1 Introduction

Surface roughness length and zero-plane displacement height are important physical attributes of aerodynamics to describe land surface as well as critical parameters to study exchanges of energy and mass between land surface and atmosphere. Moreover, the accurate description of aerodynamic characteristics of land surface will meet the imperative need of enhancing the land surface parameterization scheme in regional climate models and improving simulation results. The variation of sub-scale roughness length is one of the main factors affecting the calculation of grid turbulent fluxes (Chen et al., 2010). Surface roughness length, aka aerodynamic roughness length, is defined as the height where the wind speed is forced to decrease to zero with height (Martano, 2000). Surface roughness length is related to physical and geometric surface features. Near-ground wind profile under nearly neutral atmospheric conditions is one of the most used means in a variety of methods for estimating surface roughness length and zero-plane displacement height. Theoretically, surface roughness length and zero-plane displacement height can be calculated when wind speed gradient data are observed for at least three levels (Stull, 2012). The method of wind speed profile has been used to calculate surface roughness length in many studies, for example, the roughness length of city canopy (Zhang and Lü, 2003), the mid-eastern Qinghai-Tibetan Plateau in rainy season (Li and Tao, 2005), and over the heterogeneous land surface of Loess Plateau (Zhang et al., 2009). Stanhill (1969) presented the empirical equation of zero-plane displacement height and the mean length of surface roughness based on a great number of experiments. Chen et al. (1993) proposed a technique for independent evaluation of surface roughness length using mean wind speed and simultaneous measurements of turbulent flux at a single level without the need for wind profile data. The Chen's technique has been validated using Kansas experimental data (Izumi, 1971). In the literature, surface roughness lengths over Gebi surface of Dingxin (Wang et al., 2007) were calculated using the Chen's technique. Rotach (1994) proposed a Temperature-Variance-Method (TVM) to estimate surface roughness length based on the variance of temperature pulse. Zhang and Chen (1997) measured surface roughness length and zero-plane displacement height at a 325-meter meteorological tower in the north border of Beijing using TVM. Based on the Monin-Obukhov similarity theory for the wind speed profile, Martano (2000) suggested that the problem of finding joint values of both the roughness length and the displacement height could be reduced to a simple least square procedure for one variable only when focusing on single-level datasets from one sonic anemometer. With the method of Martano (2000), roughness lengths of urban areas (Gao et al., 2002), forest canopy in Changbaishan (Zhou et al., 2007) and reed wetland in Panjin (He et al., 2007) were calculated.

The Qinghai-Tibetan Plateau is the largest and highest plateau in the world, with an area of about 2.5 million km² and an average altitude of more than 4,000 m (Ye and Gao, 1979; Li et al., 2016). Due to its unique topographical and landscape features, the Qinghai-Tibetan Plateau has profound dynamic and thermal influences on the global general atmospheric circulation, climate and weather (Yanai and Wu, 2006; Song et al., 2014). The land surface heterogeneity of the Qinghai-Tibetan Plateau leads to different aerodynamic and thermodynamic parameters (Ma et al., 2008). Studying the physical process between the land surface and the atmosphere on the Qinghai-Tibetan Plateau is beneficial to improving the parameterization scheme of global and regional weather/ climate models. Surface roughness length is a basic and important parameter in land surface models. Surface roughness length in the Qinghai-Tibetan Plateau has been studied by a few scholars (Li and Tao, 2005; Peng et al., 2005). However, most studies calculated surface roughness length based on the dataset of a whole year or a season (either summer or winter), whereas land cover characteristics shows a distinct intra-seasonal variation. Different from previous studies, our study calculated surface roughness length at a much shorter time scale (monthly scale). In this paper, a scheme to estimate surface roughness length was proposed first, and the surface roughness length over an alpine meadow on the eastern Qinghai-Tibetan Plateau was then estimated using this scheme.

2 Materials and method 2.1 Site description

The measurement site is one of the sites of Zoige Plateau Wetlands Ecosystem Research Station. The Zoige Plateau is situated in the eastern Qinghai-Tibetan Plateau. The site (33.89°N, 102.14°E, and 3,423 m above sea level) is located at an alpine meadow grassland, Maqu grassland (Figure 1). The grassland is more than 3,300 m above sea level and dominated by Cyperaceae and Gramineae with an average height of about 0.2 m during the growing season. The grassland is a typical meadow used for sheep and yak grazing. Topography at the study site is flat, homogenous, with the slope less than 3%. The climate at the site is generally cold and damp with wet mild summers and dry cold winters. Based on climate data measured at a meteorological station (34°N, 102.08°E, 3,471 m above sea level) located approximately 14 km north of the study site, annual mean air temperature from 1981 to 2010 was 1.9 °C and annual mean precipitation was 593 mm. Most of the precipitation occurred between May and September and little precipitation occurred during winter.

2.2 Method

In the Monin-Obukhov similarity theory (Monin and Obukhov, 1954), the wind speed profile U is written as,

$U(z) = \frac{{{u_*}}}{k}\left[ {\ln \frac{{z - d}}{{{z_0}}} - \textit{ψ} \left( {\frac{{z - d}}{L}} \right)} \right]$

(1)

where u _* is the friction velocity scale, k is the von Kármán constant, z is the measuring height, d is the zero-plane displacement height, z ₀ is the surface roughness length, ψ is the integrated stability correction function (Panofsky and Dutton, 1984), and L is the Obukhov length. If we set,

$\textit{α} = \ln \left( {\frac{{z - d}}{{{z_0}}}} \right)$

(2)

then from Eq. (1), we obtain

$kU + {u_*}\textit{ψ} = \textit{α} {u_*}$

(3)

The slope α can be estimated by using least square fitting method according to Eq. (3), and the surface roughness length can then be calculated as,

${z_0} = \left( {z - d} \right){{\rm e}^{ - a}}$

(4)

The integrated stability correction function ψ is calculated by,

$\textit{ψ} \left( \textit{ζ} \right) = 2\ln \left( {\frac{{1 + x}}{2}} \right) + \ln \left( {\frac{{1 + {x^2}}}{2}} \right) - 2{\tan ^{ - 1}}\left( x \right) + \text{π} /2,\;\textit{ζ} < 0$

(5)

$\textit{ψ} \left( \textit{ζ} \right) = - 5\textit{ζ} ,\;\textit{ζ} > 0$

(6)

$x = {\left( {1 - 16\textit{ζ} } \right)^{1/4}}$

(7)

where ζ is the stability and calculated by,

$\textit{ζ} = \frac{{z - d}}{L}$

(8)

The zero-plane displacement height d can be estimated by an empirical relation (Stanhill, 1969),

$\log d = 0.9793\log h - 0.1536$

(9)

where h is the average height of surface roughness object.

The Obukhov length L and friction velocity scale u _* are calculated as:

$L = - \frac{{u_*^3T}}{{kg\overline {w'T'} }}$

(10)

${u_*} = {\left[{\overline {u'w'} ^2} + {\overline {v'w'} ^2}\right]^{1/4}}$

(11)

where T is the absolute temperature, k is the von Kármán constant, g is the gravitational acceleration, and u, v, and w are the wind velocity components.

2.3 Data collection and processing

Turbulent flux was measured continuously using an eddy covariance (EC) system at the site. The EC system was mounted 3.15 m above the soil surface. It consists of a 3D sonic anemometer (CSAT-3, Campbell Scientific, Inc., Logan, UT, USA) and an open path and fast response infrared gas analyzer (LI-7500, LI-COR Biosciences Inc., Lincoln, NE, USA). The separation distance between the two sensors was 0.15 m. Signals from the EC instrumentation were recorded at the rate of 10 Hz, and the raw data were stored in a CR3000 data logger (Campbell Scientific, Inc.). The raw data of EC system were processed to obtain 30-min averages. The spike detection and removal method was first applied to the raw data (Vickers and Mahrt, 1997). A double coordinate rotation was then applied (Wilczak et al., 2001). Sonic temperature correction (Schotanus et al., 1983) and Webb corrections (Webb et al., 1980) were finally applied to estimates of heat flux.

Meteorological and soil variables were also measured continuously with an array of sensors. Precipitation was measured with a tipping bucket rain gauge (52202, RM Young, Traverse City, MI, USA). Soil temperature was measured at 1, 3, 5, 10 cm depths and other deeper layers with CS107 temperature probes (Campbell Scientific, Inc.). Volumetric soil water content was measured at 5 and 10 cm depths and other deeper layers with CS616 Time Domain Reflectometer (TDR) probes (Campbell Scientific, Inc.). Soil heat flux was measured using heat flux plates (HPF01, Wohlwend Engineering, Sennwald, Switzerland) buried at 2 and 7 cm below the soil surface and deeper depths. Signals from meteorological and soil sensors were recorded as 30-min averages with a CR23XTD data logger (Campbell Scientific, Inc.). More details on the system have been reported in previous documents (Shang et al., 2015; Wang et al., 2016).

Seasonal variation of daily averaged soil temperature (T _s) at 5 cm depth during the winter season is presented in Figure 2. In order to investigate the variation of surface roughness length, the study period was divided into three different periods based on the variation of soil temperature at 5 cm depth: unfrozen (October 1 to November 28, 2006), frozen (November 29, 2006 to March 10, 2007) and melted (March 11 to April 30, 2007) periods. All data used in the study were observed in clear days. Thus, the EC data from October 1 to 7, 2006 and November 9 to 24, 2006 were used to estimate surface roughness length for unfrozen period, data from December 11, 2006 to January 14, 2007 were used for frozen period, and data from April 3 to 30, 2007 were for melted period.

3 Results and discussion

For all the study periods, measurements taken under low wind speed (U < 1.5 m/s) have been excluded from the datasets. The correlations between kU+u _*ψ and u _* during different periods are presented in Figure 3. The straight lines plotted in the figure represent least square best fits to the datasets. The correlation coefficients for unfrozen, frozen, and melted periods are R² = 0.81, R² = 0.88 and R² = 0.91, respectively (Table 1). All the correlation coefficients are significant at the 0.01 level. The slopes of fitted lines for the unfrozen, frozen, and melted periods are α = 6.91, α = 7.23 and α = 7.40, respectively. The estimated roughness length z ₀ for unfrozen, frozen, and melted periods are 3.23×10⁻³, 2.27×10⁻³ and 1.92×10⁻³ m, respectively.

Wind speed can be calculated using the Monin-Obukhov similarity (Eq. (1)) since roughness length z ₀ has been estimated. In order to validate the estimated roughness length, the measured wind speeds (U _M) are compared with those calculated by the Monin-Obukhov similarity using the measured u _* and L and the estimated z ₀. Figure 4 shows the scatter plot between the wind speeds (U _E) calculated by Monin-Obukhov similarity and the measured wind speeds. The straight lines are the least square best-fit lines to the data. Statistics of the correlation between estimated and measured wind speeds during different periods of the winter season are listed in Table 2. The linear regression equations for unfrozen, frozen and melted periods are U _E = 0.960U _M (RMSE = 0.58 m/s), U _E = 0.967U _M (RMSE = 0.75 m/s) and U _E = 0.984U _M (RMSE = 0.73 m/s), respectively. The correlation coefficients for unfrozen, frozen and melted periods are R² = 0.84, R² = 0.84 and R² = 0.93, respectively. All the correlation coefficients are significant at the 0.01 level. The estimated wind speeds are slightly less than the measured wind speeds, but the differences are all less than 4%. The above comparisons between estimated and measured wind speeds indicate that the scheme used to estimate roughness length is feasible.

The roughness length shows a deceasing trend with time during the study period (Figure 5). The variation of roughness length may be caused by changes in land surface characteristic. The height of vegetation shows a decreasing trend in the same way during the study periods. The land surface in melted period is much more homogenous than that in unfrozen and frozen periods. Thereby, the roughness length is much lower in melted period. A study conducted in central Qinghai-Tibetan Plateau shows that surface roughness length had a dynamic change on a monthly time scale due to the seasonal variation of vegetation (Yang et al., 2014). The difference in roughness length in different periods is evident. Thus, setting the roughness length to be a constant value in numerical models could generate relative simulation errors.

A comparison of surface roughness length in different places of the Qinghai-Tibetan Plateau is presented in Table 3. The estimated values of surface roughness length in this study are close to the values of surface roughness length at Damxung on the central Qinghai-Tibetan Plateau (Peng et al., 2005), but less than the values of surface roughness length at Gaize, Shiquanhe (Li et al., 2000) and Shigatse (Li et al., 2002) on the western Qinghai-Tibetan Plateau, at Nagqu on the central Qinghai-Tibetan Plateau (Li et al., 2002), and at Lhasa, Nyingchi (Li et al., 2002) and Qamdo (Peng et al., 2005) on the southern Qinghai-Tibetan Plateau. Surface roughness length at different places of the Qinghai-Tibetan Plateau shows evident spatial and seasonal differences. The differences are related to land surface characteristics, i.e., topographic condition, vegetation type, and phenological characteristics. The vegetation types of most of these sites are sparse grassland. The vegetation of the site in this study is alpine meadow grassland. In addition, different methods used to estimate surface roughness length may also generate different results, such as Li et al. (2000, 2002) using the wind speed profile and Peng et al. (2005) based on the single wind speed data. More studies should be conducted to analyze impacts of various methods on roughness length estimation.

4 Conclusions

A scheme based on the Monin-Obukhov similarity theory was developed to calculate surface roughness length. Surface roughness length over the eastern Qinghai-Tibetan Plateau during the winter season was then estimated with the scheme and eddy covariance measurement data. Comparisons of the estimated and measured wind speeds indicate that the scheme is feasible to calculate surface roughness length. The correlation coefficients between estimated and measured wind speeds for unfrozen, frozen and melted periods are 0.94, 0.95 and 0.93, respectively, which are significant at 0.01 level. The estimated wind speeds are slightly less than the measured wind speeds, but the difference are all less than 4%. The estimated roughness lengths of the measurement site for unfrozen, frozen and melted periods are 3.23×10⁻³, 2.27×10⁻³ and 1.92×10⁻³ m, respectively. Surface roughness length shows a deceasing trend with time during the winter season. Thereby, setting the roughness length to be a constant value in numerical models could generate relative simulation errors. The variation of surface roughness length may be caused by changes in land surface characteristics. Surface roughness lengths at different places of the Qinghai-Tibetan Plateau show evident spatial and seasonal differences. The differences are related to land surface characteristics and the methods used to estimate roughness length.

Acknowledgments:

This work was supported by the National Natural Science Foundation of China (41275016, 41405016, 41205006, 41275014, 41375077, 91537104, and 91537106). We would like to acknowledge Zoige Plateau Wetland Ecosystem Research Station for providing data support for this study. We would like to thank all those who have contributed to the field work.