## 1. Introduction

Turbulent flux near the earth’s surface is the key quantity for hydrometeorological modeling of land–atmosphere interactions and remote sensing of water resources. Aerodynamic and thermal roughness lengths are the two crucial parameters for bulk transfer equations to calculate turbulent flux. They are defined so that a surface nonslip condition and surface skin temperature can be applied within the framework of Monin– Obukhov similarity theory. The aerodynamic roughness length *z*_{0}* _{m}* is a height at which the extrapolated wind speed following the similarity theory vanishes, whereas the thermal roughness length

*z*

_{0}

*is a height at which the extrapolated air temperature is identical to the surface skin temperature. Both parameters are not physically based and thus cannot be measured directly. Their values usually are inversely derived from observations in field experiments or empirically estimated for practical applications. Aerodynamic roughness length*

_{h}*z*

_{0}

*can be estimated according to the geometry of surface roughness elements (e.g., Wieringa 1993), whereas*

_{m}*z*

_{0}

*is usually derived from parameter*

_{h}*kB*

^{−1}[=ln(

*z*

_{0}

*/*

_{m}*z*

_{0}

*)], which in turn needs parameterization.*

_{h}In past decades, the parameterization of *kB*^{−1} has attracted a number of theoretical and experimental studies. It is generally accepted that *z*_{0}* _{m}* is different from

*z*

_{0}

*(e.g., Beljaars and Holtslag 1991). Brutsaert (1982, hereinafter B82) summarized previous works and concluded that*

_{h}*kB*

^{−1}may depend on the roughness Reynolds number Re

_{*}for aerodynamically smooth and bluff-rough surfaces, and also on the leaf area index and canopy structure for permeable roughness. Garratt and Francey (1978) recommended

*kB*

^{−1}= 2 for many natural surfaces. There have been numerous experimental studies on

*kB*

^{−1}for vegetation canopies. Many studies (e.g., Beljaars and Holtslag 1991; Stewart et al. 1994; Verhoef et al. 1997) reported large

*kB*

^{−1}values for partly vegetated surfaces. Diurnal variations of

*kB*

^{−1}were also found for homogeneously vegetated surfaces (Kustas et al. 1989; Sun 1999) and sparse canopies (Verhoef et al. 1997). Thus, some methods to formulate this parameter have been developed for various vegetation canopies (e.g., Sugita and Kubota 1994; Blümel 1999; Mahrt and Vickers 2004).

Over bare-soil surfaces, on the other hand, field experimental studies are still limited (Kohsiek et al. 1993; Verhoef et al. 1997; Ma et al. 2002; Yang et al. 2003). Flux parameterization for bare-soil surfaces is important not only for modeling heat transfer from nonvegetated surfaces but also for developing robust dual-source (canopy and undercanopy) models for vegetated surfaces (Su et al. 2001; Zeng et al. 2005). Such parameterization is particularly important for studies of arid and semiarid regions, where ground-sourced turbulent flux is the dominant term of the total flux or comparable to canopy-sourced flux. Current operational general circulation models tend to systematically underestimate the diurnal range of surface–air temperature differences in arid and semiarid regions (Yang et al. 2007a), which might be related to inappropriate schemes for bare-soil and undercanopy heat transfer. Several studies show that the widely used formula of B82 for bluff-rough surfaces may have overestimated mean values of *kB*^{−1} (Kohsiek et al. 1993; Voogt and Grimmond 2000; Kanda et al. 2007, hereinafter K07). Furthermore, diurnal variations of *kB*^{−1} for bare-soil surfaces have been reported, but there was no physical explanation (Verhoef et al. 1997; Ma et al. 2002; Yang et al. 2003).

In this study, we collected long-term datasets from seven sites with bare-soil surfaces (section 2). These sites represent a variety of surface conditions with surface roughness lengths varying from <1 to 10 mm and sensible heat fluxes from −50 to 400 W m^{−2}. We then introduced the surface flux parameterization theory (section 3a) and data filtering (section 3b) before estimating aerodynamic roughness length and surface emissivity (section 4). The surface emissivity is required to determine surface temperature from longwave radiation. Turbulent heat transfer over these surfaces was investigated in section 5. Major findings were 1) the diurnal variation of *kB*^{−1}, which means diurnal variation of excessive heat transfer resistance, and 2) negative values of *kB*^{−1} at night, which indicated that heat transfer can be more efficient than momentum transfer. Then, we used these datasets to evaluate several *kB*^{−1} schemes for bare-soil surfaces and attempted to identify an appropriate scheme to use with land surface models.

## 2. Data

Data were collected from seven sites in arid, semiarid, and semihumid regions of China through several international projects and a national project. Site information is summarized in Table 1, and the measurements associated with this study are given in Table 2. The datasets encompass a wide geographic distribution: two in Tibet, two in northwestern China, and three in northeastern China.

For the Tibetan Plateau, the Global Energy and Water Cycle Experiment (GEWEX) Asian Monsoon Experiment–Tibet (GAME-Tibet) research group provided data from two plateau sites that was collected during an intensive observing period (May–September 1998). The project was implemented through cooperation among scientists from Japan, China, and Korea (Koike et al. 1999). The two sites represented two typical surfaces: the NPAM (also called MS3478) site’s surface was a rough earth hummock whereas the Amdo (also called Anduo) site had a relatively smooth surface. The surfaces were covered with bare soils until late June after which they were partially covered with short grasses that were evenly grazed for the rest of the season. Hence, in our study, we only used the data for the May–June period. Detailed descriptions for the two sites can be found in Tanaka et al. (2001) and Ma et al. (2002) for Amdo, and Ma et al. (2002) and Yang et al. (2002, hereinafter Y02) for NPAM. All of the data are accessible on the GAME-Tibet Web site (http://monsoon.t.u-tokyo.ac.jp/tibet/).

The Heihe River Basin Field Experiment (HEIFE) was a cooperative project between China and Japan that was implemented in an arid river basin in northwestern China from 1990 to 1992. In this very dry area, two flux sites (Gobi and Desert) were selected for this study. The Gobi site was essentially flat, but the Desert site was characterized with sand dunes. Details for the two sites can be found in Wang and Mitsuta (1991) and Tamagawa (1996). The data were available from the HEIFE Internet site (http://ssrs.dpri.kyoto-u.ac.jp/~heife/).

In northeastern China, the Coordinated Enhanced Observing Period (CEOP; Koike 2004) Tongyu (TY) experiment was implemented in Jilin Province by Chinese scientists and is ongoing. This experiment provided data at two nearby sites, the so-called Tongyu-cropland (TY-crop) and Tongyu-grassland (TY-grass), from October 2002 to September 2003. TY-crop was a flat cropland and TY-grass was a flat and degraded grassland in the summer season, but they turned to bare soils in the winter season. We used the data for the bare-soil period (October 2002 to March 2003). Details about the experiments can be found in Liu et al. (2006). The data are available from the CEOP Web site (http://www.ceop.net/). Another experiment in northeastern China was implemented at Xiaotangshan (XTS) near Beijing by Beijing Normal University (BNU) in the summer of 2005, when the surface was covered with bare soil. Later the surface was turned into cropland (Liu et al. 2007).

At all seven sites, wind speed and direction, temperature, humidity, turbulent momentum and heat flux, and radiation were measured. Turbulent fluxes were measured by eddy-covariance technique with 30-min averaging time at all sites, except at the XTS site where an interval of 10 min was used. The downward and upward radiation components were measured at all sites. Surface skin temperature was converted from the upward and downward longwave radiation data. The surface emissivity used for this conversion was determined as described in section 4b. An exception was the Gobi site, where we used surface temperature measured by four thermometers because there was a big discrepancy between the measured surface temperature and the temperature converted from the measured longwave radiation.

## 3. Theoretical consideration and data filtering

### a. Surface flux parameterization

*U*(m s

^{−1}) at level

*z*(m), air temperature

_{m}*T*(K) at level

_{a}*z*(m), ground skin temperature

_{h}*T*(K), and roughness lengths

_{g}*z*

_{0}

*(m) and*

_{m}*z*

_{0}

*(m), surface fluxes can be parameterized aswhere*

_{h}*τ*(kg m

^{−1}s

^{−2}) is the surface stress,

*H*(W m

^{−2}) is the sensible heat flux,

*r*(s m

_{m}^{−1}) is the momentum transfer resistance,

*r*(s m

_{h}^{−1}) is the heat transfer resistance,

*ρ*(kg m

^{−3}) is the air density,

*θ*(=

_{a}*T*+

_{a}*z*/

_{h}g*c*) and

_{p}*θ*(=

_{g}*T*) are local potential temperatures,

_{g}*c*(=1004 J kg

_{p}^{−1}K

^{−1}) is the specific heat of air at constant pressure,

*g*(=9.81 m s

^{−2}) is the gravitational constant,

*k*(=0.4) is the von Kármán constant; Pr is the Prandtl number (=1 if

*z*/

*L*≥ 0 and 0.95 if

*z*/

*L*< 0),

*L*[≡

*T*

_{a}

*u*

^{2}

_{*}/(

*kgT*

_{*})] is the Obukhov length (m),

*u*

_{*}[≡(

*τ*/

*ρ*)

^{1/2}] is the frictional velocity (m s

^{−1}),

*T*

_{*}[≡−

*H*/(

*ρc*

_{p}u_{*})] is the frictional temperature (K), and

*ψ*and

_{m}*ψ*are the integrated stability correction terms for wind and temperature profiles, respectively.

_{h}*x*= (1 − 19

*z*/

_{m}*L*)

^{1/4},

*x*

_{0}= (1 − 19

*z*

_{0}

*/*

_{m}*L*)

^{1/4},

*y*= (1 − 11.6

*z*/

_{h}*L*)

^{1/2}, and

*y*

_{0}= (1 − 11.6

*z*

_{0}

*/*

_{h}*L*)

^{1/2}.

The above bulk flux parameterization requires roughness lengths *z*_{0}* _{m}* and

*z*

_{0}

*. In general,*

_{h}*z*

_{0}

*and*

_{m}*z*

_{0}

*can be derived from turbulent flux data; however, we normally want turbulent flux and hence need a parameterization of*

_{h}*z*

_{0}

*and*

_{m}*z*

_{0}

*(or*

_{h}*kB*

^{−1}). Table 3 shows several parameterization schemes available in the literature. Verhoef et al. (1997) introduced details of Sheppard (1958, hereinafter S58), Owen and Thompson (1963, hereinafter OT63), and B82. Zilitinkevich (1995, hereinafter Z95) has been widely used in weather forecasting models since Chen et al. (1997). Zeng and Dickinson (1998, hereinafter Z98) has been used in a land surface model to unify undercanopy heat transfer processes between dense and sparse canopies (Zeng et al. 2005). K07 was derived from urban canopy experiments. Yang et al. (2007b, hereinafter Y07b) has been incorporated in a land data assimilation system for arid and semiarid regions. Y07b is a revised version of Yang et al. (2002) and a note is given in Table 3 for this revision. All the schemes in Table 3 will be evaluated in section 6.

### b. Data filtering

*z*

_{0}

*and ε*

_{m}*(or*

_{g}*T*) are estimated from the observed data. In this analysis, we excluded the data under the following conditions, which deviate far from the similarity theory:where

_{g}*H*

_{obs}is the observed heat flux,

*H*

_{prf}is the flux that best fits observed wind and temperature profiles, and

*H*

_{sfc}is the flux derived from Eqs. (1)–(4) with a scheme in Table 3.

Equations (5a) and (5b) are the minimum requirements to be applied for data filtering. Equations (5c) and (5d) are based on the assumption that the true heat flux should be within the range of heat flux values predicted by the schemes in Table 3. This assumption is generally true because some schemes in Table 3 overestimate heat flux while others underestimate (see details in section 6). This range is relaxed by 20% in Eqs. (5c) and (5d) because we cannot exclude the possibility that some data may lie beyond such a range. Equations (5e) and (5f) are applied to satisfy the similarity theory and to consider the high sensitivity of *kB*^{−1} to measurement errors of small heat fluxes, respectively. In summary, Eq. (5a) is applied to estimate *z*_{0}* _{m}*, Eqs. (5a) and (5b) are applied to estimate surface emissivity ε

*, Eqs. (5a)–(5d) are applied to evaluate schemes, and all are applied to derive*

_{s}*kB*

^{−1}.

## 4. Determination of surface roughness length and emissivity

### a. Aerodynamic roughness length

*z*

_{0}

*, is physically related to the geometric roughness of underlying elements for aerodynamically rough surfaces. It is not sensitive to diurnal variations of atmospheric stability (Sun 1999). Kohsiek et al. (1993) estimated*

_{m}*z*

_{0}

*from observed*

_{m}*U*/

*u*

_{*}under near-neutral conditions. To derive stable and reliable

*z*

_{0}

*, Yang et al. (2003) suggested fully using observed data under both neutral and nonneutral conditions. Following the idea, we estimated*

_{m}*z*

_{0}

*using a statistical method. The logarithmic wind profile is rewritten as*

_{m}Given all the observed *u*_{*}, *T*_{*}, and wind speed, a dataset of ln(*z*_{0}* _{m}*) was generated. Because of observation errors in the input data or meteorological conditions that did not satisfy the similarity theory, the derived ln(

*z*

_{0}

*) data were not single values. The optimal value of*

_{m}*z*

_{0}

*would correspond to the peak frequency in the histogram of ln(*

_{m}*z*

_{0}

*). For example, Fig. 1 shows the frequency distribution of ln(*

_{m}*z*

_{0}

*) for the Amdo site, with a bin width of 0.2; ln(*

_{m}*z*

_{0}

*) = −7.1 has the maximum frequency in the smoothed curve, and therefore the optimal value of*

_{m}*z*

_{0}

*is exp(−7.1) m.*

_{m}Table 4 shows the estimated *z*_{0}* _{m}* for each site. The rough earth hummock surface of NPAM resulted in a larger value than the smoother surface of Amdo. The Desert site with dunes had a larger

*z*

_{0}

*than the flat Gobi site. The Tongyu cropland had a larger length than the nearby grassland. The*

_{m}*z*

_{0}

*for XTS (9.1 mm) is comparable to the value in Liu et al. (2007) and was the largest among all sites. For the two plateau sites (Amdo and NPAM), Ma et al. (2002) and Yang et al. (2003) also reported*

_{m}*z*

_{0}

*values. The values presented here are comparable to that in Yang et al. (2003) but smaller than those in Ma et al. (2002) who reported the averaged*

_{m}*z*

_{0}

*for a longer period, from bare soil to the grass-growing season. For the Gobi and Desert sites, Ma et al. (2002) reported*

_{m}*z*

_{0}

*of 2.6 mm, greater than ours for the Gobi site (0.63 mm) but the same for the Desert site (2.7 mm). In summary, these sites represent a variety of conditions for surface roughness lengths from smooth to rough.*

_{m}### b. Surface emissivity

*T*

_{g}is converted from observed upward longwave radiation (

*R*

^{↑}

_{lw}) and downward longwave radiation (

*R*

^{↓}

_{lw}):where

*σ*= 5.67 × 10

^{−8}W m

^{−2}K

^{−4}.

*= 1 while Verhoef et al. (1997) assumed ε*

_{s}*varying from 0.91 to 0.94. There was no direct evidence to justify such selection for different study sites. In this study, we used a physically based, semiempirical method to estimate ε*

_{s}*. According to heat transfer theory, heat flux (positive if upward) must have the same sign as that of*

_{s}*θ*(ε

_{g}*) −*

_{s}*θ*; that is,

_{a}Under near-neutral conditions, if ε* _{s}* is either overestimated or underestimated slightly, then the estimated

*H*

_{sfc}may have the sign opposite to the observed

*H*

_{obs}; therefore, the difference between

*H*

_{sfc}and

*H*

_{obs}is sensitive to the value of ε

*. Considering this sensitivity, we estimated ε*

_{s}*using near-neutral heat fluxes by minimizing the root-mean-square difference (RMS) between*

_{s}*H*

_{obs}and

*H*

_{sfc}.

The emissivity is assumed to be a constant throughout the observing period for each site, though it may change with soil moisture. The algorithm is as follows: 1) Given ε* _{s}*, estimate surface temperature

*T*(ε

_{g}*) by Eq. (7). 2) If −10 W m*

_{s}^{−2}<

*H*

_{obs}< 30 W m

^{−2}then calculate

*H*

_{sfc}from Eqs. (2)–(4) and Eq. (8), with

*z*

_{0}

*in Table 4 and*

_{m}*z*

_{0}

*given by a*

_{h}*kB*

^{−1}scheme. Note that small heat flux may occur in very stable cases and these cases should be rejected. 3) Calculate the RMS between

*H*

_{obs}and

*H*

_{sfc}. 4) Go back to step 1 until RMS(ε

*) is minimized.*

_{s}Figure 2 shows the variation of RMS with ε* _{s}* for the Amdo site. It is clear that the ε

*value corresponding to the minimum RMS is not very sensitive to the choice of*

_{s}*kB*

^{−1}schemes. Similar conclusions for other sites can be drawn from Table 5. However, the estimated values seemed too low for XTS (0.855) and too high for NPAM (1.055); thus the values were adjusted to be 0.9 for XTS and 1.0 for NPAM in the following analyses. These unrealistic values can be attributed to errors in measured

*R*

^{ ↑}

_{lw}in Eq. (7) or the mismatch of footprints between the radiation measurements and turbulent flux measurements.

## 5. Characteristics of turbulent flux transfer

### a. Diurnal variation of kB^{−1}

Given *z*_{0}* _{m}*,

*θ*,

_{g}*U*, and

*θ*,

_{a}*kB*

^{−1}can be inversely derived from

*H*

_{obs}through the following iterations: 1) assume

*z*

_{0}

*=*

_{h}*z*

_{0}

*, 2) calculate*

_{m}*H*

_{sfc}from Eqs. (1)–(4) with an analytical solution of Yang et al. (2001); 3) if

*H*

_{sfc}≠

*H*

_{obs}then adjust

*kB*

^{−1}according to the difference in heat transfer resistance; 4) go back to step 2 until

*H*

_{sfc}=

*H*

_{obs}. If there were multiple combinations of wind speed and air temperature, then

*kB*

^{−1}was calculated for each combination and their average was used in the analysis.

Figure 3 shows that *kB*^{−1} exhibited a large variability at each site and diurnal variations were particularly obvious at Amdo and NPAM sites, with higher values during the day and lower values at night. Figure 4a shows mean values and standard deviations of *kB*^{−1} for the individual sites in ascending order of *z*_{0}* _{m}*. Because of the diurnal variations, data have been grouped into two classes: an

*H*> 0 (or daytime) case and an

*H*< 0 (or nighttime) case;

*kB*

^{−1}generally increased with respect to

*z*

_{0}

*, but this tendency was contaminated by its large variance (1.6–3.2) at night when the derived*

_{m}*kB*

^{−1}was more sensitive to measurement errors of heat flux. Also, it is clear that the diurnal variability of

*kB*

^{−1}at individual sites (Fig. 3) was larger than or comparable to its cross-site variability (Fig. 4a).

Figure 4b shows the mean values of *z*_{0}* _{h}* for each site. It indicates the mean

*z*

_{0}

*does not significantly change with*

_{h}*z*

_{0}

*. Therefore, the concept of*

_{m}*kB*

^{−1}, which scales

*z*

_{0}

*by*

_{h}*z*

_{0}

*, is questionable. Accordingly, the heat transfer coefficient*

_{m}*C*increases with respect to

_{H}*z*

_{0}

*, but its increase is not as fast as for the momentum transfer coefficient*

_{m}*C*, as shown in Figs. 4c,d. (Note

_{D}*C*and

_{H}*C*are the transfer coefficient values that have been normalized to a height of 10 m so that they are comparable at the individual sites.) Mahrt (1996) speculated that individual roughness elements may enhance momentum transfer through form drag but contribute little to area-averaged heat transfer. According to our results, this speculation is partially true and it may be more appropriate to say that the increase of surface roughness lengths contributes more to momentum transfer than to heat transfer.

_{D}### b. Negative values of kB^{−1}

Verhoef et al. (1997) reported negative *kB*^{−1} values for a nearly aerodynamically smooth bare-soil surface (Re_{*} ∼ 1), which is consistent with those predicted by theory (Kondo 1975; B82). In this study, all the sites were aerodynamically rough. Momentum transfer for aerodynamically bluff and rough flows is traditionally considered to be more efficient than heat transfer (or *kB*^{−1} > 0) because momentum transfer can be enhanced through form drag. However, a number of negative values of *kB*^{−1} occurred during the night for these surfaces. This finding indicates that heat transfer efficiency can exceed momentum transfer, which was also reported by Su et al. (2001) for forced convection.

However, there is a lack of theory to explain such a mechanism. Possibly, our findings can result from the breakdown of the Monin–Obukhov similarity theory due to interactions between active and inactive turbulence in the atmospheric surface layer (ASL). Choi et al. (2004) reported a lower efficiency of momentum exchange over a Tibetan site than over terrains at low altitudes. Unlike the similar magnitudes of transfer efficiency of heat and water vapor, momentum exchange was less efficient than the Monin–Obukhov similarity prediction. Recent experimental results show that inactive motions play an important role in the ASL and transport processes are sensitive to outer-layer scaling parameters such as boundary layer depth (e.g., McNaughton 2004; Hong et al. 2004). In fact, the above-mentioned diurnal variations of *kB*^{−1} could be attributed to those of boundary layer depth and the associated roles of inactive (nonlocal) eddies in the outer layer. Interestingly, for two Tibetan sites, Hong et al. (2004) reported that such inactive eddies in low frequencies did not affect momentum flux but caused heat flux to deviate from the Monin–Obukhov similarity theory.

### c. Excess resistance

Heat transfer resistance *r _{h}* is linked with

*z*

_{0}

*or*

_{h}*kB*

^{−1}through Eq. (2b), and a small z

_{0}

*would result in a large resistance. Table 6 shows mean values of observed*

_{h}*r*and heat flux

_{h}*H*

_{obs}, together with mean values of aerodynamic resistance

*r*derived with

_{ah}*kB*

^{−1}= 0 and the associated heat flux

*H*

_{est}. The excess resistance

*δr*(=

*r*−

_{h}*r*) usually increases with

_{ah}*z*

_{0}

*and is larger during the day than at night. For some surfaces, the excess resistance even becomes negative at night. The excess heat flux*

_{m}*δH*(=

*H*

_{est}−

*H*

_{obs}) during the day is much larger than at night. So the daytime excess resistance affects heat transfer far more than that of nighttime, because of smaller total resistance during the day. Heat flux parameterized with

*kB*

^{−1}= 0 is nearly double the observed for the daytime period and rough surfaces, strongly suggesting the necessity to account for the excess resistance in bulk flux parameterizations.

### d. Comparisons with previous experiments and theories

Figure 5 shows mean *kB*^{−1} for each site of this study (for both *H* > 0 and *H* < 0 cases) and other bare-soil experimental data in the literature (Kohsiek et al. 1993; Stewart et al. 1994; Verhoef et al. 1997), formula B82 for bluff-rough surfaces, formula K07 for urban canopies, and the value −1.1 of Kondo (1975) for aerodynamically smooth surfaces. Our mean *kB*^{−1} values were larger than that of Verhoef et al. (1997) while smaller than or close to that of Kohsiek et al. (1993) and Stewart et al. (1994), because *kB*^{−1} increased with *z*_{0}* _{m}* and our surfaces were rougher (

*z*

_{0}

*= 0.7–9 mm) than the former study (*

_{m}*z*

_{0}

*= 0.1 mm) while smoother than or comparable to the latter two studies (*

_{m}*z*

_{0}

*= 13 mm). Therefore, all of the experimental results in previous studies are essentially consistent with our findings. For the two plateau sites (Amdo and NPAM), the diurnal variations of*

_{m}*kB*

^{−1}have been reported by Ma et al. (2002) and Yang et al. (2003). However, the reported mean values were different from our study because they either included a vegetated period or used a different criterion for data filtering.

## 6. Evaluation of *kB*^{−1} schemes

### a. Intercomparisons of kB^{−1}

Schemes for *kB*^{−1} are developed to derive *u*_{*} and *T*_{*}, which in turn are variables of the schemes in Table 3. Therefore, the following numerical iteration algorithm was applied to derive *kB*^{−1}: 1) assume *kB*^{−1} = 0; 2) derive the value of *z*_{0}* _{h}* by

*z*

_{0}

*=*

_{h}*z*

_{0}

*exp(−*

_{m}*kB*

^{−1}); 3) given

*z*

_{0}

*and*

_{m}*z*

_{0}

*, calculate*

_{h}*u*

_{*},

*T*

_{*}, and

*H*

_{sfc}from Eqs. (1)–(4) with an analytical solution of Yang et al. (2001); 4) given

*u*

_{*}and

*T*

_{*}, calculate

*kB*

^{−1}according to one of the schemes in Table 3; 5) go to step 2 until the difference in

*T*

_{*}between two successive iterations is less than 0.0001 K, a threshold value used in this study. Table 7 shows the correlation coefficient squared

*R*

^{2}between observed

*kB*

^{−1}(in Fig. 3) and that parameterized with schemes in Table 1. Except for the sites with a small number of data samples (Gobi and Desert), Y07b gives a higher

*R*

^{2}than other schemes. Figure 6 shows comparisons of composite diurnal variations of

*kB*

^{−1}between observation and schemes for the individual sites. The composite values for a time slot were calculated only when there was enough data (i.e., sample number ≥5). All of the schemes parameterized with Re

_{*}produced a general increase in

*kB*

^{−1}with respect to

*z*

_{0}

*. Overall, S58 and OT63 produced*

_{m}*kB*

^{−1}more or less comparable to the observed values, but other schemes either overestimated or underestimated significantly. No scheme produced clear diurnal variations and negative values of

*kB*

^{−1}(as observed in section 5) except Y07b, which gave better agreements.

In fact, the different performance between Y07b and other schemes is not surprising. The former uses *u*^{0.5}_{*}|*T*_{*}|^{0.25} to parameterize *kB*^{−1}, and therefore the diurnal variation of *kB*^{−1} can be accounted for with *T*_{*}. Other schemes use *u*_{*} or Re_{*} for the parameterization [ln(Re_{*}) in S58; Re^{0.25}_{*} in B82 and K07; Re^{0.45}_{*} in OT63 and Z98; and Re^{0.5}_{*} in Z95]. This suggests a parameter combining both *u*_{*} and *T*_{*} can be a potential index for more realistic parameterizations of *kB*^{−1}.

### b. Intercomparisons of turbulent fluxes

At our sites wind speed and air temperature were measured at multiple levels, so there were many combinations of wind speed and air temperature. Bulk parameterization with these different combinations and surface conditions (surface skin temperature and roughness lengths) may result in different flux. The following evaluation is based on the combination that gives the minimum root-mean-square error (RMSE) in heat flux.

All of the schemes produced similar mean biases (MBE) and RMSE in momentum flux for all the sites (data not shown). However, the errors in heat flux were distinct. Tables 8 and 9 show MBE in predicted heat flux and the standard deviation of the difference between the observed and the predicted, respectively. The boldface numbers represent the three best schemes. The two indices show that Y07b is among the three best schemes for all sites and it has the smallest errors on average. OT63 and S58 also have small errors except at XTS for S58 and at Amdo for OT63. B82 produces good results for Amdo and TY-grass but tends to underestimate heat flux for other sites. Three other schemes (Z95; Z98; K07) clearly overestimate flux for all sites. K07 has small errors for the roughest site (XTS) because K07 was fitted with urban canopy data. Recalling Fig. 6, it is clear that a scheme that gives high (low) *kB*^{−1} values has produced low (high) heat flux.

### c. Sensitivity analyses

First, the sensitivity to the surface emissivity was investigated. We calculated heat flux with surface emissivity varying from 0.85 to 1.0 for all sites except for Gobi, where the ground temperature was directly measured by four thermometers. Figures 7 and 8 show the variations of RMSE and *R*^{2} with emissivity, respectively. The vertical dashed line in each panel corresponds to the optimal emissivity value in Table 5. Despite some uncertainties in determining the emissivity, Y07b obviously gives small RMSE and the highest *R*^{2} values over a range near the optimal emissivity, showing better prediction than other schemes.

Second, the sensitivity to universal functions for stability correction was tested. We applied Dyer’s (1974) universal functions to the analyses, in comparison to Högström’s (1996) universal functions used above. Only minor changes in errors and the similar overall performance (data not shown) suggest our results are not sensitive to universal functions of the similarity theory.

### d. The role of diurnal variation of kB^{−1}

Understanding the diurnal variation of *kB*^{−1} is important in estimating heat flux. Figure 9 shows the averaged diurnal variations of relative mean biases in heat flux prediction for the seven sites. OT63, Z95, Z98, and K07 produce clear diurnal variation of errors in heat flux, positive biases during the day, and negative biases at night. S58 and B82 underestimate flux for almost all time slots. Y07b shows no more than 10% mean bias for all time slots, indicating its capability to reflect the diurnal variation of *kB*^{−1}. In summary, it is important for a scheme to give not only the mean value but also the diurnal variation of *kB*^{−1}.

## 7. Conclusions and comments

Understanding the characteristics of turbulent transfer over bare-soil surfaces is crucial for parameterizing turbulent flux over nonvegetated surfaces. We presented a comprehensive analysis on characteristics of heat transfer over bare-soil surfaces in arid and semiarid regions and also an extensive evaluation of several schemes in the literature. The major findings from our study are as follows:

- Mean
*z*_{0}does not change significantly with_{h}*z*_{0}, and therefore there was no robust basis to parameterize_{m}*z*_{0}through_{h}*kB*^{−1}or*z*_{0}, although it is widely used. Observations also indicated that the heat transfer coefficient increases with_{m}*z*_{0}but not as much as the momentum transfer coefficient does._{m} - Diurnal variations of
*z*_{0}are common for all the bare-soil surfaces. The diurnal variability of_{h}*kB*^{−1}at individual sites can be larger than or comparable to cross-site variability. This indicates that*z*_{0}and_{h}*kB*^{−1}are flow dependent and the consideration of both*u*_{*}and*T*_{*}is important for improving flux parameterization. - Diurnal variations of
*kB*^{−1}cause much larger excessive heat transfer resistances during the day than at night. Using a mean value of*kB*^{−1}may lead to significant overestimation (underestimation) in the daytime (nighttime). A complete neglect of this resistance may give rise to more than 50% overestimation of heat flux in the daytime for rough surfaces. - Negative values of
*kB*^{−1}are often observed for aerodynamically rough surfaces, requiring theoretical explanations. Such occurrence indicates heat transfer efficiency may exceed that of momentum transfer, or the excess resistance for heat transfer can become negative if the aerodynamic transfer resistance becomes too large. This is in contrast to the traditional opinion that momentum transfer is more efficient than heat transfer because of the enhanced momentum transfer through form drag around individual roughness elements (Thom 1972; Roth 1993). This “abnormal” phenomenon may be attributed to heat transport by inactive (nonlocal) eddies in the outer layer. - All of the parameterization schemes considered here perform equally well for momentum flux prediction, but they show different skills for heat flux prediction. In general, the schemes parameterized with
*u*_{*}cannot produce the diurnal variations of*kB*^{−1}whereas a scheme (Y07b) parameterized with*u*_{*}and*T*_{*}does. For the sites with*z*_{0}ranging from <1 to 10 mm, most schemes either significantly underestimate or overestimate heat flux. Y07b generally performs better for these land sites and may be a better choice to be incorporated into current land surface models._{m}

Last, we have not considered in this study the potential problem in surface energy budget closure that has been widely observed (e.g., Twine et al. 2000; Wilson et al. 2002; Baker and Griffis 2005). If future work confirms that the reported sensible heat flux was underestimated by the current eddy-covariance technique, *kB*^{−1} and excessive resistance should have smaller values than reported here. In accord with this, the Y07b scheme and/or other schemes would require recalibrations, but most of the above conclusions should be still valid.

The GAME-Tibet project was supported by the MEXT, JST, FRSGC, and NASDA of Japan, the Chinese Academy of Sciences, and the Asian Pacific Network, and Dr. Kenji Tanaka from Kumamoto University provided turbulent flux data for the Amdo site. The CEOP/Tongyu project was supported by Institute of Atmospheric Physics, CAS. The Xiaotangshan experiment was supported by an NSFC Project (40671128) and the GEF Project (TF053183) of China. HEIFE was a cooperative project between China and Japan and implemented by DPRI, Kyoto University, Japan, and Lanzhou Institute of Plateau Atmospheric Science of CAS. Joon Kim acknowledges the support from the Eco-Technopia 21 Project of the Ministry of Environment and the BK21 program of the Ministry of Education and Human Resource of Korea. We are grateful to the reviewers whose suggestions and discussions have helped the authors to improve the quality of the paper.

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Project, location, observing period, and vegetation information at the seven sites.

Measuring levels of mean variables and turbulent fluxes at the seven sites (upward and downward longwave radiation were measured at all the stations).

Flux parameterization schemes selected for this intercomparison study; Re_{*} = *z*_{0}_{m}u_{*}/*ν*, Pr = 0.71, *k* = 0.4, *ν* is the fluid kinematical viscosity, *α* = 0.52 in OT63 and Z98, and *β* = 7.2 in Y07b.

Estimated aerodynamic roughness lengths for the seven sites.

Estimated surface emissivity for the seven sites except the Gobi, using different *kB*^{−1}. The estimated values seem too low for XTS and too high for NPAM, and thus the optimal value was adjusted to be 0.9 for XTS and 1.0 for NPAM in this study.

Mean values of aerodynamic parameters, resistance (*r _{h}*: total resistance for heat transfer, derived from observed fluxes;

*r*: resistance calculated with

_{ah}*kB*

^{−1}= 0;

*δr*: excess resistance (=

*r*−

_{h}*r*), and heat fluxes (

_{ah}*H*

_{obs}: observed fluxes;

*H*

_{est}: fluxes calculated with

*kB*

^{−1}= 0;

*δH*: excess heat fluxes (=

*H*

_{est}−

*H*

_{obs}). Sites are listed in the ascending order of

*z*

_{0}

*.*

_{m}Correlation coefficient squared between observed *kB*^{−1} (in Fig. 3) and that parameterized with schemes in Table 3. The two columns Gobi and Desert have small numbers of samples (see Table 6 sample column).

MBE (W m^{−2}) in heat fluxes produced by the seven schemes for the seven sites. Boldface numbers are the best three among these schemes.

Similar to Table 8, but for std dev (W m^{−2}) of the difference between observed and predicted heat fluxes.