Turbulence Intensity and Turbulent Kinetic Energy Parameters over a Heterogeneous Terrain of Loess Plateau

YUE Ping,ZHANG Qiang,WANG Runyuan,LI Yaohui,and WANG Sheng

Key Laboratory of Arid Climatic Change and Reducing Deserter of Gansu Province,Institute of Arid Meteorology, China Meteorological Administration,Lanzhou 730020

Turbulence Intensity and Turbulent Kinetic Energy Parameters over a Heterogeneous Terrain of Loess Plateau

YUE Ping∗,ZHANG Qiang,WANG Runyuan,LI Yaohui,and WANG Sheng

Key Laboratory of Arid Climatic Change and Reducing Deserter of Gansu Province,Institute of Arid Meteorology, China Meteorological Administration,Lanzhou 730020

A deep understanding of turbulence structure is important for investigating the characteristics of the atmospheric boundary layer,especially over heterogeneous terrain.In the present study,turbulence intensity and turbulent kinetic energy(TKE) parameters are analyzed for different conditions with respect to stability,wind direction and wind speed over a valley region of the Loess Plateau of China during December 2003 and January 2004.The purpose of the study is to examine whether the observed turbulence intensity and TKE parameters satisfy Monin–Obukhov similarity theory(MOST),and analyze the wind shear effect on,and thermal buoyancy function of,the TKE,despite the terrain heterogeneity.The results demonstrate that the normalized intensity of turbulence follows MOST for all stability in the horizontal and vertical directions,as well as the normalized TKE in the horizontal direction.The shear effect of the wind speed in the Loess Plateau region is strong in winter and could enhance turbulence for all stability conditions.During daytime,the buoyancy and shear effect together constitute the generation of TKE under unstable conditions.At night,the contribution of buoyancy to TKE is relatively small,and mechanical shearing is the main production form of turbulence.

heterogeneous terrain,turbulence intensity,turbulent kinetic energy,Monin–Obukhov similarity function

1.Introduction

Turbulent transport is one of the most important characteristics of the atmospheric boundary layer.The exchange of momentum,heat,water and other substances between land and atmosphere mainly takes place in the form of turbulent diffusion(Louis,1979;Powell et al.,2003;Martins et al., 2009;Mahrt,2010).Therefore,the characteristics of the atmospheric turbulence near-surface layer become the important characterization parameters of the land–atmosphere interaction(Monin and Yaglom,1971;Louis,1979;Teixeira et al.,2008).An accurate description of the land–atmosphere turbulence exchange process depends on the understanding of the characteristics of atmospheric turbulence(Muschinski et al.,2004;Acevedo et al.,2007;Teixeira et al.,2008). However,it is clear that,for atmosphere turbulent flows,we cannot directly describe the exchange process(Massman and Lee,2002;Moraes et al.,2005).Instead,previous studies(Nieuwstadt,1984;Sorbjan,1987)have concentrated on understanding the statistical properties of atmosphere turbulence.

As a globally unique and important geographical region, the Loess Plateau of China is an important part of the country’s arid and semi-arid landscape,and the heterogeneity of the land surface is obvious(Huang et al.,2008;Yue et al., 2011).The region features a gully–hilly crisscross pattern, and the underlying surface is highly undulating.Therefore, the turbulence characteristics of the region are complicated, while the turbulent transport is more typical(Huang et al., 2008;Yue et al.,2012;Zhang et al.,2013).There are significant differences in the resulting turbulence characteristics, even at the same observation station,when airflow from different directions passes the observation point.This is because of the different characteristics of the underlying surfaces and the“memories”they impose(Martins et al.,2009;Liu et al., 2012).

In fact,the factors affecting the inhomogeneity of the underlying surface of the Loess Plateau are not only topographic;the complexity of the vegetation in the region is also regarded asa very importantnon-uniform factor(Zhang etal., 2013).However,changes in wind speed in the surface layer will also affect the structure and morphology of this kind of roughness element,even when the underlying surface conditions are exactly the same.Thus,the dynamic roughness size can change(Yue et al.,2013;Zhang et al.,2013),which makes it even more challenging to understand the regional characteristics of turbulent flow.To eliminate the influence of the underlying surface vegetation on the characteristics of turbulence,bare soil data for the winter season are used in the present study.To analyze the effects of topographic heterogeneity on the characteristics of turbulence,the wind direc-tion and wind speed at the observation site are classified,and verify the applicability of MOST in research on the complex underlying surface of the Loess Plateau.In addition,the effects of shear and buoyancy contribution on turbulent kinetic energy(TKE)are studied through the classification of wind directions.

The remainder of the paper is structured as follows:First, the observational data and the parameterization of turbulence intensity are introduced in section 2.In section 3,the statistical characteristics of TKE and the contribution of shear and buoyancy to TKE are analyzed.Conclusions are presented in section 4.

2.Material and Methods

2.1.Observations

The observations were made in a valley region of Dingxi, over the Loess Plateau in Northwest China[(35◦35′N, 104◦37′E),elevation:1896.7 m above sea level;Fig.1a maps the topography of the study area,and Fig.1b is a photograph of the flux observation station].The research area belongs to a semi-arid climate region,with an annual average temperature of 6.3◦C,average annual precipitation of 419 mm, annual average wind speed of 1.8 m s−1,and average annual sunshine of 2500 hours.The maximum potential evaporation is greater than 1526 mm.

The observational data for December 2003 to January 2004 provide half-hour records of velocity from a sonic anemometer(CSAT3,Campbell Scientific,USA)located at height z=2 m on the northern side ofa 20 m tower.The sonic anemometer is aligned with local gravity and its boom is directed north.The three wind velocity components and virtual temperature are sampled at 10 Hz.Basic quality control of the raw 10 Hz data involve the detection of“soft”and“hard”spikes(Vickers and Mahrt,1997;Schmid et al.,2003;Zuoet al.,2009;Liu et al.,2012).Half-hour records occurring during precipitation,and runs with frictional velocity(u∗)of≤0.01 m s−1,are rejected(Song et al.,2010).Following the above screening process,we have available to us 320 simultaneous samples averaged for 30 min to stable stratification, and 445 samples averaged for 30 min to unstable atmospheric stratification.

Figure 2 shows that the most frequent wind direction range are 105◦–150◦(southeast)and 285◦–310◦(westnorthwest).Houses with different low heights of 3–5 m are distributed about 100 m away from the southeast direction of the observation station.There is relatively flat open land to the northwest,with a length of about 500 m and width of 300 m,without tall buildings and trees.Table 1 presents the prevailing wind direction aerodynamic roughness length and friction velocity at the Dingxi site for different stability conditions.

2.2.Turbulence flux source areas

To analyze the effects of the inhomogeneity of the topography on the characteristics of turbulence,the Flux Source Area Model(FSAM)(Schmid,1994)is selected in the present study to calculate the distribution of the turbulent flux source areas of Dingxi under different stability conditions in the dominant wind directions(Fig.3).The location of the observation point is used as the origin.The direction opposite to the horizontal wind speed is used as the x-axis. The direction perpendicular to the x-axis direction is used as the y-axis.When the contribution of the flux source area at the observation height of 2 m at Dingxi station reaches 90%: (1)In the southeast direction,a,d,e and Xm(where Xmis the maximum source location,i.e.,the upwind distance of the surface element with the maximal effect on a given sensor;a is the distance from the near end of the area to the sensor;e is the distance from the far near end of the area to the sensor (Schmid,1994);and d is the maximum lateral half-width of the source area),under conditions of stable atmospheric stratification,are 9.9,22.8,71.4 m and 21.7 m,respectively. Under neutral conditions their values are 12.4,29.3,99.3 m and 27.9 m,respectively,and under unstable conditions they are 13.6,32.2,114.9 m and 31.4 m,respectively.(2)In the west-northwest direction,under conditions of stable atmospheric stratification,a,d,e and Xmare 10.1,20.4,75.0 m and22.4 m,respectively;under neutral conditions they are 12.8, 25.0,99.6 m and 28.6 m,respectively;and under unstable conditions they are 14.0,27.4,114.6 m and 28.6 m,respectively.This shows that the contributing ranges of flux source area in the dominant wind direction are as follows:stable conditions＞neutral conditions＞unstable conditions.At the same time,the tensile range in the crosswind direction of the flux source area in the direction of southeast wind is significantly greater than that in the west-northwest direction, and this difference is mainly caused by topography.

Table 1.Aerodynamic roughness and friction velocity in different wind directions.

3.Results

3.1.Normalized standard deviation of the velocity fluctuations

In theory,the difference in the topography of uniform terrain and the density and structure of the roughness length and other physical properties is very small,meaning the turbulence can be regarded as isotropic,and the impact of changes in wind direction on the characteristics of turbulence can be ignored(Zhang et al.,2013).However,observational results (Nieuwstadt,1984;Smedman,1988;Martins et al.,2009; Liu et al.,2012)indicate that the constant values of the normalized speed variances with z/L andφx(z/L)also have significant differences,because of the different underlying surface vegetation states,even under conditions of uniform terrain.For complex terrain,the effects of topography on turbulence characteristicscannotbe ignored(Panofsky etal.,1977; Founda et al.,1997;Martins et al.,2009).Figures 4 and 5 present the changes inσu/u∗,σv/u∗andσw/u∗with z/L according to the southeast and west-northwest wind directions at Dingxi.Equations(1–3)and(4–6)are the optimal universal functions in the southeast and west-northwest directions, respectively:

The observations indicate thatσu/u∗,σv/u∗andσw/u∗in the semi-arid region of the Loess Plateau are functions of z/L under convective conditions and follow a 1/3 power law,and that the dispersion in the vertical direction is smaller than that in the horizontal direction.Founda et al.(1997),Al-Jiboori et al.(2001),Moraes et al.(2005),Martins et al.(2009)and Liu et al.(2012)reported that,under convective conditions, σw/u∗behaves similarly to that over flat terrain.Zhang et al.(2001)also found that the values ofσw/u∗tend to follow similarity relations,irrespective of the terrain,under unstable conditions.According to Panofsky and McCormick (1960),theσwis connected with the rates of shear and buoyant production of TKE.Because the turbulent exchange in the vertical direction is stronger and the turbulent adaptability is faster,the difference of the variance of velocityσw/u∗in different wind directions is relatively small.The differences of the ratio in the horizontal direction are more obvious,which is mainly caused by the heterogeneity of the underlying surface atthe observation station.Panofsky and Dutton(1984)hypothesized that,over heterogeneous terrain,the vertical fluctuations near the surface layer are produced by small-scale eddies that rapidly adjust to the terrain changes, and their hypothesis was verified by Moraes et al.(2005)and Martins et al.(2009)for convective and weakly stable conditions.

Recent studies show that,for stable conditions,σu/u∗, σv/u∗andσw/u∗satisfy the 1/3 power law.Theoretically, the atmospheric turbulence will be restricted when the atmospheric stratification is stable,so the standard deviation of wind velocity will decrease with z/L increasing.However, many observational results have demonstrated that the standard deviation of wind velocity increases with the enhanced atmospheric stability(Ma et al.,2002;Yue et al.,2011).This is because intermittent turbulence and other movements may be triggered when the atmospheric stability of the boundary layer increases to a certain extent(Zeri and S´a,2011).The results reported by Al-Jiboori et al.(2001)and Moraes et al.(2005)showed that the ratio ofσw/u∗,under stable conditions,increases slightly with stability—a finding laterverified by Martins et al.(2009),only for 0≤z/L≤1.5.

Table 2.Aerodynamic roughness and normalized standard deviation of wind speed.

Interestingly,the normalized standard deviation of vertical velocity of the Loess Plateau at Dingxi is very close to that of the observational results of the Qinghai–Tibetan Plateau(Ma et al.,2002)and the Mongolian Plateau(Yue et al.,2011).Al-Jiboori et al.(2001),Zhang et al.(2001)and Moraes et al.(2005)also showed the normalized standard deviation of vertical velocity over complex topography to beclose to that of uniform terrain for unstable conditions.Figures 4 and 5 present the function betweenσi/u∗(i=v,v,w) and z/L of our dataset and the Qinghai–Tibetan Plateau and Mongolian Plateau for comparison purposes.The results show that theσu/u∗andσv/u∗of the Loess Plateau at Dingxi are less than those of the Qinghai Tibetan Plateau, but larger than those of the Mongolian Plateau,which agrees with the notion that the topographic effects on horizontal wind speed are substantial.From the general topographic characteristics of the Qinghai–Tibetan Plateau,the Loess Plateau and the Mongolia Plateau,the topographic relief of the Qinghai–Tibetan Plateau is more marked than that of the Loess Plateau,and the changes of the terrain on the Loess Plateau are more prominent to those of the relatively flat Mongolia Plateau(Ma et al.,2002;Yue et al.,2011).From the results of the two prevailing wind directions at Dingxi, the difference in the normalized standard deviation of horizontal velocity is significant.The wind velocity fluctuation in the horizontal direction is mainly produced by quasi horizontal turbulence with relatively large scale,and its typical scale is generally several hundred meters or more,meaning its adaptability to the changes in terrain is slow.

3.2.Effects of horizontal wind speed on normalized standard deviation

Moraes et al.(2005)found that,for unstable conditions, there is good correlation betweenσu/u∗andσv/u∗and z/L, but only when the wind speed over the complex underlying surface is greater than a threshold(U＞1 m s−1).Therefore, the variances of the horizontal wind components are influenced by large convective cells.Anfossi et al.(2005)found that there is a tendency for slightly higher values ofσv/u∗with increasing stability for stable conditions over complex terrain.Figures 6 and 7 present the change of turbulent intensity with atmospheric stability in the southeast and westnorthwest wind directions under different wind speed conditions at the Dingxi site.There is a close connection between σu/u∗,σv/u∗andσw/u∗with z/L for all stability conditions, and the variances of the turbulence intensity are affected by the horizontal wind speed.Under unstable conditions,the decreasing trend of turbulence intensity with stability increases more significantly under the conditions of high speed wind than low speed wind.Under stable conditions,the increasing trend of turbulence intensity with stability increases more significantly under the conditions of high speed wind than low speed wind.The characteristics are consistent with the results of Martins et al.(2009).

3.3.Statistical characteristics of TKE

TKE is a measure of turbulence intensity,and it is one of the most important variables in micrometeorology(Niu et al.,2012).TKE involves the transfer of momentum,heat and moisture in the whole boundary layer.Research on TKE should concentrate on trying to understand the statistical properties of turbulence.Due to the complex nonlinear nature of the atmosphere,unresolved scales can fundamentally influence the resolved larger scales.Since explicitly characterizing the unresolved processes in not feasible,the statistics need to be parameterized as a function of the unresolved flow (Teixeira et al.,2008).According to MOST,the TKE after its nondimensionalization by the friction velocity will follow the 1/3 power law

Table 3.Standard deviation of the velocity over difference land surfaces for neutral stratification conditions.

(here,e is TKE and u∗is the friction velocity).

Figure 8 shows the scatter relationship between the dimensionless TKE of the dominant wind direction and the atmospheric stability of the study area.Equations(7)and(8) are the optimal functions of the TKE in the southeast and west-northwest directions:

It can be seen that dimensionless TKE of the near-surface at Dingxi follows MOST under convective and stable conditions.Notably,the values of the dimensionless turbulence intensity of the two prevailing wind directions are close to one another under neutral conditions,and the values are 11.1 and 10.5,respectively.Even when compared with the result of 12.85 for a city suburb under neutral conditions(Niu et al., 2012),the difference is relatively small,indicating that the constant coefficient a has certain universality.However,the differences between b and c values are relatively large,which reflects the effects of the heterogeneity of the near-surface on the turbulence intensity(Yue et al.,2010).

3.4.Contribution of the shear effect and buoyancy on TKE

Each item of the TKE budget equation describes a different part of the physical process of turbulent formation except the turbulence dissipation rate.Comparing the interactions among these parts helps to determine the ability of the airflow to maintain or change the turbulence flow.The coordinate system is selected to be consistent with the average wind direction.When assuming that the horizontal direction is uniform,and descent is ignored,a simplified form of the TKE equation can be obtained as

When the stratification is unstable,there is a good correlation between TKE and mechanical shear and buoyancy effects(Figs.9a and b).Under conditions of significant levels of 0.1‰the fitting relationship equations in the southeast direction are

respectively.In the west-northwest direction,the fitting formulas are

The fitting formula in the west-northwest direction is

4.Conclusions

Turbulent transport is one of the basic characteristics of the atmospheric boundary layer.Detailed knowledge of turbulence characteristics is important for understanding atmospheric phenomena,especially over heterogeneous terrain. Turbulence intensity and TKE parameters are beneficial for describing the exchange of properties between the surface and atmosphere effectively.

In this study,the standard deviations of velocities over the heterogeneous terrain of Dingxi are calculated for a valley region with the data for December 2003 to January 2004,and classified according to the wind direction and wind speed. The TKE is then also classified according to the wind direction.The applicability of MOST is investigated,and the results indicate that the normalized standard deviation of velocity fluctuations and TKE follow similar rules for the two prevailing wind directions.The ratio ofσw/u∗is 1.3 and 1.4 in the southeast and west-northwest directions,respectively, and the values are close to those of flat terrain under neutral conditions.However,σu/u∗andσv/u∗are 3.7 and 3.3 in southeast direction,and 2.9 and 3.2 in west-northwest direction,respectively.The values of dimensionless turbulence intensity in the southeastand west-northwestdirections under neutral conditions are 11.1 and 10.5,respectively.

Close correlation is found among the variances ofσu/u∗, σv/u∗andσw/u∗with z/L over the Dingxi site under different wind speed conditions,for all stability conditions.The decreasing trend of the ratio with z/L increases more significantly under the conditions of high speed wind than low speed wind for unstable conditions.Under stable conditions, the increasing trend of the ratio with z/L increases slightly more under the conditions of high speed wind than low speed wind.

Whether or not the conditions of stratification are stable, the shear effect of airflow enhances the turbulence,because the shear effect of the wind speed in winter over the Loess Plateau is strong.In the daytime,the buoyancy and shear effect of wind speed together constitute the production items of TKE under unstable stratification.At night,the mechanical shear becomes almost the only production form of turbulence.

Acknowledgements.This work was supported by the National Basic Research Program of China(Grant No.2012CB955304), the National Natural Science Foundation of China(Grant Nos. 41075008 and 40830957),the Special Financial Grant of China Postdoctoral Science Foundation(Grant No.2013T60901),the Arid Meteorology Foundation of the Institute of Arid Meteorology of the China Meteorological Administration(Grant No.IAM201408),and the Ten Talents Program of Gansu Meteorology Bureau.

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19 November 2014;revised 02 March 2015;accepted 17 March 2015)

∗Corresponding author:YUE Ping

Email:jqyueping@126.com