## Abstract

In this study, eddy covariance flux data collected from three research stations on the Tibetan Plateau—Qomolangma for Atmospheric and Environmental Observation and Research, Nam Co for Multisphere Observation and Research, and Southeast Tibet Station for Alpine Environment Observation and Research, Chinese Academy of Sciences—are used to analyze the variation of momentum transfer coefficient (*C _{D}*), heat transfer coefficient (

*C*), aerodynamic roughness length (

_{H}*z*

_{0m}), thermal roughness length (

*z*

_{0h}), and excess resistance to heat transfer (

*kB*

^{−1}, where

*k*is von Kármán’s constant and

*B*

^{−1}is a non-dimensional bulk parameter). The following results are found. The monthly average surface roughness, bulk transfer coefficient, and excess resistance to heat transfer at all three stations are obtained. The values of average heat bulk transfer coefficients are larger than those of average momentum bulk transfer coefficients at all three stations. The parameter

*kB*

^{−1}exhibits clear diurnal variations with lower values in the night and higher values in the daytime, especially in the afternoon. Negative values of

*kB*

^{−1}are often observed in the night for relatively smooth surfaces on the Tibetan Plateau, indicating that heat transfer efficiency may exceed that of momentum transfer.

## 1. Introduction

As the largest and highest plateau in the world, the Tibetan Plateau affects the general circulation of the atmosphere and plays a very important role in the Asian monsoon system. The land–atmosphere interactions not only affect the development of the local atmospheric boundary layer, but also change the horizontal gradient of temperature and moisture at a continent scale (Yang et al. 2003). What is more, the land surface heterogeneity leads to differences in the surface roughness, bulk transfer coefficient, and excess resistance to heat transfer over the different land surfaces on the Tibetan Plateau (Ma et al. 2008). Thus, an observational analysis of land–atmosphere interaction parameters in different landscapes of the Tibetan Plateau is of great significance. Some interesting detailed studies concerning these key parameters have been reported (e.g., Miao et al. 1998; Li et al. 2001, 2002; Li and Tao 2005; Ma et al. 2002; Yang et al. 2003, 2008) during the past few years. However, most of these studies used AWS data without using eddy covariance flux data for a whole year.

In this study, eddy covariance flux data collected from three research stations on the Tibetan Plateau—Qomolangma for Atmospheric and Environmental Observation and Research (hereafter Qomolangma), Nam Co for Multisphere Observation and Research (hereafter Nam Co), and Southeast Tibet Station for Alpine Environment Observation and Research (hereafter Southeast Tibet station), Chinese Academy of Sciences—are used to analyze the variation of momentum transfer coefficient (*C _{D}*), heat transfer coefficient (

*C*), aerodynamic roughness length (

_{H}*z*

_{0m}), thermal roughness length (

*z*

_{0h}), and excess resistance to heat transfer (

*kB*

^{−1}, where

*k*is von Kármán’s constant and

*B*

^{−1}is a non-dimensional bulk parameter). The purpose of this paper is to present the characteristics of these key parameters over different landscapes of the Tibetan Plateau for the whole year of 2007.

## 2. Data

Data used in this paper were collected from three research stations on the Tibetan Plateau: Qomolangma, Nam Co, and Southeast Tibet. All three stations (Fig. 1 shows their location) are established by the Institute of Tibetan Plateau Research, Chinese Academy of Sciences. Qomolangma (28°13′N, 86°34′E, 4276 m MSL) is located on the northern slope of Mt. Qomolangma (Mt. Everest). The surface of the site is covered by sandy soil with small rocks. Nam Co (30°46′N, 90°59′E, 4730 m MSL) is located at the southeast shore of Nam Co Lake, on the northern slope of the Nyainqentanglha Mountains. The site has a relatively smooth surface and is covered by very sparse and short grasses in the monsoon season. Southeast Tibet station (29°46′N, 94°44′E, 3230 m MSL) is located on the southeast Tibetan Plateau. The site’s surface is covered with dense canopy, and the site is surrounded by forest. We collected data from these stations for the whole year of 2007 (there is no data collected at Nam Co in May and July of 2007). Eddy fluxes were measured with an eddy covariance system consisting of an open-path infrared CO_{2}/H_{2}O gas analyzer (LI-7500, LI-COR Inc.) and a 3D sonic anemometer (CSAT3, Campbell Scientific Inc.) at a height of 3 m above ground level and the data average recording interval was set to 30 min at Qomolangma and Nam Co, while data from Southeast Tibet station was measured with 10-min averaging. All data collected were corrected for coordinate rotation (Kaimal and Finnigan 1994; Wilczak et al. 2001), Webb-Pearman-Leuning (WPL) correction (Webb et al. 1980), and sonic temperature correction. As a feasible method for coordinate rotation, the planar fit method (Wilczak et al. 2001) was used in this study.

## 3. Methodology

### a. Determination of surface roughness length

From the Monin–Obukhov similarity theory, the dimensionless wind shear and temperature gradient in a horizontally homogeneous surface layer are usually expressed as (Yang et al. 2002)

where *U* (m s^{−1}) is wind speed, *T* (K) is temperature, *u*_{*} (m s^{−1}) is friction velocity, *T*_{*} (K) is temperature scale (or friction temperature), *ζ* is stability parameter, and *z* is the height above the zero-plane displacement. The quantity *ϕ _{m}* is the stability function for momentum, and

*ϕ*is the stability function for heat. The

_{h}*k*is von Kármán’s constant.

The equations above can be integrated from the roughness height level to the reference level (*z*), which results in (Yang et al. 2001)

where *T _{s}* is the surface temperature,

*T*is the air temperature,

_{a}*ζ*≡

*z*/

*Lz*is the height above the zero-plane displacement,

*L*is Monin–Obukhov length,

*z*

_{0m}is the aerodynamic roughness length, and

*z*

_{0h}is the thermal roughness length. We have

*ζ*(=

_{m}*z*

_{0m}/

*L*) as the stability function for momentum, and

*ζ*(=

_{h}*z*

_{0h}/

*L*) as the stability function for heat. The quantity Pr is Prandtl number (=1 if

*z*/

*L*≥ 0 and 0.95 if

*z*/

*L*< 0). The term

*ψ*is the integrated form of the stability function for momentum, and

_{m}*ψ*is the integrated form of the stability function for heat.

_{h}Following the universal functions in Högström (1996) and the mathematical form of the correction terms in Paulson (1970), for stable surface layers, we obtain

for unstable surface layers,

where , , , and .

The logarithmic wind profile can be rewritten from Eq. (3) as

Given all the observed *u*_{*} and wind speed *U*, a set of ln(*z*_{0m}) can be generated, and thus aerodynamic roughness length can be obtained. For an average value of roughness length, a method developed by Yang et al. (2008) can be applied, as the optimal value of *z*_{0m} would correspond to the peak frequency in the histogram of ln(*z*_{0m}). It is generally accepted that *z*_{0h} is different from *z*_{0m} (e.g., Beljaars and Holtslag 1991), which can be derived from some *kB*^{−1} schemes shown in Table 1; we chose the Y07 parameterization scheme in this study.

### b. Determination of excess resistance to heat transfer

The excess resistance to heat transfer *kB*^{−1} is used to parameterize the sensible heat exchange between the land surface and atmosphere. In past decades, the parameterization of *kB*^{−1} has attracted a number of theoretical and experimental studies (e.g., Garratt and Francey 1978; Brutsaert 1982; Verhoef et al. 1997; Ma et al. 2002; Yang et al. 2003, 2007, 2008; Kanda et al. 2007). It appears as a variable in many numerical models and satellite remote sensing parameterization methods, and we simply computed *kB*^{−1} using the *z*_{0m} obtained by the above-mentioned method with the following equation (Owen and Thomson 1963):

### c. Determination of bulk transfer coefficient

The bulk transfer coefficients *C _{D}* and

*C*are not only important for indicating the intensity of turbulent transfer but are also necessary for dealing with some theoretical and practical problems, such as energy budget computation, diagnostic weather analysis, and numerical simulation for the atmospheric circulation or climate (Li et al. 2001). It is very important in theory and practice to study the value and variation of the bulk transfer coefficients over the Tibetan Plateau. The most popular approach to determine bulk transfer coefficients is to use profile relationships established from surface layer similarity and to express them as functions of surface roughness and Monin–Obukhov stability parameter (Li et al. 2001). The momentum bulk transfer coefficients and heat bulk transfer coefficients can be parameterized as (Garratt 1992)

_{H}where *ψ*_{m}(*ζ*) is the integrated form of the stability function for momentum and *ψ _{h}*(

*ζ*) is the integrated form of the stability function for heat. The

*z*is the height above the zero-plane displacement, and

*L*is the Monin–Obukhov length;

*z*

_{0m}is the aerodynamic roughness length and

*z*

_{0h}is the thermal roughness length. The

*k*is von Kármán’s constant, and Pr

_{0}(=0.74) is the turbulent Prandtl number for neutral stability.

## 4. Analysis of the results

Figure 2 shows the frequency distribution of ln(*z*_{0m}) at Nam Co in October. A value of ln(*z*_{0m}) = −4.78 has the maximum frequency in the smoothed curve, and therefore the optimal value of *z*_{0m} is 0.0084 m. Covered with snow, the surface of the site became more smooth at that time of year. The monthly average *z*_{0m} for the whole year of 2007 is derived, and it is shown in Table 2. The intermonthly variations of aerodynamic roughness length at Nam Co and the Southeast Tibet station are more evident than that at Qomolangma.

The parameter *kB*^{−1} exhibits clear diurnal variations with lower values in the night and higher values in the daytime, especially in the afternoon at all three stations (see Figs. 3–5). Negative values of *kB*^{−1} are often observed in the night for relatively smooth surfaces on the Tibetan Plateau. Negative *kB*^{−1} values were also reported by previous studies (e.g., Verhoef et al. 1997; Su et al. 2001; Yang et al. 2008). This finding indicates that heat transfer efficiency may exceed that of momentum transfer (Yang et al. 2008). This is in contrast to the traditional opinion that momentum transfer is more efficient than heat transfer. Yang et al. (2008) reported that the “abnormal” phenomenon may be attributed to heat transport by inactive eddies in the outer layer. Possibly, negative values of *kB*^{−1} result from overestimation of downward heat flux in the night. We have to mention that negative *kB*^{−1} values might relate to the breakdown of Monin–Obukhov similarity when the thermal stratification is very stable. Figure 3 shows the diurnal variations of observed *kB*^{−1} at Qomolangma from 1 to 15 March. Figure 4 and Fig. 5 show the variations of observed *kB*^{−1} at Nam Co and Southeast Tibet station from 1 to 15 March, respectively. Table 3 illustrates intermonthly variations of *kB*^{−1} for all three stations. It can be seen that *kB*^{−1} at Southeast Tibet station is a little larger.

Figure 6 and Fig. 7 show the diurnal variations of the momentum transfer and heat transfer coefficients at Qomolangma, respectively. The average value of momentum transfer coefficient at Qomolangma in October is 0.73 × 10^{−3}, while that of heat transfer coefficient is 1 × 10^{−3}. Table 4 is the average momentum bulk transfer coefficients of the whole year, and Table 5 is the average heat bulk transfer coefficients. The values of average heat bulk transfer coefficients are larger than those of average momentum bulk transfer coefficients on the Tibetan Plateau, which was also reported by previous studies (e.g., Miao et al. 1998; Li et al. 2002).

## 5. Conclusions and remarks

The variation of momentum transfer coefficient (*C _{D}*), heat transfer coefficient (

*C*), aerodynamic roughness length (

_{H}*z*

_{0m}), thermal roughness length (

*z*

_{0h}), and excess resistance to heat transfer (

*kB*

^{−1}) at three stations on the Tibetan Plateau are analyzed in this study. The intermonthly variations of aerodynamic roughness length at Nam Co and the Southeast Tibet station are more evident than those at Qomolangma. The values of average heat bulk transfer coefficients

*C*are larger than those of average momentum bulk transfer coefficients

_{D}*C*. The parameter

_{H}*kB*

^{−1}exhibits clear diurnal variations with lower values in the night and higher values in the daytime, especially in the afternoon. Negative values of

*kB*

^{−1}are often observed in the night for relatively smooth surfaces on the Tibetan Plateau, indicating that heat transfer efficiency may exceed that of momentum transfer. This is in contrast to the traditional opinion that momentum transfer is more efficient than heat transfer. We suspect that negative

*kB*

^{−1}values might relate to very stable stratification where Monin–Obukhov similarity does not hold.

In fact, these parameters are quite changeable even over only over a few days. What is more, they vary with atmospheric stability and the upwind area where the atmospheric flux is measured. Thus, further study is necessary, including applying footprint models to assess flux data quality for these sites with respect to both fetch (the length of the homogeneous surface in the direction of wind) and surface homogeneity.

## Acknowledgments

This work was under the auspices of the Chinese National Key Programme for Developing Basic Sciences (2010CB951701), the National Natural Science Foundation of China (40825015 and 40810059006), Innovation Projects of the Chinese Academy of Sciences (KZCX2-YW-Q11-01), and EU-FP7 project “CEOP-AEGIS” (212921). The authors thank all the colleagues for their very hard work in the construction and the field work of the Tibetan Observation and Research Platform (TORP).

## REFERENCES

^{−1}for sparse vegetation