## 1. Introduction

In large-scale numerical climate, weather prediction, air quality, and hydrological modeling, the terrain is often heterogeneous over the area represented by the models’ grid size. Land cover characteristics—such as surface roughness, albedo, and Bowen ratio—govern the local vertical surface fluxes of momentum, heat, water vapor, and other scalars (e.g., Milly and Shmakin 2002). Hence, it is necessary to consider the properties of the atmospheric inertial sublayer (ISL; Garratt 1994) or the so-called atmospheric surface sublayer (ASL; Brutsaert 1982) and the underlying heterogeneous terrain averaged over the grid in the model. For example, Taylor (1987) described these area-averaged problems and introduced the flux formulation methodologies for determining an effective roughness length over an area of heterogeneous terrain. A few models have been developed for estimating the effective roughness length of heterogeneous terrain (e.g., Mason 1988; Garratt 1994; Goode and Belcher 1999; Baldauf and Fiedler 2003; Hasager et al. 2003; Tsai and Tsuang 2005). Nonetheless, there is a lack of reliable datasets that can be used for evaluating such effective roughness concepts.

Rice paddies are a major land use type in Asia. The unique irrigation management of intermittent flooding makes the land cover characteristics of rice paddies different from those of other agricultural and forest ecosystems (e.g., Harazono et al. 1998; Hong et al. 2002; Tsai et al. 2007). In several field studies, discrepancies in the values of the aerodynamic roughness of a rice paddy have been reported with values ranging from approximately 10^{−3} to 10^{−1} m (Gao et al. 2003; Kotani and Sugita 2005; Tsai and Tsuang 2005) (Table 1). On the other hand, in some state-of-the-art models, the roughness lengths are assigned values that vary from 0.06 to 0.2 m (Dudhia et al. 2005; ENVIRON 2006; Grell et al. 1995; Hagemann 2002; U.S EPA 2004). From these studies, it can be seen that the representative values for aerodynamic roughness over a rice paddy vary with sites. Zeng and Wang (2007) have shown the representative value for aerodynamic roughness over a cropland site is not only dependent on individual paddies but also on obstacles in the area, such as buildings, trees and the aboveground biomass of the paddy vegetation.

Tethersonde and eddy covariance (EC) systems are often utilized to study the ISL located within the atmospheric surface layer but above the roughness sublayer (e.g., Kitchen et al. 1983; Verma et al. 1986; McMillen 1988; Parlange and Brutsaert 1993; Sugita et al. 1997; Baldocchi et al. 2001; Kustas et al. 2005). Although both methods used are based on similar assumptions, the tethersonde system measures the vertical profiles of properties within a certain temporal period (e.g., 30 min or an hour). In contrast, the EC can measure single-level data continuously and automatically (also 30 min, an hour, etc.). Intercomparisons of aerodynamic roughness measured by independent systems are valuable for identifying the characteristics derived from the two systems (e.g., Meek et al. 2005).

In this study, data are analyzed separately for wind flow over a paddy-dominated area (PDA) and a rice paddy interspersed with buildings (PIB). The aerodynamic roughness lengths *z*_{0m}, friction velocities *u**, and the Bowen ratios *B* from two footprint areas determined by both the EC system and the profile method are presented and compared. Additionally, the height ranges of the ISL determined from the tethersonde profile data are also reported. Finally, the observed values of aerodynamic roughness are compared with some classical effective roughness models of Taylor (1987), Mason (1988), and Tsai and Tsuang (2005).

## 2. Methodology

### a. Profile method

*ρ*and

*c*are the density and the specific heat capacity of the air, respectively;

_{p}*u*,

*θ*, and

*q*are wind speed, potential temperature and specific humidity measured at height

*z*, respectively;

*u** is the friction velocity;

*z*

_{0m}is the aerodynamic roughness of momentum;

*L*is the M-O stability length;

*H*= (

_{υ}*H*+ 0.61

*θc*) (Brutsaert 1982);

_{p}E*H*is the sensible heat flux;

*E*is the evaporation rate;

*θ*

_{0}and

*q*

_{0}are the potential temperature and specific humidity at (

*d*

_{0}+

*z*

_{0m}), respectively. Note that in Eq. (2), if we change aerodynamic roughness

*z*

_{0m}to the roughness for heat

*z*

_{0T}, then

*θ*

_{0}becomes the potential temperature at the height of (

*d*

_{0}+

*z*

_{0T})—that is,

*θ*

_{0}=

*θ*

_{0}(

*d*

_{0}+

*z*

_{0T}). Nonetheless, because both

*θ*

_{0}(

*d*

_{0}+

*z*

_{0T}) and

*z*

_{0T}were not measured, this change will add an additional unknown. Similarly, an additional unknown will be added if

*z*

_{0m}is substituted by the roughness for moisture

*z*

_{0q}in Eq. (3). These changes will increase the complexity to retrieve the aerodynamic roughness from the profile data using Eqs. (1)–(4). Therefore, we did not use

*z*

_{0T}and

*z*

_{0q}in Eqs. (2) and (3), respectively, for retrieving aerodynamic roughness

*z*

_{0m}. The forms of stability functions for heat Ψ

*and water vapor Ψ*

_{h}*is determined according to Businger et al. (1971); however, for momentum Ψ*

_{υ}*, a modified form of the stability function by Brutsaert (1992) is adopted.*

_{m}Aerodynamic roughness *z*_{0m}, zero-displacement height *d*_{0}, *u**, surface sensible heat flux *H*, surface latent heat flux *LE*, *L* and the height range of the ISL can all be determined by fitting Eqs. (1)–(4) using profile data to have the maximum correlation between calculated and observed wind speeds at heights within the ISL height range (e.g., Parlange and Brutsaert 1990; Mikami et al. 1996; Jacobs and Brutsaert 1998; Tsuang et al. 2003; Tsai and Tsuang 2005). The integral forms (Tsuang et al. 2003) of Businger et al. (1971)’s equations are used for fitting the profile data when the profiles of wind speed, potential temperature, and specific humidity within the ISL, along with the net radiation and ground heat flux, are measured (Tsuang et al. 2003; Tsai and Tsuang 2005). Please see appendix A for more details. The fitting error is much less under unstable conditions (Tsai and Tsuang 2005), and thus only data under unstable conditions were used.

*B*) using the profile data can be determined (e.g., Grimmond and Oke 1991) as

_{p}*L*is the latent heat of vaporization, and ∂

_{υ}*θ*/∂

*z*and ∂

*q*/∂

*z*are the gradients of potential temperature and specific humidity profile gradients within the ISL, respectively.

*V*is the available energy;

*R*is the net radiation;

_{n}*G*is the ground heat flux measured by heat flux plate sensors;

*D*is heat storage in between the soil surface and soil heat flux plate (e.g., Tsuang 2005);

*W*is the heat storage in flood water;

*C*is the canopy heat storage (e.g., Garratt 1994);

*A*is the local advected heat flux (Brutsaert 1982; Guo and Schuepp 1994); and

*F*is the photosynthetic energy flux (e.g., Meyers and Hollinger 2004). All the terms on the right-hand side of Eq. (8) were calculated. Please refer to Tsai et al. (2007) for details, where the local advection heat flux was estimated based on the simplified, steady-state, two-dimensional mean thermodynamic equation as

*ρ*is the density of the air;

*h*is the height of the EC system installation, and

_{c}*u*and

*υ*are wind components in the

*x*and

*y*directions, respectively. The upwind numerical scheme is used for the calculation of advected heat flux (e.g., Griebel et al. 1998). The horizontal temperature (specific humidity) gradients are determined using the temperatures (specific humidities) interpolated at locations 1 km north, south, east, and west from the study site. The inverse-distance weighting technique (Scire et al. 2000; Tsuang 2003) was used for the interpolation from nearby stations. There were nine meteorological stations located within 15 km from the study site. These stations are maintained with routine quality assurance and quality control protocols.

### b. The EC method

*u*′

*w*′

*w*′

*T*′

*w*′

*q*′

*w*′ and horizontal velocity

*u*′, temperature

*T*′, and specific humidity

*q*′. These flux data in conjunction with wind speed and air temperature measurements can be used to determine

*z*

_{0m}and

*d*

_{0}(Martano 2000; Prueger et al. 2004); see appendix B for details.

*B*

_{e}) can be determined directly according to its definition as

*H*and

*LE*are the surface sensible heat and latent heat fluxes observed by the EC system, respectively.

## 3. Field experiments and instruments

The study site was located at the Taiwan Agricultural Research Institute (TARI) (24°01′N, 120°41′E, 50 m above sea level) in the Taichung basin of central Taiwan (Fig. 1). The field experiment was conducted in a rice paddy field from 24 to 29 April 2005. During the study period, the rice paddy was at active growing phase with a height of 60 cm. For irrigating these crops, there were several irrigation channels crossing the area. In addition, a few two-story buildings were located within a radius of 1 km. During the study period, wind directions alternated by day and night partly as a result of the valley–mountain effect, a regular feature of this basin (Tsai and Tsuang 2005).

The study site had dimensions of about 1 km in the north–south direction by 0.8 km in the east–west direction. Including the surrounding area of TARI, the land types north of the instrumentation site were more homogeneous and dominated by rice paddies than in the other directions. The observed data were divided into two dominant groups: northern wind directions (NWD, or PDA) and southern wind directions (SWD, or PIB). PDA was for winds originating between 300° and 360° and PIB, for winds originating between 145° and 255°. From Fig. 1, it can be seen from PDA that the nearest non-rice-paddy land type (orchard) was about 700 m upwind; however, from PIB, the nearest non-rice-paddy land type (buildings) was about 300 m upwind.

### a. Profile observations

A tethersonde system developed by Atmospheric Instrumentation Research Inc. was set up in the paddy field (Fig. 1) to measure the vertical profiles of temperature, specific humidity, and wind vector from 3 to 200 m AGL. It consisted of a balloon with a buoyancy of about 9.3 kg at sea level; an AIR-TS-3AW winch with tether; an IS-5A-RCR, 403-MHz receiver with preamp and antenna; a lap top computer; and a TS-4A-SP-403 tunable sensor package. The accuracy of the temperature, relative humidity, and wind vector are 0.5K, 3%, and 0.5 m s^{−1}, respectively. The response time of the sensors is 3 s. During each measurement, the tethersonde system was held at a height of 3 m for half a minute to adapt itself to the ambient atmosphere and then ascended with the balloon up to a height of around 200 m AGL. As the balloon ascended at a constant speed of 0.3 m s^{−1}, data were collected at a vertical resolution of about 1 m. The sensor acquired data at 3-s intervals. The tethersonde was then lowered at the same speed. Each launch took about 20 min to complete. The tethersonde balloon was launched every half hour during daylight hours except under rain or high wind conditions. During the study period, 46 profile samples were collected. The data were averaged into 5-m bins to obtain the representative values. The heights of descending data were corrected proportionally according to the height at launch and the maximum height of ascent under the observation that atmospheric pressure changed significantly during the launch. An example of the observed vertical profile of potential temperature and specific humidity is shown in Fig. 2.

The profile method is only valid for heights within the ISL (Britter and Hanna 2003). The thickness of the ISL may extend from a few meters to nearly 100 m, depending on the atmospheric stability conditions and surface roughness (Wieringa 1993). To ensure the data were adequate for this method, the appropriate height range of the ISL had to be determined first. An example of wind speed, wind direction, potential temperature, and specific humidity measured by the tethersonde at the study site are shown in Fig. 2. Similar ascending and descending profiles were shown, indicating that the response time and the accuracy of the tethersonde sensors could resolve the vertical structure of the IBL. Visual inspection of the tethersonde profiles can give a general idea of the extent of the ISL, which ranges roughly from a few meters to about 50 m AGL, where the wind speed increased with height but the potential temperature and specific humidity decreased with height. Above 50 m, the wind speed and potential temperature were almost constant, implying that the height ranges from 50 m to the top of the observation height (∼200 m AGL) were within the mixed layer. Therefore, only profile data from a few meters up to about 50 m AGL are used for the profile method to determine the turbulence characteristics within the ISL.

To satisfy the conditions of unstable atmosphere, condensation-free, steady-state, and constant wind direction, the following criteria are used for data screening: 1) the Bowen ratio and available energy should be positive; 2) relative humidity should be less than 95%; 3) wind speed should increase with height with friction velocity >0.15 m s^{−1}; and 4) wind direction fluctuation should be <22.5° within the ISL of each profile and within 1 h. Out of the 46 collected profiles, only 18 profile datasets satisfied these four criteria. There were 10 qualified profile datasets belonging to the PDA and 8 belonging to the PIB. Among the 46 profile datasets, 1 profile datum fails to meet criterion 1, 12 profile data fail to meet criterion 3, and 15 profile data fail to meet criterion 4.

The 18 qualified tethersonde profile data are used to derive *d*_{0}, *z*_{0m}, *u**, *H*, *LE*, and *L* according to the aforementioned profile method. The results are shown in Table 2 (and Fig. 4). More detail discussions of the results will be presented in section 4.

### b. Surface meteorology and EC observations

Micrometeorological instruments were installed to collect shortwave and longwave radiation and ground heat flux. Each radiation component was measured separately using two Eppley precision spectral pyranometers (model PSP) with an accuracy of ±0.5% and two Eppley infrared radiometers (model PIR) with an accuracy of ±1%. All of the radiation instruments were mounted on a 5-m mast 10 m away from the EC system. Ground heat flux was measured from two soil heat flux plate sensors (Campbell Scientific model REBS HFT-3.l) buried at a depth of 8 cm. The soil temperature was measured at a depth between the HFT-3.ls and the soil surface using four averaging soil thermocouple probes (Campbell Scientific model TCAVs), which were divided into two groups and buried at depths of 3 and 6 cm, respectively. In addition, the distance between the TCAVs in the same level was 1 m.

An EC system was erected in the paddy field a few meters away from the tethersonde system. The EC system consisted of a three-dimensional sonic anemometer (Campbell Scientific Inc. model CSAT3) to measure the wind velocity components *u*, *v*, and *w* and virtual temperature; a fine-wire thermocouple (Campbell Scientific FW05) to measure air temperature; and an open path CO_{2}/H_{2}O fast-response infrared gas analyzer (LI-COR model LI-7500) to measure the densities of both scalar quantities CO_{2} and water vapor. All signals from the sensors were recorded at a sampling rate of 20 Hz and averaged over 30-min periods. All components of the EC system were mounted on a mast at a height of 5 m AGL. Note that we have tried several heights (3, 5, among others) for installing EC instruments. It was found that the energy closure using the observation at 5-m height was better than the observation at 3-m height, likely because irrigation channels and terrace might produce wakes near the surface.

Coordinate rotation (Wilczak et al. 2001) was applied to all EC estimates to correct the deviation caused by the tilt of the instruments and the slope terrain where the instruments were installed. Moreover, latent heat flux was corrected for the effects of density fluctuations (Webb et al. 1980). More detailed discussion on the closure of the above budget equation [Eq. (8)] can be found in Tsai et al. (2007). In addition, frequency response and sensor separation corrections of eddy covariance fluxes were conducted according to Massman (2000), which corrected 4%–6% of the measured fluxes during daytime unstable conditions in this study.

The energy imbalance of the turbulent heat flux (*H* + *LE*) observed by the EC system compared to the available energy was found to be 9% in this study. This imbalance is close to those of other studies (e.g., Fritschen et al. 1992; Panin et al. 1998; Twine et al. 2000; Wilson et al. 2002; Prueger et al. 2005). In Wilson et al. (2002), for example, the values of the energy imbalance ranged from 32% to −20% with a mean value of 13% over agricultural sites.

Before determining *z*_{0m} and *d*_{0} from the measured wind speed of the EC system, data were screened to ensure the data quality using the criterion *u**σ* < *u*(*t*) < *u**σ* (e.g., Gao et al. 2003), where *u*(*t*) denotes the measured wind speed, *u**σ* denotes the standard deviation. The qualified EC data are grouped according to wind direction into 15° intervals. Data in each wind direction interval are used to determine *d*_{0} and *z*_{0m}. More detailed discussions of the results will be presented in section 4.

### c. Footprint and fetch analysis

*C*(

_{F}*x*,

*z*) can be expressed (Hsieh et al. 2000) as

_{m}*k*is the von Kármán constant (=0.4);

*D*and

*P*are similarity constants (dimensionless);

*x*is the distance upwind of the measuring point; and

*z*is a length scale defined as

_{u}*z*=

_{u}*z*[ln(

_{m}*z*/

_{m}*z*

_{0m}) − 1 +

*z*

_{0m}/

*z*], where

_{m}*z*is the measurement height. The footprint estimation of scalar fluxes is applied to the EC and profile methods based on the respective instrument heights. For the results analyzed in this study, which were all under unstable conditions,

_{m}*D*= 0.28 and

*P*= 0.59 were chosen according to Hsieh et al. (2000). Adopting the suggestion of Horst (1999), the

*z*of the profile method was defined as

_{m}*z*=

_{m}*z*

_{h}z_{l}*z*and

_{h}*z*were the highest and lowest levels of the mean measured ISL height, respectively. The value of

_{l}*z*was 13 m from the PDA of the profile measurement, 24 m from the PIB of the profile measurement, and 5 m from both the PDA and PIB of the EC measurement.

_{m}Figure 3 shows the footprint areas of EC and profile methods using the mean aerodynamic roughness and harmonic mean of M-O stability length (Table 2) during the studied period. It shows that from PDA, the area within 700 m upwind contributed 90% of the EC measurement and 89% of the profile measurement. In contrast, from PIB, the area within 300 m upwind contributed 80% of the EC measurement but only 64% of the profile measurement. Note again, from PDA, the nearest non-rice-paddy land type (i.e., orchard) was about 700 m upwind; however, from PIB, the nearest non-rice-paddy land type (i.e., buildings) was about 300 m upwind (Fig. 1). It reveals that over the PDA, the footprint areas of both the EC system and the tethersonde system were dominated by rice paddy. But over the PIB, the footprint areas of both systems were of mixed rice paddy and buildings (Fig. 1; Table 4); nonetheless, the footprint area of the tethersonde system consisted of a lower fraction of rice paddy and a higher fraction of buildings than those of the EC system.

## 4. Results

### a. Height range of the ISL

The computed height ranges of the ISL for each of the tethersonde profiles are listed in Table 3 and Fig. 4. A comparison of the mean height range of the ISL with other studies is listed in Table 3. Over the PDA, the mean height range was 7–25 m. Note that the lower limit of the ISL over the PDA can be lower than 7 m, because we launched the tethersonde balloon from 5 m AGL. We do not have data to examine the vertical structure below 5 m AGL.

Over the PIB, the mean height range of the ISL was 14–42 m. The height range over the PDA was lower than over the PIB, likely as a result of the roughness elements over the PDA being lower than those over the PIB (Fig. 1). The upper limit of the ISL, or the top of the ISL, over the PDA was close to those observed in a few nearby sites in the same basin (Tsai and Tsuang 2005) and lower than in other locations (Brutsaert and Sugita 1990; Parlange and Brutsaert 1990; Brutsaert and Parlange 1992; Parlange and Katul 1995; Asanuma et al. 2000). Note that at about 100 m AGL (the lowest height of the rim of the basin), wind shear was commonly observed in the basin (Tsai and Tsuang 2005), which caused discontinuous vertical structures of the temperature, humidity, and wind vector profiles at the height. Therefore, the upper limit of the ISL in the basin was lower than in other locations. The corresponding dimensionless upper limit [≡(*z* − *d*_{0})/*z*_{0m}] of the ISL at the study site ranged from 124 to 720 over the PDA and from 26 to 102 over the PIB.

### b. Roughness length for momentum and zero-plane displacement height

The *d*_{0} and *z*_{0m} derived from the tethersonde profile and the EC data are listed in Table 2 and Fig. 4. It is observed that both the *d*_{0} (within 0.7–8 m) derived from EC measurements and the profile data were higher than the height of rice paddy (∼0.6 m) (Fig. 4). This is likely caused by the contributions of other obstacles to the measurements, such as an orchard and buildings within 1 km upwind of the study site. Note that the canopy heights in the orchard ranged from 0.2 to 2 m, and nearby building heights ranged from 3 to 12 m. Besides, in estimating the *z*_{0m} and *d*_{0} using Martano’s method, nonsensical *d*_{0} values (*d*_{0} < 0) (Fig. 4a) may result (Kustas et al. 2005). Under this nonsensical condition, the data record (*z*_{0m}, *d*_{0}) was discarded from further analysis.

Over the PDA, the mean values of *z*_{0m} estimated by both methods were similar to each other at 0.02–0.03 m (Fig. 4b). However, over the PIB it can be seen that the mean of *z*_{0m} determined according to the profile data was 0.37 m, which was about 5 times larger than the mean of 0.07 m estimated from the EC system. This is expected, because as the flow moves past this complex area, the turbulence changes significantly in response to the presence of large obstacles, such as buildings (Mason 1988; Prueger et al. 2008).

Table 1 lists the aerodynamic roughness of rice paddies listed in the literature or suggested in state-of-the-art weather and air quality models as mentioned earlier. It can be seen that at this study site, although the aerodynamic roughness of 0.03 m for PDA derived from the EC data (for wind from 300° to 360°) is close to that derived from the profile method, and close to those of other homogeneous rice paddy studies (e.g., Gao et al. 2003; Kotani and Sugita 2005), it is, however, almost an order lower than the values used in the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5), the Weather Research and Forecasting Model (WRF), the American Meteorological Society–Environmental Protection Agency Model (AERMOD), and the Comprehensive Air Quality Model with extensions (CAMx). In contrast, for wind from PIB (for wind from 145° and 255°), a much larger value of 0.37 m was observed using the profile method. It is close to those observed in Kondo and Yamazawa (1986) and at a nearby PIB site (Tsai and Tsuang 2005).

### c. Friction velocity, sensible heat flux, latent heat flux, and Bowen ratio

The *X*–*Y* plots of the friction velocity, sensible heat flux, latent heat flux, and Bowen ratio measured by the EC system versus those observed from the tethersonde system are shown in Fig. 5. It can be seen that although the instrumentation between the profile and the EC methods is completely different, the derived friction velocity, latent and sensible heat fluxes, and Bowen ratio were similar to each other, especially for wind blowing over the PDA with correlation coefficients of 0.82–0.86. But for wind blowing over the PIB, the correlations decreased to 0.67–0.86.

Besides, over the PIB, the friction velocities and Bowen ratios observed by the EC system were lower than those from the tethersonde profiles, by 0.07 m s^{−1} and 0.04, respectively. This is likely attributable to the discrepancy of the footprint areas associated with both systems. Over the PIB, the footprint area of the EC system was still dominated by the rice paddy (∼80%). Nonetheless, the footprint area of the tethersonde system was composed of a lower fraction of rice paddy and a higher fraction of buildings than those of the EC system (Fig. 1). Note that buildings produce higher wind shear stress and friction velocity than a rice paddy; hence, the friction velocities measured by the EC system were lower than those computed from the tethersonde system. On the other hand, the rice paddy was flooded with water, which favored the land–atmosphere energy exchange in the form of latent heat rather than sensible heat flux. Therefore, the Bowen ratios measured by the EC system were lower than those by the tethersonde system.

The time series of the Bowen ratios observed by the tethersonde profile (*B _{p}*) and the EC system (

*B*) from 22 to 29 April 2005 are shown in Fig. 6, except for the periods around sunrise and sunset as a result of very large Bowen ratio values because of low latent heat fluxes. During the daylight hours, potential temperature and specific humidity decreased with height. This implies that during the daylight hours, surface sensible and latent heat fluxes were upward (positive). During the nighttime period, stable stratification of the atmosphere near the ground resulted in the surface sensible heat flux to be always downward (negative), as observed by the EC system. As a result, the Bowen ratios (

_{e}*B*) were negative during the night.

_{e}## 5. Comparison with models for determining effective roughness length based on land use type

This section compared the observed values of aerodynamic roughness with those estimated from the effective roughness models of Taylor (1987), Mason (1988), and Tsai and Tsuang (2005). Mason (1988) estimates the effective roughness length model for having the same shear stresses at the blending height, Taylor (1987) estimates it to be the geometric mean, and Tsai and Tsuang (2005) estimates it as the arithmetic mean of the representative roughness of each consisted land type in the footprint area.

*z*

_{0e}for having the same shear stress at the blending height (

*h*) of the representative horizontal length scale

_{b}*L*:

_{x}*z*

_{0mi}and

*f*are the aerodynamic roughness and areal fraction of land type

_{i}*i*, respectively;

*h*is set at

_{b}*L*/200. Although the determination of

_{x}*L*is uncertain (Goode and Belcher 1999; Baldauf and Fiedler 2003), fortunately, from the tethersonde measurement, the ISL range and the corresponding footprint area were determined. From the previous footprint analysis, it can be seen that about 92% and 87% of the ISL properties were contributed from 1-km upwind areas over the PDA and PIB, respectively (Fig. 3). Hence, this study sets

_{x}*L*at 1 km for applying the model to the study site.

_{x}*z*

_{0e}under neutral condition as

*z*

_{0e}is the areal geometric mean of the aerodynamic roughness (

*z*

_{0mi}) of the consisted land type

*i*. Moreover, Tsai and Tsuang (2005) estimated the value of the effective roughness to be the arithmetic mean of the consisted land type of its footprint area as

In Eqs. (15)–(17), the value of *z*_{0mi} is set at 2.1 m for residential areas (Tsai and Tsuang 2005), 0.2 m for dry and fruit farmlands (Grell et al. 1995; Dudhia et al. 2005), 0.026 m for paddy fields (Gao et al. 2003; this study), 0.03 m for water body (Brutsaert 1982), and 0.07 m for other land types. A land use type dataset by CTCI Corporation (2007) is used to determining the areal fractions *f _{i}* of each land type over the PDA and the PIB (Table 4). Note that CTCI constructed 1-km-resolution land use type based on a 1/25 000 map, published by Department of Interior/Taiwan using the land inventory data in 2004. Table 4 also shows the estimated

*z*

_{0e}by applying Eqs. (15)–(17) to the site. Over the PDA, the estimated values of

*z*

_{0e}by Taylor (1987), Mason (1988), and Tsai and Tsuang (2005) are close to the observed

*z*

_{0m}by the tethersonde profile. Over the PIB, however, the estimated value of

*z*

_{0e}by Taylor (1987) is much lower than the observed

*z*

_{0m}by the tethersonde profile. Taylor’s (1987) method was known to have the drawback of neglecting the fact that the friction velocity increases with increasing roughness length (e.g., Goode and Belcher 1999). Similarly, the result of Tsai and Tsuang (2005) also underestimates the

*z*

_{0e}over the PIB. As described in Goode and Belcher (1999), the determination of

*z*

_{0e}is more sensitive to the larger roughness length (such as that of buildings) of each consisted land type in the footprint area. Hence, the values of

*z*

_{0e}estimated by both the geometric mean and the arithmetic mean of each consisted land type are not adequate. In contrast, the

*z*

_{0e}of Mason (1988) shows more consistency with that of the profile method. Over all, Mason (1988)’s method [Eq. (15)] is suggested to estimate effective roughness length over heterogeneous land use types.

## 6. Conclusions

From this discussion, it can be seen that although the instrumentation between the profile and the EC methods is completely different, the derived latent and sensible heat fluxes, friction velocity, Bowen ratio, and aerodynamic roughness were similar to each other for wind blowing over a rice-paddy-dominated area. But for wind blowing over a rice paddy interspersed with buildings area, the correlations decreased to 0.67–0.86, and most of their discrepancies can be associated with the difference in their footprint areas.

In Asia, because of high population and dense habitation patterns, land use types are often intermixed with cultivated areas and buildings. Determining the *z*_{0m} for the area by installing an EC system alone over its major land use type (such as rice paddy) will usually cause critical underestimation. For example, most numerical models (AERMOD, CAMx, MM5, WRF, ECHAM) assign the *z*_{0m} for paddy (or cultivated land) in the range from 0.03 to 0.20 m (Table 1), which are lower than our observation at 0.37 m for wind blowing over a rice paddy interspersed with buildings from the ISL profile data, or 0.27 m observed at a nearby site (Tsai and Tsuang 2005). In turn, these underassignments in aerodynamic roughness can produce stronger surface wind speed in numerical models, as found over Taiwan (Hong 2003). Alternatively, installing a tethersonde system over a heterogeneous landscape for determining aerodynamic roughness is more appropriate.

In respect to effective roughness length models, the results show that the observed aerodynamic roughness lengths by a tethersonde system are close to the model results of Mason (1988), having the same shear stresses at the blending height. In contrast, both the geometric mean model of Taylor (1987) and the arithmetic mean model of Tsai and Tsuang (2005) underestimate the effective roughness over the PIB.

Both the profile and EC methods are complementary to each other (Rotach et al. 2004). The EC method can provide near-real-time continuous temporal coverage of turbulent characteristics, but it is usually limited to a relatively smaller footprint area compared to the profile method. In contrast, the labor-intensive profile method, using the measurements of wind speed, temperature, and humidity at multiple levels covering the entire height range of the ISL, provides the characteristics of the entire ISL. In a numerical model such as MM5, the characteristics (such as aerodynamic roughness) representing the entire ISL are the values that should be assigned in the model.

## Acknowledgments

This work is supported by NSC/Taiwan under Contracts NSC 94-2211-E-005-039, NSC 95-EPA-Z-005-001, NSC 95-2111-M-005-001, NSC 96-2111-M-005-001, and NSC 97-2111-M-005-001, and MOE/Taiwan under the ATU plan. We are also indebted to the students in our laboratory for helping with the instrumentation and the experiment. Thanks to Noel Dallow and Alagesan Arumugam for proofreading.

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## APPENDIX A

### Determining Aerodynamic Roughness Using Tethersonde and Heat Flux Measurements

For each profile, the height range of the ISL, the aerodynamic roughness, and other values are calculated using a six-step process.

An initial height range of the ISL is assigned (5–50 m in this study).

The parameters

*z*_{0m},*u**,*H*,*LE*and*L*are determined simultaneously by fitting them to the observed wind, temperature, and humidity profiles, which is done by solving the integral forms of Businger’s equations (Tsuang et al. 2003) and by assigning a prescribed*d*_{0}.The obtained surface sensible heat flux and latent heat flux are compared with the corresponding fluxes determined by the Bowen ratio method when available energy is available.

Another

*d*_{0}is chosen and steps (2)–(3) are repeated until the surface sensible heat flux and the latent heat flux solved by step (2) are close to those obtained by the Bowen ratio method (within 10% error).Other height ranges of the ISL are tested systematically and steps (2)–(4) are repeated. (6) Finally, the height range of the ISL is set at the range having the maximum correlation between calculated and observed wind speeds at heights within the range (e.g., Parlange and Brutsaert 1990; Mikami et al. 1996; Jacobs and Brutsaert 1998; Tsuang et al. 2003; Tsai and Tsuang 2005).

*and water vapor Ψ*

_{h}*can be found in Businger et al. (1971) as*

_{υ}*, a modified form of the stability function by Brutsaert (1992) is adopted in this study as*

_{m}## APPENDIX B

### Determining Aerodynamic Roughness Using Eddy Covariance Data by Martano’s Method

*z*

_{0m}and

*d*

_{0}from EC data, the least squares method is chosen as the best fit estimator and Eq. (1) is rewritten as

*S*and

*p*are defined as

*S*and

*p*, the optimal values of

*z*

_{0m}and

*d*

_{0}can be determined using observed

*u*,

*u**, and

*L*as inputs. That is, the objective function is written as

*z*

_{0m}and

*d*

_{0}can be found in Martano (2000).

Comparison of *z*_{0m} observed in this study with those observed at rice paddy and those in numerical models.

Friction velocity (*u**), zero-plane displacement (*d*_{0}), aerodynamic roughness (*z*_{0m}), Monin–Obukhov stability length (*L*), sensible heat flux (*H*), latent heat flux (*LE*), and ISL range of all the unstable profiles that met the criteria of condensation-free, steady-state, and constant wind direction (wd) in 2005, where 04221230, time of tethersonde launched, means 12:30 22 Apr local time. Below, asc. and desc. denote ascending and descending, respectively.

Height range of atmospheric ISL in the literature.

Comparison of observed aerodynamic roughnesses (Obs) retrieved from the entire ISL data at the study site with the effective roughness length models (Calc) suggested by Mason (1988), Taylor (1987), and Tsai and Tsuang (2005) [or Eqs. (15)–(17) in this study]. “Other” includes the land types of asphalt roads, windbreak forest, cement squaresm and isolated farmhouse.