Abstract

Accurate parameters that describe land–air exchange processes are essential for studying and predicting atmospheric processes over the Tibetan Plateau. Radiation, atmospheric thermal and moisture conditions, and turbulent heat and momentum fluxes were measured in the Yarlung Zangbo River, southeast Tibet, in May–July 2013. Based on the data, land–air exchange parameters were derived over the grassland surface, including the aerodynamic roughness length z0m, thermal roughness length z0h, the excess resistance to heat transfer kB−1 (where k represents the von Kármán constant and B−1 represents the Stanton number), and momentum and heat transfer coefficients (CD and CH, respectively). The average z0m was 7.0 cm, with a standard deviation of 1.4 cm; these values are higher than those observed in the central and western plateau regions and may have been affected by the tall grass and bush surface covers that surrounded the observation site. The average kB−1 was 5.7 ± 1.8, which is higher than that in other plateau regions in the same season. The average CD during the observation period, (11.9 ± 1.6) × 10−3, is also higher than that of other plateau regions. The commonly used iterative scheme and three noniterative turbulent flux parameterization schemes were evaluated over southeast Tibet using the above observational data. Parameter CD was underestimated by most schemes, whereas CH was overestimated by all schemes. Additional studies suggested that the iterative scheme performed best in retrieving the land–air exchange parameters and can be applied over southeast Tibet.

1. Introduction

The Tibetan Plateau interacts with the regional climate and environmental systems in Asia via air mass/energy exchange processes between the surface air and the free atmosphere (Ye and Gao 1979; Wu et al. 2015). Accurate parameters that describe these land–air exchange processes are essential for the study and prediction of atmospheric processes over the Tibetan Plateau. Studies have shown that different land–air exchange parameters can result in large discrepancies in estimating the near-surface momentum and heat transfer fluxes. Ye and Gao (1979) obtained a constant heat transfer coefficient CH of 8 × 10−3, which resulted in a sensible heat flux Hs of 80.0 W m−2 over the Tibetan Plateau. Chen et al. (1985) derived CH from the surface energy budget and estimated an average CH of 3.6 × 10−3; they also estimated Hs to be approximately half that estimated by Ye and Gao (1979). Duan and Wu (2008) used a constant CH of 4.0 × 10−3 for the central and eastern plateau and 4.75 × 10−3 for the western plateau, which caused an Hs weakening trend of −14% from 1980 to 2003 over the Tibetan Plateau. Guo et al. (2011) parameterized CH by combining Monin–Obukhov similarity theory and estimated a weak Hs decreasing trend of −4.6% from 1981 to 2006 over the plateau.

The aerodynamic roughness length z0m, thermal roughness length z0h, excess resistance to heat transfer kB−1 (where k represents the von Kármán constant and B−1 represents the Stanton number), and the momentum and heat transfer coefficients (CD and CH, respectively) are important land–air exchange parameters. Studies have shown that these land–air parameters vary greatly across the Tibetan Plateau. For example, z0m has been observed to vary from less than 1.0 cm in the central plateau to more than 20.0 cm in the southeast plateau (Liu et al. 2002; Ma et al. 2002; Yang et al. 2008, hereafter Y08; Wang and Ma 2011; Wang et al. 2016) during May–July, which is directly related to the surface cover. Parameter kB−1 has been reported to exhibit large variability in the plateau, ranging from 2.0 in the central plateau to 7.4 in the west plateau (Wang et al. 2016). The momentum transfer coefficient was measured to be 2.3 × 10−3 at Gerze, west Tibet (Li et al. 1999); 2.5 × 10−3 at Amdo, northeast Tibet (Y08); 5.5 × 10−3 at Qamdu, east Tibet (Bian et al. 2002); and 4.4 × 10−3 at Rikeze, south-central Tibet (Li et al. 1996). The heat transfer coefficient was measured as ranging from 1.0 × 10−3 to 3.0 × 10−3 in central Tibet (Y08; Gu et al. 2011; Wang and Ma 2011); was 3.0 × 10−3 at Gerze, west Tibet (Li et al. 1999); and was 2.1 × 10−3 at Amdo, northeast Tibet (Y08). Given the large spatial variations, the land–air exchange parameters over one plateau region may not be applicable for use in another region. It is necessary to calculate the land–air exchange parameters using in situ data to accurately evaluate the land–air mass/energy fluxes over a specific plateau region.

The bulk transfer method has been applied to calculate land–air exchange fluxes using numerical models in which CD and CH are key parameters (Jacobson 2005; Stensrud 2007). The two coefficients in the surface layer have been parameterized based on Monin–Obukhov similarity theory (Monin and Obukhov 1954). In early numerical models, the iterative algorithm was applied and considered to be the most accurate method. This method is computationally expensive, and many analytical approximations have been investigated to improve computational efficiency over the last 40 years. The early parameterization schemes assumed that z0h equaled z0m (kB−1 = 0) or assumed a constant kB−1 (Louis 1979; Pleim 2006), in which the bulk Richardson number RiB was used to estimate CD and CH. Later, analytical approaches were based on varying kB−1 with different similarity functions and under different z/z0m and z0m/z0h conditions. For example, Yang et al. (2001, hereinafter Y01) derived the exact solution of the stability parameter equation for stable conditions and an approximate analytical solution for unstable conditions based on the iterative solution. This scheme is widely used and considered close to the iterative result (Yang et al. 2003; Ma et al. 2006; Wouters et al. 2012, hereinafter W12; Sharan and Srivastava 2014). Li et al. (2010, hereinafter L10) derived the relationship between RiB and the Obukhov stability parameter (z/L; where L is the Obukhov length) by the regression analysis method. This scheme has been applied in some numerical models (Miyazawa et al. 2013; Varlamov et al. 2015). Recently, W12 derived an analytical expression between RiB and z/L that can be applied for a wide range of z0m and z0h conditions, especially over surfaces of high kB−1 (Trusilova et al. 2016). Therefore, to accurately derive the land–air exchange parameters from the model, it is necessary to evaluate the above commonly used parameterization schemes over the Tibetan Plateau based on in situ data.

Southeast Tibet is a typical plateau region adjacent to the South Asia regions that could be affected by the South Asian atmospheric systems and have land–air exchange parameters different from other plateau regions. For example, Zou et al. (2012) found that the land–air heat transfer is dominated by the latent heat flux instead of sensible heat flux as in other plateau regions. A research campaign was carried out over southeast Tibet in the summer of 2013 to further investigate the land–air exchange processes over the inhomogeneous surface covers. The near-surface turbulent heat and momentum fluxes were measured over the grassland surface during the campaign, which provided an opportunity to derive the land–air exchange parameters from the observational data and evaluate the different parameterization schemes in the model. Based on the observational data, our purpose in this study was to derive the land–air exchange parameters over southeast Tibet and provide a preliminary evaluation of commonly used land–air parameterization schemes. In this paper, the data and methodologies are first presented, followed by a description of the local atmospheric and exchange processes. Then, the flux parameters are presented. Finally, the conclusions are given in the last section.

2. Data and methodologies

a. Data

Observations were conducted in the Yarlung Tsangpo River valley, southeast Tibet, from 21 May to 10 July 2013. Figure 1 shows the topography of the observation region. The observation site was located at 29.449°N, 94.691°E and was 2970 m above mean sea level (denoted by the circle in Fig. 1a). It was mainly covered by grass, with scattered short bushes. The grass had an average height of approximately 0.1 m (with a maximum height of 0.2 m at the end of the observation period), and the vegetation coverage was approximately 90% (Fig. 1b). The bushes were mainly distributed in the east and west directions and were much denser in the west than in the east. During the observation period, an eddy covariance system was installed 2.2 m above ground level (AGL); it included a 3D ultrasonic anemometer (Gill Windmaster Pro, Gill Instruments, Inc., United Kingdom) and a CO2/H2O infrared gas analyzer (LI7500A, Li-Cor Inc., United States). The eddy covariance data were sampled at a frequency of 10 Hz. The upward and downward shortwave and longwave radiation fluxes were measured at 1.5 m AGL using a four-component net radiometer (NR01, Hukseflux Thermal Sensors, the Netherlands). Air temperature and humidity were measured using a MetPak II (Gill Instruments, Inc.) at 1.5 m AGL. Soil temperature was measured using a 109-L temperature probe (Campbell Scientific Inc., United States) at six levels from 2 to 50 cm below the ground surface. The soil heat fluxes were measured with heat flux plates (HFP01, Hukseflux Thermal Sensors) at soil depths of 2 and 5 cm.

Fig. 1.

(a) Topography of the observation region in the Yarlung Tsangpo River valley, southeast Tibet, with a contour interval of 300 m. The observation site is denoted by the solid black dot. (b) Photograph of the underlying surface at the observation site.

Fig. 1.

(a) Topography of the observation region in the Yarlung Tsangpo River valley, southeast Tibet, with a contour interval of 300 m. The observation site is denoted by the solid black dot. (b) Photograph of the underlying surface at the observation site.

b. Methods

The eddy covariance data were quality controlled and processed using EddyPro software (Li-Cor Inc.) to calculate the turbulent sensible heat flux (i.e., Hs) and latent heat flux Le, friction velocity , and the Obukhov length L at 30-min intervals. During processing and in the software’s “advanced mode,” we performed a sonic temperature correction for humidity (van Dijk et al. 2004), a compensation for density fluctuations (Webb et al. 1980), angle-of-attack corrections for Gill anemometers (Nakai et al. 2006), planar fitting for tile correction (Wilczak et al. 2001), block averaging, time lag compensation, analytic high-pass-filtering correction (Moncrieff et al. 2004), and low-pass-filtering correction (Moncrieff et al. 1997). Raw data statistical tests (Vickers and Mahrt 1997) were performed in the software’s “advanced mode.” We also estimated the footprint to understand the source area of the measured fluxes using the footprint model developed by Kormann and Meixner (2001) and EddyPro software.

The surface energy balance can be described as follows (Arya 2001):

 
formula

where Rn is the surface net radiation; Hs and Le are the sensible and latent heat fluxes, respectively; G0 is the surface soil heat flux; and S is the storage of internal energy, which is ignored in this study. Parameter Rn was obtained from four radiation components, as follows:

 
formula

where DR is the downward shortwave radiation, UR is the upward shortwave radiation, DLR is the downward longwave radiation, and ULR is the upward longwave radiation.

The surface soil heat flux was estimated using Eqs. (3) and (4) (Arya 2001; Chen and Dudhia 2001):

 
formula
 
formula

where G1 is the soil heat flux at 2.0 cm depth; Δz is the depth (2.0 cm in this study); T is the average temperature between the surface and a depth of 2.5 cm; Cs is the soil volume heat capacity; t is time; ηs is the soil porosity; η is the volumetric moisture content; and Cd and Cw are the volumetric heat capacities for dry soils and water, respectively.

According to the Monin–Obukhov similarity theory, the relationship between wind speed and height is as follows (Garratt 1992):

 
formula

where z is the distance between the zero-displacement height and measurement height; U is the mean wind speed at z; is the friction velocity, where u′ and υ′ and w′ are the fluctuations in the horizontal and vertical wind components, respectively; k = 0.4 is the von Kármán constant; is the integral form of the universal similarity function, where ; L is the Obukhov length, which is calculated as ; θυ is the potential virtual temperature; g is the gravity constant; is the air density; and Cp is the specific heat of air at constant pressure. We used the universal functions of Högström (1996) in this study. Based on Eq. (5), we could obtain z0m using an independent method as follows (Ma et al. 2008):

 
formula

The thermal roughness length and the excess resistance to heat transfer can be derived as follows (Verhoef et al. 1997):

 
formula
 
formula

where Ts and Ta are the temperatures of the surface and air, respectively, and is the integrated stability function of heat (Högström 1996). The surface temperature was calculated as the surface thermal balance using the following formula (Y08; Chen et al. 2013):

 
formula

where ULR and DLR are the upward and downward longwave radiations, respectively; is the emissivity; and a value of 0.96 was used for this site over grass surfaces (Garratt 1992). Parameter is the Stefan–Boltzmann constant.

In this study, we selected two commonly used kB−1 schemes and evaluated them with the observed values; one was from Y08 and the other was from Chen and Zhang (2009, hereinafter C09). In the Y08 scheme, z0h is calculated as follows:

 
formula

where ν is the air kinematic viscosity, u* is the friction velocity, and θ* is the temperature scale.

The C09 scheme relates the z0h to canopy height via z0m, based on an AmeriFlux dataset. In this study, we used the “alternative formula” of the C09 scheme, as shown in Eq. (11), which was also applied in the Noah land model, the WRF Model, and several other studies (Chen et al. 2010; Li et al. 2014; Zheng et al. 2014, 2015), as follows:

 
formula

The momentum and heat transfer coefficients were derived from the ultrasonic data using Eqs. (12) and (13), respectively (Garratt 1992):

 
formula
 
formula

3. Local atmosphere and land–air exchanges

To determine the atmospheric thermal and dynamic land–air exchange parameters over southeast Tibet, the average radiation, thermal and moisture conditions, local circulations, and the land–air fluxes are first presented.

a. Radiation, thermal, and moisture conditions

Figure 2a shows the diurnal variations in the downward shortwave (i.e., DR) and net radiation fluxes (NR), which were averaged for the entire observation period from 21 May to 10 July. The DR varied as a sine curve during the daytime, with an average of 221.4 W m−2 and a maximum of 720.2 W m−2 at noon. Similar diurnal variation was found in the net radiation flux, with an average of 114.4 W m−2 and a maximum of 463.5 W m−2 (net heating) at 1200 local time (LT) and a minimum of −45.2 W m−2 (net cooling) at 1900 LT. Driven by solar irradiance, the air temperature and surface temperature exhibited diurnal variations similar to those of the radiation fluxes (Fig. 2b). The air temperature varied from a minimum of 11.3°C at midnight to a maximum of 21.9°C at noon, with an average value of 16.1°C. The surface temperature varied from a minimum of 11.4°C in the early morning to a maximum of 33.7°C before noon, with an average of 19.9°C. The surface temperature was generally higher than the air temperature during the day, and the difference between the surface and air temperatures (TsTa) reached a maximum of 12.7°C at noon.

Fig. 2.

Diurnal variations in (a) the downward shortwave radiation flux (DR) and net radiation flux (NR), which were averaged for the entire observation period. (b) The average air temperature Ta, surface temperature Ts and surface–air temperature contrast (TsTa), and (c) the specific humidity q.

Fig. 2.

Diurnal variations in (a) the downward shortwave radiation flux (DR) and net radiation flux (NR), which were averaged for the entire observation period. (b) The average air temperature Ta, surface temperature Ts and surface–air temperature contrast (TsTa), and (c) the specific humidity q.

Figure 2c presents the diurnal variations in the specific humidity averaged for the entire observation period. The specific humidity was high in the early morning and low in the afternoon, with a maximum of 10.8 g kg−1 at approximately 0800 LT, a minimum of 9.5 g kg−1 at approximately 1400 LT, and an average of 10.2 g kg−1. Southeast Tibet is more humid than the western and middle regions of the Tibetan Plateau based on comparisons of specific humidity (Liu et al. 2002; Zou et al. 2008).

b. Local circulations

Figure 3 shows the occurrence frequency of wind speed and the average diurnal variations of zonal and meridional winds during the observation period. Wind speed was generally much lower in southeast Tibet, with a maximum value of less than 6.0 m s−1, compared with that in other plateau regions (Egger et al. 2000; Liu et al. 2002; Bian et al. 2003; Zou et al. 2008). The airflow was predominantly from the south and east, which accounted for more than 50% of the total occurrence frequency (Fig. 3a). Weak southerly winds dominated the occurrence frequency of wind speed, with wind speeds less than 2.0 m s−1 and an occurrence percentage greater than 30%. These dominant weak southerly winds could have been mountain–valley winds from the small valley to the south. Strong easterly winds had a 20% occurrence frequency in the observation period, with wind speeds ranging from 1.0 to 6.0 m s−1. This large percentage and wind speed variation could be related to the west–east direction of the Yarlung Zangbo River.

Fig. 3.

(a) Wind rose diagram over the observation site during the observation period. The label around the circle is the wind direction, and the radius length is the occurrence frequency in each 45° segment. The wind speed is denoted by the shaded color. (b) Diurnal variations in the average near-surface zonal U and meridional V wind speeds.

Fig. 3.

(a) Wind rose diagram over the observation site during the observation period. The label around the circle is the wind direction, and the radius length is the occurrence frequency in each 45° segment. The wind speed is denoted by the shaded color. (b) Diurnal variations in the average near-surface zonal U and meridional V wind speeds.

The zonal wind U clearly varied diurnally, with an easterly (negative zonal) wind persisting during the daytime and a westerly wind persisting throughout the rest of the day (Fig. 3b). Compared with the westerly wind, the easterly wind was stronger, with an average daily maximum of 2.1 m s−1. Because of the shielding effect of the valley, the meridional wind V was weaker than the zonal wind. The diurnal variation in the meridional wind was complex, which may be attributed to the effects of airflow from the tributary valleys.

c. Heat and momentum fluxes

Both the sensible and latent heat fluxes exhibited clear diurnal variations, with large values around noon and small values at night (Fig. 4). The sensible heat flux began to increase in the morning and reached a maximum of 127.6 W m−2 at noon before decreasing to a minimum of −10.0 W m−2 at night; the daily average was 33.9 W m−2. A similar diurnal variation occurred in the latent heat flux, with a maximum of 204.3 W m−2, a minimum of 5.8 W m−2, and a daily average of 70.4 W m−2. The average total heat flux was 104.3 W m−2, which is within the range of 80.0–144.0 W m−2 cited for other plateau regions (Li et al. 1999; Bian et al. 2002; Gao et al. 2000; Zhou et al. 2015). However, the dominant latent heat flux (average value of 70.4 W m−2) in the total heat transfer greatly differed from that in the other plateau regions, which was in the range of 28.0–59.0 W m−2 (Zhou et al. 2015). The larger latent heat flux than sensible heat flux may reflect the larger evaporation over southeast Tibet (Zou et al. 2012).

Fig. 4.

The average diurnal variations in the sensible heat flux Hs, latent heat flux Le, and momentum flux τ.

Fig. 4.

The average diurnal variations in the sensible heat flux Hs, latent heat flux Le, and momentum flux τ.

The momentum flux also clearly varied diurnally (Fig. 4), which corresponds with the variations recorded in the wind speed. The momentum flux was transported downward throughout the day, with large magnitudes recorded at noon and small magnitudes at night. The maximum negative value was −0.17 kg m−1 s−2 at 1400 LT and the average was −0.05 kg m−1 s−2.

4. Land–air exchange parameters

The average atmospheric conditions during the observation period were calculated from the preceding data, which made it possible to retrieve the land–air exchange parameters based on the observational data.

a. Energy balance closure

A surface energy balance ratio was applied to examine the quality of the eddy covariance data and processing methods before the land–air flux parameters were retrieved. The surface energy closure ratio (CR) is calculated as the ratio of the sum of the sensible heat and latent heat fluxes to the available energy fluxes: [see Eqs. (1) and (2)]. The CR was 0.86 during the observation period, and the correlation coefficient between Hs + Le and RnG0 was 0.97 (Fig. 5). The surface sensible and latent heat fluxes were lower than the available energy fluxes and had an RMSE of 43.6 W m−2.

Fig. 5.

Scatterplot of the sensible and latent heat fluxes (Hs + Le) and the available energy fluxes (RnG0). The least squares regression represents the surface energy balance closure.

Fig. 5.

Scatterplot of the sensible and latent heat fluxes (Hs + Le) and the available energy fluxes (RnG0). The least squares regression represents the surface energy balance closure.

The CR obtained in this study was larger than those reported in previous results; this indicated the high quality of the data, which could thus be effectively used for further calculations of land–air flux parameters. For example, Tanaka et al. (2003) reported an energy balance ratio of approximately 0.90 during the premonsoon period, which decreased to approximately 0.50 during the monsoon period on the eastern Tibetan Plateau. Ma et al. (2005) reported a CR of 0.70 on the central Tibetan Plateau.

b. Aerodynamic roughness length

The aerodynamic roughness length is generally estimated from observed data under near-neutral conditions (Garratt 1992; Ma et al. 2008). However, this method discards a large amount of data collected under stable and nonstable conditions. In this study, we estimated z0m at individual time points by Eq. (6) and produced a frequency distribution of z0m (Fig. 6). From this distribution, the “average z0m” was determined by averaging the most frequent (top 50%) individual time point values of z0m. The average z0m was 7.0 cm, with a standard deviation of 1.4 cm. This z0m value is close to that measured over grassland at other sites (Stull 1988; Arya 2001). The z0m in southeast Tibet was larger than in the central and western regions of the Tibetan Plateau, which are mainly covered by bare soil (Table 1). For example, the z0m values measured at Amdo, Gerze, and Damxung were less than 1.0 cm in the same season (Liu et al. 2002; Ma et al. 2002; Y08; Wang et al. 2016). The z0m measured in this study is similar to that in eastern Tibet, which is mainly covered by trees and grassland; for example, z0m was 8.0 cm over grassland in Qamdo in the same season (Bian et al. 2002). Note that our result is much smaller than that measured in Nyingchi by Wang and Ma (2011) and Wang et al. (2016), which could be because of the surface cover differences.

Fig. 6.

Frequency distribution of the aerodynamic roughness length with a bin of 1.0 cm.

Fig. 6.

Frequency distribution of the aerodynamic roughness length with a bin of 1.0 cm.

Table 1.

Parameters z0m and kB−1 over different regions of the Tibetan Plateau.

Parameters z0m and kB−1 over different regions of the Tibetan Plateau.
Parameters z0m and kB−1 over different regions of the Tibetan Plateau.

Given the heterogeneous surfaces at the observation site, the directional dependence of the aerodynamic roughness length on the surface should be considered (Lu et al. 2009; Liu et al. 2011). A footprint is specified based on the relative contributions of different wind directions to z0m. From Fig. 7a, the main source area that contributed to these measurements was located to the south and extended approximately 700 m southward from the observation site. In other directions, the affected regions were generally within 300 m. The averaged source area varied from a northerly minimum (approximately 60 m from the observation site) to a southerly maximum (approximately 340 m from the observation site) during the observation period. The different source areas represented different land surface characteristics that contributed to the measurements, and the aerodynamic roughness length varied accordingly. Figure 7b shows the variation in z0m with wind direction. The z0m values were 5.1 ± 1.0, 8.9 ± 1.4, 6.0 ± 0.9, and 7.3 ± 1.5 cm in the northerly, easterly, southerly, and westerly directions, respectively. Dense bushes in the easterly and westerly directions contributed to z0m values that were larger than those of grassland in the northerly and southerly directions. Because the source area was to the south (see Fig. 7a), the vegetative surface mainly contributed to the aerodynamic roughness length during our observations.

Fig. 7.

(a) Footprint of the eddy covariance measurement system at the observation station. The black squares denote the footprint corresponding to 30-min data, and red squares denote the average footprint. (b) Variation in z0m with wind direction (error bars denote the std dev).

Fig. 7.

(a) Footprint of the eddy covariance measurement system at the observation station. The black squares denote the footprint corresponding to 30-min data, and red squares denote the average footprint. (b) Variation in z0m with wind direction (error bars denote the std dev).

c. Thermal roughness length

In addition to z0m, the thermal roughness length is a critical parameter in land–air exchange processes; z0h depends on the sensible heat flux, surface and air temperatures, and the stability of the atmosphere (Verhoef et al. 1997; Sun 1999). Parameter z0h is defined as the level at which the extrapolated semiempirical Monin–Obukhov air temperature equals the surface temperature (Verhoef et al. 1997; Sun 1999). During the observation period, z0h varied significantly on a diurnal basis, with small values in the afternoon and large values at night (Fig. 8a). Overall, ln(z0h) exhibited large variations and varied diurnally from −12.0 to −3.6 m, with an average of −8.2 m and a standard deviation of 2.1 m.

Fig. 8.

Average diurnal variations in (a) ln(z0h) and (b) kB−1.

Fig. 8.

Average diurnal variations in (a) ln(z0h) and (b) kB−1.

In numerical models, z0h is usually replaced by kB−1 , which is calculated as a function of z0m and the roughness Reynolds number (Brutsaert 1982; Verhoef et al. 1997; Yang et al. 2007). The observed kB−1 had obvious diurnal variations, with an average of 5.7 and a standard deviation of 2.8; it increased from a minimum of 2.1 at 0100 LT to a maximum of 9.3 at 1430 LT before a later decrease (Fig. 8b). The large scatter of kB−1 at night may be related to the small sensible heat flux and stable stratification at night and was also found in other studies (Verhoef et al. 1997; Yang et al. 2003). The average kB−1 value in southeast Tibet was larger than that in other plateau regions (Table 1), such as 3.7 at Qomolangma (south-central Tibet), 4.5 at Nam Co, 5.1 at Amdo, and 3.8 at Nagqu (central Tibet) in the same season (Yang et al. 2003; Wang and Ma 2011). The inhomogeneous surface cover could have contributed to the larger kB−1 over southeast Tibet.

d. Excess resistance to heat transfer parameterization schemes evaluation

Studies have shown kB−1 to be critical for the parameterization of land–air exchange processes (Chen et al. 1997; Chen et al. 2010; Zeng et al. 2012). To evaluate kB−1 in the model with respect to the observed value, we selected two commonly used parameterization schemes: the Y08 and the C09 schemes. With the observed z0m, the parameterized kB−1 was derived from the two schemes and its diurnal variation is presented in Fig. 8b. Both the Y08 and C09 schemes could predict the diurnal variations in kB−1 but underestimated kB−1, with average values of 3.8 and 4.7, respectively. The C09 scheme performed better than Y08 over southeast Tibet. It can be clearly seen in the z0h formulas [Eqs. (10) and (11)] in the two schemes that the canopy height is considered in the C09 scheme but not in Y08. Given that southeast Tibet is mainly covered by dense grass, shrubs, and forests, consideration of canopy height likely caused the better performance of the C09 scheme.

e. Momentum and heat transfer coefficients

The momentum and heat transfer coefficients are key parameters in model simulations and are critical for correctly estimating land–air interactions over inhomogeneous Tibet (Ye and Gao 1979; Chen et al. 1985; Duan and Wu 2008; Guo et al. 2011). Figure 9a shows the diurnal variation in the momentum transfer coefficient during the observation period. Parameter CD increased from a minimum of 8.9 × 10−3 at 0500 LT in the early morning to a maximum of 14.4 × 10−3 at 1300 LT in the afternoon, with an average of (11.9 ± 1.6) × 10−3. For comparison, the CD at 10 m AGL CD10 was derived from the flux profile method and the observed aerodynamic and heat roughness values (Garratt 1992; W12). The average CD10 was 5.7 × 10−3, which is much larger than those in other regions during the same season (Table 2), such as 2.3 × 10−3 at Gerze, west Tibet (Li et al. 1999); 2.5 × 10−3 at Amdo, northeast Tibet (Y08); 5.5 × 10−3 at Qamdu, east Tibet (Bian et al. 2002); and 4.4 × 10−3 at Rikeze, south-central Tibet (Li et al. 1996).

Fig. 9.

Average diurnal variations in the (a) momentum transfer coefficient and (b) heat transfer coefficient.

Fig. 9.

Average diurnal variations in the (a) momentum transfer coefficient and (b) heat transfer coefficient.

Table 2.

Parameters CD and CH over different regions of the Tibetan Plateau. All values are obtained at 10 m AGL unless otherwise noted.

Parameters CD and CH over different regions of the Tibetan Plateau. All values are obtained at 10 m AGL unless otherwise noted.
Parameters CD and CH over different regions of the Tibetan Plateau. All values are obtained at 10 m AGL unless otherwise noted.

Figure 9b presents the diurnal cycle of the thermal transfer coefficient averaged for the entire observation period. Parameter CH increased from a minimum of 2.0 × 10−3 at 0530 LT in the early morning to a maximum of 7.3 × 10−3 at 1900 LT in the afternoon, with an average of (3.8 ± 1.7) × 10−3. For comparison, we retrieved the CH value at 10 m AGL CH10, which averaged 2.8 × 10−3. Our result is consistent with previous results measured over other regions of the Tibetan Plateau in the same season (Table 2). For example, CH was measured to range from 1.0 × 10−3 to 3.0 × 10−3 in the central Tibetan Plateau region (Y08; Gu et al. 2011; Wang and Ma 2011); was 3.0 × 10−3 at Gerze, west Tibet (Li et al. 1999); and was 2.1 × 10−3 at Amdo, northeast Tibet (Y08).

The relationship of bulk transfer coefficients and wind speed at 2.2 m AGL is illustrated in Fig. 10. Parameter CD rapidly decreased with increasing wind speed under both stable and unstable conditions when the wind speed was low (less than 1 m s−1) and then tended to become constant. Parameter CH was smaller under stable conditions than unstable conditions. Parameter CH slightly increased with increasing wind speed and then tended to a constant value under stable conditions. Under unstable conditions, similar to that of CD, CH rapidly decreased with increasing wind speed when the wind speed was less than 2 m s−1 and then tended to become constant. As wind speed increased, the stability tended to become neutral, and CD and CH were close to their values under neutral conditions (CD,N and CH,N), 14.8 × 10−3 and 3.3 × 10−3, respectively. Parameter CD under neutral conditions was much larger than the values in the other plateau regions reported by Wang et al. (2016). This larger momentum transfer coefficient over southeast Tibet may be related to a larger aerodynamic roughness length and weak wind speed, which may have been influenced by mountain effects (Han et al. 2015; Wang et al. 2016).

Fig. 10.

The variations of CD and CH with wind speed for (a),(c) stable and (b),(d) unstable conditions.

Fig. 10.

The variations of CD and CH with wind speed for (a),(c) stable and (b),(d) unstable conditions.

f. Turbulent parameterization schemes evaluation

We evaluated different turbulent parameterization schemes over southeast Tibet based on the observed land–air heat and momentum fluxes. We selected four possibly suitable schemes for evaluation, including that of Y01, L10, and W12, as well as the iterative (ITE) scheme (see the  appendix for scheme details). In these schemes, CD and CH were obtained with different similarity functions and under different z/z0m and z0m/z0h conditions.

Figure 11 shows the CD and CH variations for the four parameterization schemes and the observations. Parameter CD was overestimated by the L10 scheme (with a slope of 1.12) and underestimated by the others (with slopes smaller than 1.0), whereas CH was overestimated by all schemes (see Table 3 for detailed slope values). Table 3 also presents mean biases (MBs) and root-mean-square errors (RMSEs) of CD and CH between the schemes and observations. The MB of CD was largest for the L10 scheme, with an overestimation of 21.9%, and smallest for the Y01 scheme, with an underestimation of −1.3%. The RMSE of CD was largest for the L10 scheme and smallest for the ITE scheme, which showed that the Y01 and ITE schemes performed best in retrieving CD. The MB and RMSE of CH were largest for the L10 scheme, with an overestimation of 55.8%, and smallest for the ITE scheme, with an overestimation of 35.5%, which showed that the ITE scheme performed best in retrieving CH. The estimated CD and CH differences among the schemes strongly depended on the applied conditions and similarity functions of each scheme. For example, the L10 scheme is suitable for kB−1 < 4.6 (L10) and may not apply to southeast Tibet where kB−1 is large (average of 5.7); this caused the largest MB between the scheme and observation (see Table 3).

Fig. 11.

Comparisons of (a) CD and (b) CH from four schemes using eddy covariance methods. Linear least squares fitting was applied for an overall evaluation and referenced the 1:1 dashed line.

Fig. 11.

Comparisons of (a) CD and (b) CH from four schemes using eddy covariance methods. Linear least squares fitting was applied for an overall evaluation and referenced the 1:1 dashed line.

Table 3.

The linear least squares fitting slope, correlation coefficients R, MB, and RMSE for CD and CH between four schemes and observations.

The linear least squares fitting slope, correlation coefficients R, MB, and RMSE for CD and CH between four schemes and observations.
The linear least squares fitting slope, correlation coefficients R, MB, and RMSE for CD and CH between four schemes and observations.

The momentum and sensible heat fluxes were also retrieved from the four schemes and compared with observations (see Fig. 12 and Table 4). The momentum flux τ was overestimated by the L10 scheme and underestimated by the others, whereas the sensible heat flux was overestimated by all schemes. The MB and RMSE of τ differed little between the four schemes, with MB values less than 6.0%, except for L10, which had an MB of 14%. The MB and RMSE of Hs were largest for the L10 scheme, with an overestimation of 63.8%, and smallest for the ITE scheme, with an overestimation of 36.8%, which showed that the ITE scheme performed best in retrieving Hs.

Fig. 12.

Comparisons of (a) momentum flux and (b) sensible heat flux of four schemes using eddy covariance methods. Linear least squares fitting was applied for an overall evaluation and referenced the 1:1 dashed line.

Fig. 12.

Comparisons of (a) momentum flux and (b) sensible heat flux of four schemes using eddy covariance methods. Linear least squares fitting was applied for an overall evaluation and referenced the 1:1 dashed line.

Table 4.

The linear least squares fitting slope, correlation coefficients (i.e., R), MB, and RMSE for momentum flux and sensible heat flux between four schemes and observations.

The linear least squares fitting slope, correlation coefficients (i.e., R), MB, and RMSE for momentum flux and sensible heat flux between four schemes and observations.
The linear least squares fitting slope, correlation coefficients (i.e., R), MB, and RMSE for momentum flux and sensible heat flux between four schemes and observations.

In summary, the ITE scheme was best at retrieving both the land–air turbulent parameters and the fluxes and can be applied in studies of land–air exchange processes in southeast Tibet.

5. Conclusions

In this paper, observational data obtained from a grassland site in southeast Tibet from 20 May to 9 July 2013 were used to retrieve accurate land–air exchange parameters, including the aerodynamic and thermal roughness lengths, excess resistance to heat transfer, and momentum and heat transfer coefficients. With the observed values, commonly used land–air turbulent parameterization schemes were evaluated over southeast Tibet. The land–air exchange parameters over southeast Tibet were found to be different from those of other plateau regions. The aerodynamic roughness length z0m over southeast Tibet was 7.0 cm during the observation period, which was much larger than the values in other plateau regions during the same period. Footprint analysis results indicated that z0m was sensitive to wind direction and was affected by the underlying conditions in the source area. The average kB−1 was 5.7 in southeast Tibet, which was much larger than that of other plateau regions. The momentum transfer coefficient CD was larger than that in other regions in the same season, with mean values of 11.9 × 10−3 and 5.8 × 10−3 at 2.2 and 10 m AGL, respectively. The thermal transfer coefficient CH varied more than CD and averaged 3.8 × 10−3 and 2.8 × 10−3 at 2.2 and 10 m AGL, respectively, which was similar to the values observed in other plateau regions.

Using the observed values, kB−1 was obtained from both the Y08 and C09 parameterization schemes. Both schemes underestimated kB−1 over southeast Tibet, although they predicted a diurnal variation similar to that observed. The momentum and heat transfer fluxes and their coefficients were also obtained from four land–air turbulent parameterization schemes: Y01, L10, W12, and ITE. All schemes overestimated the sensible heat flux and underestimated the momentum flux, except for L10. Parameter CD was overestimated by the L10 scheme and underestimated by the others, whereas CH was overestimated by all schemes. Among the four schemes, the ITE scheme had the least bias with respect to observations in retrieving the land–air heat transfer coefficients and fluxes and can be applied in studies of land–air exchange processes in southeast Tibet.

Acknowledgments

This study was supported by the Beijing Municipal Science and Technology Commission (Grant D171100000717003), the Project of Comprehensive Evaluation of Polar Areas on Global and Regional Climate Changes and Polar Environment Comprehensive Investigation and Assessment (2016–2020; Grant CHINARE2016-04-04-08), the CAS Key Subordinate Project (KGFZD-135-16-023), and the China Meteorological Administration Special Public Welfare Research Fund (GYHY201206041).

APPENDIX

Brief Descriptions of Turbulent Parameterization Schemes

In numerical models, the bulk transfer coefficients in the surface layer are parameterized based on Monin–Obukhov similarity theory (Monin and Obukhov 1954). Parameters CH and CD are estimated as follows:

 
formula
 
formula

where z is the first model level height above the surface and Pr is 0.95. Many analytical approximations have been constructed to avoid the computation time of the iterative method. In this paper, we evaluated three analytical schemes based on observational data.

The Y01 scheme is based on the iterative solution and derives the exact solution of the stability parameter equation for stable conditions and an approximate analytical solution for unstable conditions. Y01 is applicable in the range of 50 < z/z0m < 104 and 0 ≤ kB−1 ≤ 9.2. The z/L for stable conditions is expressed as

 
formula
 
formula
 
formula

where z0m and z0h are the aerodynamic and heat roughness lengths, respectively; RiB is the bulk Richardson number; and , , and for the Högström (1996) profile functions. For unstable conditions, z/L is calculated as follows:

 
formula

where , , and for Högström (1996) profile functions and p is estimated as follows:

 
formula

where i, j, and k = 0, 1, and 2, and ; are coefficients that depend on profile functions that can be referenced to Y01.

L10 derived the relationship between RiB and z/L based on iterative computation results of the Högström (1996) profile function for unstable condition and the Beljaars and Holtslag (1991) function for stable condition. L10 classifies the stability into unstable (RiB < 0), weakly stable (0 < RiB ≤ 0.2), and strongly stable conditions (RiB > 0.2). The L10 scheme is applicable for the conditions of −2 ≤ RiB ≤ 1, 102z/z0m ≤ 105, and −0.7 ≤ kB−1 ≤ 4.6. The z/L values for unstable conditions, weakly stable conditions, and strongly stable conditions are estimated by Eqs. (A8), (A9), and (A10), respectively:

 
formula
 
formula
 
formula

where , , and other coefficients can be referenced to L10.

W12 derived the relationship between RiB and z/L based on iterative solutions of the Businger (1966) profile function for unstable conditions and the Cheng and Brutsaert (2005) function for stable conditions. W12 also classifies the stability into unstable, weakly stable, and strongly stable conditions. The z/L values for unstable conditions, weakly stable conditions, and strongly stable conditions are estimated by Eqs. (A11), (A12), and (A13), respectively:

 
formula
 
formula
 
formula

The coefficients in the equations can be referenced to W12.

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Footnotes

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