship.

Table 1. Coefficients of determination (R2, p ＜0.05) for the relationships of LE with U, Δe, and UΔe, and H with U,ΔT, and UΔT, under six stability ranges.

The relative impacts of meteorological variables on heat and water vapor transfer across the lake–air interface were regulated by the ASL stability conditions.Yusup and Liu (2016) studied a large temperate reservoir and found that U had a stronger influence on LE (H) than Δe (ΔT) under unstable conditions, while Δe (ΔT) was the major driver of LE (H) under stable conditions. For a small lake in the Tibetan Plateau, ΔT and Δe were more strongly correlated with H and LE than U under unstable conditions, while under weakly unstable to neutral conditions U had a stronger impact on H and LE (Wang et al.2017). In Lake Ngoring, the largest freshwater lake on the Tibetan Plateau, Δe and ΔT made a greater contribution than U to the LE and H under unstable conditions, but vice versa under near-neutral and weakly stable conditions (Li et al. 2015). The results for Erhai Lake are similar to the results of the two different lakes on the Tibetan Plateau mentioned above, which can be summarized as Δe having a major influence on LE under unstable(ζ ＜- 0.1) and stable (ζ ＞0.1) conditions, while U contributes more to LE from the weakly unstable to weakly stable range. The impacts of U and ΔT on H are only significant under stable conditions. The different roles of these atmospheric variables might be attributable to the different lake morphology, geography, and weather conditions, which determine the stability conditions and atmospheric forcing over lake surfaces.

4. Conclusions

Based on one year of data measured by the EC technique over Erhai Lake in 2015, the characteristics and drivers of LE and H fluxes under different stability conditions were analyzed in this study. Large evaporation still occurred under stable conditions, attributable to the relatively larger wind speed and vapor pressure difference between the lake and the atmosphere. The effect of U on LE was more significant than Δe from the weakly unstable to weakly stable range, whereas under unstable and stable conditions Δe made a large contribution to LE. The impacts of U and ΔT on H were only notable under stable conditions. These results for Erhai Lake have important implications for a better understanding of the parameterization of turbulent fluxes in lowlatitude highland lakes, but might not be appropriate for other inland lakes because the stability condition, as well as the water vapor and heat exchange at the water–air interface and its driving factors, will be site-specific and atmospheric-forcing-specific.

Acknowledgments

We appreciate the staffat the Yunnan Provincial Institute of Meteorology and Dali National Climatic Observatory for their help in the maintenance of the measurement site and instruments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This study was supported by the National Key Research and Development Program of China (No. 2017YFC1502101) and National Natural Science Foundation of China (Nos. 91537212 and 41775018).