A Sensitivity Study of an Effective Aerodynamic ... - AMS Journals

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A Sensitivity Study of an Effective Aerodynamic Parameter Scheme in Simulating Land–Atmosphere Interaction for a Sea–Land Breeze Case Around the Bohai Gulf of China ZHONG ZHONG AND YUAN SUN College of Meteorology and Oceanography, National University of Defense Technology, Nanjing, China

XIU-QUN YANG AND WEIDONG GUO Collaborative Innovation Center for Climate Change, School of Atmospheric Sciences, Nanjing University, Nanjing, China

HAISHAN CHEN Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Key Laboratory of Meteorological Disaster of Ministry of Education, Nanjing University of Information Science and Technology, Nanjing, China (Manuscript received 1 August 2016, in final form 19 May 2017) ABSTRACT Numerical simulations of the atmospheric boundary layer require careful representation of the surface heterogeneity, which involves the upscaling parameterization scheme for the heterogeneous surface parameters. In this study, the sensitivity comparisons of an effective aerodynamic parameter scheme against the area-weighted average scheme in simulating the land–atmosphere interaction over heterogeneous terrain were carried out by conducting multinested simulations with the Weather Research and Forecasting (WRF) Model at coarse and fine resolutions, for a typical sea–land breeze case in the Bohai Gulf of China. The results show that the limited-area model is sensitive to the aerodynamic parameter scheme and the effective aerodynamic parameter scheme exhibits a better performance in simulating the variables and parameters in the land–atmosphere interaction process, such as surface wind speed, sensible heat flux, latent heat flux, friction velocity, and surface air temperature, among others, for short-term simulations. Particularly, the underestimation of sensible heat flux and overestimation of latent heat flux over heterogeneous terrain with area-weighted average scheme for aerodynamic parameters can be improved with the effective parameter scheme in the coastal regions, where the mean simulation error with the effective parameter scheme is about one-half of that with the average scheme for sensible heat flux and one-third for latent heat flux.

1. Introduction In numerical models for meteorological and environmental applications, surface roughness length z0 and zero-plane displacement d are two features among many meteorological and wind-engineering activities concerning the dispersion of contaminants, water cycle, environmental wind effect, and other forms of atmospheric boundary layer behaviors, and they are usually considered as external parameters for the land surface models (Dai et al. 2003). It has been proven that z0 has a strong impact on modeling results through sensitivity Corresponding author: Zhong Zhong, [email protected]

experiments (Sud and Smith 1985; Sud et al. 1988), and it exhibits more in regional scales (Henderson-Sellers and Pitman 1992). Concerning how to account for the effect of the spatial variability of surface conditions on scales smaller than the model grid cell, namely, the surface heterogeneity, is a fundamental issue in successfully modeling the surface hydrologic and atmospheric processes, which is important for the numerical models to describe the exchange of water, heat, and momentum across the land–atmosphere interface (Brutsaert 1998; Albertson and Parlange 1999). Substantial progresses in representing the role of surface heterogeneity on land– atmosphere interaction has been achieved (HendersonSellers and Pitman 1992; Lyons and Halldin 2004; Kanda

DOI: 10.1175/JHM-D-16-0184.1 Ó 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

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et al. 2007; Ma et al. 2008; Brunsell et al. 2011). Numerous efforts have attempted to address the land surface parameters, such as roughness length, to ascertain area-weighted average fluxes, which play an important role in improving the simulation of meteorological fields in heterogeneous terrain (Baklanov et al. 2008). However, how the roughness length, as well as zero-plane displacement, of such heterogeneity should be represented in general circulation models (GCMs) and numerical weather prediction (NWP) models still requires exploration. One can estimate the effect of a heterogeneous underlying surface on land–atmosphere interaction flux by introducing the so-called effective roughness length zeff 0 , which represents the integrated frictional effect for different land-use categories. Since the 1980s, many estimation schemes for zeff 0 have been proposed (André and Blondin 1986; Kondo and Yamazawa 1986; Taylor 1987; Mason 1988; Vihma and Savijärvi 1991; Wood and Mason 1991; Schmid and Bünzli 1995; Hasager and Jensen 1999; Albertson and Parlange 1999; Bou-Zeid et al. 2004, 2007; Zeng and Wang 2007; Kanda et al. 2007; Jiménez and Dudhia 2012; Han et al. 2015), and have demonstrated that area-weighted logarithmic average scheme (Taylor 1987; Mason 1988; Zeng and Wang 2007) is a good approximation of zeff 0 when the roughness length does not vary much in a grid cell of the numerical models (Zhong et al. 2003). Whereas for the effective zero-plane displacement deff , there is no previous work and the simple area-weighted linear average scheme is widely used and considered acceptable (Zeng and Wang 2007). Among the schemes for effective surface parameters, a eff was proposed by Zhong et al. joint scheme for zeff 0 and d (2011), based on the Monin–Obukhov similarity theory of the atmospheric surface layer and the flux and mass coneff could be obtained servation laws, with which zeff 0 and d simultaneously through a numerical iterative method from the derived two-equation system. It has been shown that the determined zeff 0 with this scheme (referred to as ZS hereafter) is more realistic than that calculated by the area-weighted logarithmic average scheme (referred to as AS hereafter), compared to that derived from the largeeddy simulation (LES) by Bou-Zeid et al. (2004, 2007) for some configuration cases over surfaces with varying roughness length and multiple variability scales. It has also been shown that zeff 0 with ZS is greater than that with AS because the contribution of horizontal roughness gradient (i.e., roughness step) and rough-portion zero-plane displacement is taken into consideration, and deff with ZS is smaller than that with AS, which may happen because of the dynamic constraint in atmospheric surface layer according to the similarity theory. Though the features of zeff 0 with ZS have been evaluated with those from LES (Zhong et al. 2011), the

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eff performance of zeff in numerical models has not 0 and d been conducted. With the Weather Research and Forecasting (WRF) Model at both coarse and fine resolutions, the present study will assess ZS in simulating land– atmosphere interaction fluxes and atmospheric surface variables by comparing simulation results with zeff 0 and deff determined with ZS and AS, respectively, for a sea– land breeze case on the coast of Bohai Gulf of China, where the coastal city buildings, water body, and croplands make the land surface exhibit great heterogeneity. Section 2 gives a brief description of ZS. Section 3 describes the experimental design and model configurations. The preliminary evaluations of ZS against AS are presented in section 4, and final remarks are given in section 5.

2. A brief description of the effective aerodynamic parameter scheme Based on the Monin–Obukhov similarity theory of the atmospheric surface layer and the flux and mass conservation laws, as well as the analytical solution of the flux-profile relationships proposed by Byun (1990) and Kou-Fang Lo (1996), it was suggested that the effective aerodynamic paeff could be estimated through the folrameters zeff 0 and d lowing two-equation system (Zhong et al. 2011): n

eff CD (zeff 0 ,d )5

å ri CD (z0i , di )

and

# " z u* z 2 deff dz ln 2 cm L k zeff deff 1zeff 0 0 ð zm n z u* z 2 di dz , ln 5 å ri 2 cm L z0i i51 di 1z0i k

ð zm

(1a)

i51

(1b)

where CD is the drag coefficient for momentum, with a widely used form k2 CD (z0 , d) 5 h i2 , z2d ln 2 cm (z) z0

(2)

where z is height, k is the von Kármán constant, the number of land surface categories in a grid cell is given by n and ri , z0i , and di are the fraction, roughness length, and zero-plane displacement for the ith category, respectively. Parameter zm is the reference height and cm is the integrated diabatic influence function for momentum, which is dependent to the bulk Richardson number Rib. For the stable case (Rib $ 0), cm 5 2bm (z 2 z0 ) , and for the unstable case (Rib , 0),

(3a)

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FIG. 1. Schematic diagram of (a) quadruple- and (b) triple-nested grid system domains.

cm 5 2 ln

and for the unstable case (Rib , 0), (1 1 x) (1 1 x2 ) 1 ln 2 2 tan21 (x) 1 2 tan21 (x0 ) , (1 1 x0 ) (1 1 x20 ) n eff p(zeff 0 ,d )5

(3b) where z 5 (z 2 d)/L, z0 5 z0 /L, Monin–Obukhov length L 5 uu2* /kgu*, here u is potential temperature, u* is the friction velocity and u* is the temperature scale, g is the gravity acceleration, and x 5 (1 2 g m z)1/4 and x0 5 (1 2 gm z0 )1/4 with empirical constants bm 5 4.67 and gm 5 15 (Businger et al. 1971). Similar to the derivation of Kou-Fang Lo (1995), the integration of Eq. (1b) gives the mass conservation relationship as follows. For the stable case (Rib $ 0), n

eff x(zeff 0 ,d )5

å ri x(z0i , di ),

(4a)

å ri p(z0i , di ),

(4b)

i51

where x(z0i , di ) 5 (zm 2 di ) 2

bm b (z 2 di )2 2 z0i 2 m z20i 2L m 2L zm 2 di bm (z 2 di 2 z0i ) ln 1 z0i L m (5a)

(zm 2 di ) 1

and

i51

p(z0i , di ) 5 (zm 2 di ) 1

4L 3g m

(x3m 2 x30 ) , z 2 di 1 1 xm 1 1 x2m 21 21 ln m 2 2 ln 2 ln 1 2 tan (x ) 2 2 tan (x ) m 0 z0i 1 1 x0 1 1 x20

where xm 5 zm /L. Equations (1a) and (4) lead to algebraic expreseff sions for zeff 0 and d , which form the two-equation

(5b)

eff system. They can be solved for zeff via nu0 and d merical iteration method from the fraction of all land surface categories, roughness lengths, and zero-plane

TABLE 1. Model configurations for the simulations with quadruple-nested grid system for FRR and with triple-nested grid system for CRR.

Domain

Resolution (km)

FRR CRR FRR CRR D1 D2 D3 D4

D1 D2 D3 —

45 15 5 1

45 15 5 —

Grid points FRR

CRR

Microphysics scheme FRR

CRR

40 3 40 40 3 40 Single-moment 5 class Single-moment 5 class 76 3 67 76 3 67 Single-moment 5 class Single-moment 5 class 115 3 103 97 3 85 New Thompson New Thompson 481 3 421 — New Thompson —–

Cumulus parameterization scheme FRR

CRR

Betts–Miller–Janjic´ Betts–Miller–Janjic´ Betts–Miller–Janjic´ Betts–Miller–Janjic´ None None None —

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FIG. 2. Distribution of land-use categories in D4 for FRR with main cities marked around Bohai Gulf.

displacements within a grid cell. The resulting parameeff ters (zeff 0 and d ) show the integrated dynamic effect of all those land surface categories in the grid cell of the numerical model and allow calculated turbulent fluxes and mass in the model grid to be equal to the sum of those from all individual land surface categories inside the grid cell. Refer to Zhong et al. (2011) for the calculation scheme in detail. As a comparison, here the area-weighted logarithmic and the area-weighted average roughness length zavg 0

linear average zero-plane displacement davg scheme (i.e., AS) are given as follows: i5n

lnzavg 0 5

å ri lnz0i

and

(6)

i50

i5n

davg 5

å ri di ,

(7)

i50

where symbols on the right-hand side of Eqs. (6) and (7) are the same as in Eq. (1a).

avg FIG. 3. Distributions of (a),(b) effective roughness length and (d),(e) effective zero-plane displacement calculated with AS (zavg ) and 0 , d eff ZS (zeff , d ), and (c),(f) their differences in D3 of Fig. 1b for CRA and CRE, respectively (m). 0

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FIG. 4. Distributions of (top) SH and (bottom) LH for the difference between (a),(d) CRA and FRR; (b),(e) CRE and FRR; and (c), (f) CRE and CRA averaged for the simulation period (W m22).

3. Experimental design and model configurations The model used in this study is the WRF Model, developed primarily at the National Center for Atmospheric Research (NCAR), in collaboration with many agencies (Skamarock et al. 2008). The model is employed with multinested grid systems in the horizontal on Lambert scale projection with 35 uneven layers in the vertical. To assess the performance of ZS, simulations at a coarse resolution (5 km) with the effective aerodynamic parameters with ZS and the approximate AS are compared with those at a fine resolution (1 km) for the same domain size. The quadruple-nested grid system is used for the fine-resolution simulation (Fig. 1a), while the triplenested grid system is employed for the coarseresolution simulation (Fig. 1b). Table 1 lists the model configurations for the quadruple-nested fine-resolution run (FRR) and the triple-nested coarse-resolution runs

(CRR). Note that the size of domain 4 (D4) for the fineresolution run (Fig. 1a) is identical to that of domain 3 (D3) for the coarse-resolution runs (Fig. 1b), while the configurations for domain 1 (D1) and domain 2 (D2) both for the fine-resolution run and the coarseresolution run are the same. Besides the physics process schemes presented in Table 1, the Yonsei University nonlocal K-profile planetary boundary layer scheme (Hong et al. 2006), the Noah land surface model (Chen and Dudhia 2001), the shortwave radiation of the Dudhia scheme (Dudhia 1989), and the longwave radiation of the RRTM scheme (Mlawer et al. 1997) are used. The sea–land breeze case was chosen for the sensitivity simulation in evaluating the effect of the parameter scheme, because 1) besides the surface temperature, the surface wind (speed and direction) should be with significant daily variation, since this work aims to evaluate the parameter scheme for a short-term

TABLE 2. RMSE of wind speed at 10 m, sensible heat flux, latent heat flux, friction velocity, and air temperature at 2 m averaged for the simulation period over land and ocean, between CRA and FRR and between CRE and FRR. u10 (m s21)

Land Ocean

SH (W m22)

LH (W m22)

u* (m s21)

T2 (8C)

RAF

REF

RAF

REF

RAF

REF

RAF

REF

RAF

REF

0.481 0.737

0.476 0.731

9.695 11.506

9.694 10.495

5.057 13.871

4.974 12.691

0.053 0.035

0.053 0.035

0.657 0.473

0.650 0.421

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avg TABLE 3. As in Table 2, but for the area where zeff is greater than or equal to 0.1 m over land. 0 2 z0

u10 (m s21)

Land

SH (W m22)

LH (W m22)

RAF

REF

RAF

REF

RAF

REF

u* (m s21) RAF REF

0.662

0.483

19.927

10.365

14.145

8.334

0.073

simulation, and the improvement for daily surface heat flux is much more important under daily temperature variations as well as wind conditions; 2) only with large ocean area in the model domain can the sea–land breeze develop well; and 3) the coastal area is one of the most heterogeneous regions for sea and land difference as well as urban buildings with large roughness length and zero-plane displacement. The model integration started at 1800 UTC 23 May and ended at 0000 UTC 27 May 2007, with a total of 78 h of integration for a typical sea–land breeze case along Bohai Gulf (Lu et al. 2008). The model’s lateral boundary conditions for D1 were interpolated from the 6-hourly NCEP– NCAR reanalyses data at 18 3 18 resolution, and the sea surface temperature (SST) was from the daily Tropical

0.069

T2 (8C) RAF

REF

1.385

1.186

Rainfall Measuring Mission (TRMM) Microwave Imager data at 0.258 3 0.258 resolution. The time step for the coarser domain (D1) is 270 s and the one-third regulation is used for the fine-mesh domains of D2 and D3, and it is 6 s for D4. The model output is at 30-min intervals. Three simulations were conducted: 1) the quadruplenested fine-resolution run (D1–D4 in Fig. 1a); 2) the triple-nested coarse-resolution run, where the roughness length and zero-plane displacement in D3 are calculated with AS (Fig. 1b, referred to as CRA, short for the coarse-resolution run with AS); and 3) the triplenested coarse-resolution run, where the effective roughness length and effective zero-plane displacement in D3 are determined with ZS (Fig. 1b, referred to as CRE, short for coarse-resolution run with effective

FIG. 5. (a),(c),(e) Temporal variation of mean zonal wind speed in Tianjin and mean meridional wind speed in Hekou and Longkou at 10 m for FRR, CRA, and CRE; and (b),(d),(f) the differences between CRA and FRR and between CRE and FRR during the simulation period [the abscissa represents local standard time (LST)]. (left) FRR (black), CRE (blue), and CRA (red); (right) difference between CRE and FRR (blue) and difference between CRA and FRR (red).

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TABLE 4. RMSE of wind speed at 10 m, sensible heat flux, latent heat flux, friction velocity, and air temperature at 2 m between CRA and FRR and between CRE and FRR during the simulation period in three coastal city areas. u10 (m s21)

Tianjin Hekou Longkou

SH (W m22)

RAF

REF

RAF

REF

RAF

REF

u* (m s21) RAF REF

0.77 0.51 0.57

0.67 0.40 0.62

42.16 21.22 40.48

29.05 7.61 19.76

36.15 14.13 22.53

16.06 4.08 7.21

0.063 0.117 0.050

parameter scheme ZS). For both CRA and CRE, zavg 0 or avg eff and d or d in each cell in D3 with 5-km grid zeff 0 spacing were calculated with 25 z0i and di in D4 of FRR with 1-km grid spacing (Fig. 1a). Those in D1 and D2 for the three simulations, as well as that in D3 for FRR, are all the same as the default values according to the 24 U.S. Geological Survey (USGS) land-use categories provided by the static data of the WRF Model system, and the roughness length for heat in Noah land surface model is calculated as the Zilitinkevich (1995) equation.

4. Preliminary evaluations The distribution of land surface category in D4 (Fig. 1a) for FRR at 1-km resolution is shown in Fig. 2. It can be seen that there are a total of 15 categories in the

LH (W m22)

0.058 0.052 0.046

T2 (8C) RAF

REF

1.95 0.88 1.73

1.13 0.57 1.18

domain and the main land-use/land-cover categories are water body (Bohai Sea), cropland, forest, and city. In addition, the distinct feature is that, besides the metropolis of Beijing and Tangshan faraway from Bohai, there are metropoles of Tianjin, Dalian, and many small to medium cities around Bohai Gulf, as the expansion of urbanization in recent decades. avg , and zeff Figure 3 shows the distribution of zavg 0 0 and d eff and d , as well as their differences, in D3 (Fig. 1b) for CRA and CRE at 5-km resolution, respectively. It can be seen that the most obvious differences for the two parameters in D3 between ZS and AS mainly appear in the city and suburbia, where both the local surface roughness length and zero-plane displacement are big and vary with large roughness step, which may contribeff in ZS and have never been considered ute to zeff 0 and d

FIG. 6. As in Fig. 5, but for sensible heat flux.

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FIG. 7. As in Fig. 5, but for latent heat flux.

in AS (Taylor 1987; Schmid and Bünzli 1995; Zhong et al. 2011). In the rural area, however, the differences for these two aerodynamic parameters are negligible for the relative small local roughness length and zero-plane displacement, as well as their horizontal variations. Figure 3 shows that the distribution pattern of zeff 0 (Fig. 3b) is very similar to that of deff (Fig. 3e) determined with ZS, with an abnormal correlation coefficient (ACC) of 0.95, which implies an intrinsic eff with ZS; the dynamic relationship between zeff 0 and d ACC between the independently calculated average roughness length and average zero-plane displacement with AS is 0.88 (Figs. 3a,d), smaller than that with ZS. It eff with ZS are almost should be noted that zeff 0 and d identical to those with AS in central Beijing and Tianjin, which means that the effect of heterogeneity could be neglected in the center of those metropoles at 5-km resolution, related to the scale dependence of urban representation (Brutsaert 1998; Flagg and Taylor 2011). Figure 4 shows the distributions of the sensible heat flux (SH) differences and latent heat flux (LH) differences between CRA and FRR and between CRE and FRR, as well as that between CRE and CRA, averaged for the simulation period. It can be seen that the average heat flux differences are not directly related to the areas

where cities and buildings are located with large zeff 0 and deff , and the simulated sensible heat flux both for CRA and CRE are larger than that for FRR in most areas, especially over the Bohai Sea (Figs. 4a,b). Whereas the simulated latent heat flux both for CRA and CRE are somewhat larger than that of FRR over land, however, they are less than that over the Bohai Sea (Figs. 4d,e). Though the simulated heat fluxes for CRA and CRE are different from that for FRR, the CRE gives less discrepancy than CRA does for both sensible heat flux and latent heat flux, especially over the Bohai Sea, where the underlying surface temperature, that is, SST, is given as forcing and not changed with model integration. Nevertheless, the differences between CRE and CRA show that CRE gives more sensible heat flux in most land areas, especially in coastal areas, where the simulated sensible heat flux of CRE is larger than that of CRA (Fig. 4c). For the latent heat flux, however, the difference between CRE and CRA is almost out of phase inland, which suggests that CRE gives less latent heat flux than CRA inland (Figs. 4c,f). Therefore, the underestimation for sensible heat flux and overestimation for latent heat flux in simulations over heterogeneous terrain, when the surface heterogeneity is insufficiently described (Huang et al. 2008; Brunsell et al. 2011), could

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FIG. 8. As in Fig. 5, but for friction velocity.

be overcome with ZS at a certain degree (see also Table 3, described in greater detail below). Table 2 lists the root-mean-square error (RMSE) of sensible heat fluxes and latent heat fluxes as well as other surface variables averaged for the simulation period over land and sea between CRA and FRR (RAF) and between CRE and FRR (REF). It can be seen that the RMSEs of important surface variables directly related to aerodynamic parameters between CRE and FRR are less than or equal to those between CRA and FRR not only over land but also over sea, though the improvement with ZS is negligible for those variables averaged over the model domain, suggesting that the employment of ZS will not bring negative effects for simulations in model domain and that the circulation spreads the effect of local aerodynamic parameters over land to the sea surface, where the effective parameters with ZS and AS are the same as for the homogeneous water body, just like the upstream effect of urban heat island (Zhang et al. 2011a). However, as shown in Table 3, the significant improvement is exhibited over the areas where the difference of effective roughness length with ZS and AS is greater than or equal to 0.1 m (also see Fig. 3c). It clearly shows that the mean RMSEs for all surface variables for the simulation period between CRE and

FRR are less significant than those between CRA and FRR, and it could be calculated that the percentage of the RMSE ratio of CRE versus FRR over CRA versus FRR for surface wind speed, sensible heat flux, latent heat flux, friction velocity, and surface temperature is 73%, 52%, 59%, 84%, and 78%, respectively, which suggests that the sensible heat flux and latent heat flux are much more improved when the effective aerodynamic parameter ZS is employed over the heterogeneous terrain. The impact of the changed aerodynamic parameters in numerical models on general circulation is attributed to the advection and convection processes in the atmosphere (Sud and Smith 1985; Sud et al. 1988; KirkDavidoff and Keith 2008), which transfer the changed surface physical quantities outward and upward; thus, in this work, we will focus on how the surface atmospheric variables sensitive to the effective aerodynamic parameter scheme. On the other hand, the sea–land breeze is directly related to the land–sea thermal contrast. Besides the major differences of aerodynamic parameters between ZS and AS that occur in city areas, the urban heat island effect would intensify land–sea contrast. Therefore, three cities (Tianjin, Hekou, and Longkou; see Fig. 2) around Bohai Gulf are selected for the

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FIG. 9. As in Fig. 5, but for surface air temperature at 2 m.

sensitivity evaluation for the surface physical quantity response to the aerodynamic parameter scheme in detail, since the most significant differences for heat fluxes between CRA and CRE appeared in the coastal areas, and the heat flux differences mainly come from the modification of aerodynamic parameters associated with coastal cities and buildings. The temporal variations of mean zonal wind speed in the southeastern suburb of Tianjin (referred to as Tianjin, where the sea–land breeze is mainly driven by zonal temperature gradient) and mean meridional wind speed in Hekou and Longkou (where the sea–land breeze is mainly driven by meridional temperature gradient) at 10 m for FRR, CRA, and CRE during the simulation period are shown in Fig. 5 (the first 6-h run is not considered to allow for the model spinup), where the wind speed for FRR is the mean over 10 3 10 grid points at 1-km resolution in D4 (Fig. 1a) and that for CRA and CRE is over 2 3 2 grid points at 5-km resolution in D3 (Fig. 1b). It can be seen that all the simulations give similar temporal variations of wind speed in each coastal city area, where the sea–land breeze exists from 24 to 26 May, with an apparent daily variation of the meridional wind in Hekou and Longkou (Figs. 5c,e), while it only appeared in Tianjin on 26 May (Fig. 5a). Therefore,

the fine-resolution run and the two coarse-resolution runs can reproduce the sea–land breeze process around Bohai Gulf in those days as reported by Lu et al. (2008). Though the wind speed difference at 10 m between CRA and FRR and between CRE and FRR is not so great for these short-term simulations (the maximum discrepancy is less than 2 m s21), the simulation results from CRE are closer to that from FRR for most cases, with smaller RMSE than that from CRA (Table 4). This suggests that eff than AS, namely, ZS can give more realistic zeff 0 and d ZS can better represent the integrated effects of the heterogeneous roughness length and zero-plane displacement in D4 at finer resolution, for the surface wind eff directly and the difference is sensitive to the zeff 0 and d between ZS and AS is significant in those coastal cities. It should be pointed out that the distinct discrepancies can appear aloft far away from the areas where the eff determined by AS and ZS are differences of zeff 0 and d distinct. This implies that a small difference in zeff 0 and deff at surface due to different schemes can make a great difference for the variables in the lower troposphere even for such a short-term integration, which would be more significant for a long-term integration as done in climate modeling (Sud and Smith 1985; Sud et al. 1988).

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FIG. 10. (a),(b) Temporal variations of zonal surface wind speed (m s21) along 398N and (c),(d) meridional surface wind speed (m s21) along 1208E for (left) CRA and (right) CRE.

The simulated temporal variations of sensible heat flux in three selected cities for FRR, CRA, and CRE are shown in Fig. 6. It clearly shows that all the experiments can give similar daily variation of sensible heat flux, and both the CRA and CRE have weaker upward sensible heat than FRR during daytime, whereas CRA sometimes gives a stronger downward sensible heat flux than FRR during nighttime. However, the simulated sensible heat flux of CRE is closer to that of FRR than CRA. The improvement in simulating sensible heat flux in CRE against CRA can be seen from the comparison of the simulated sensible heat flux differences more clearly (Figs. 6b,d,f). As a result, the RMSE for the sensible heat flux between CRA and FRR for the integration period is 42.16, 21.22, and 40.48 W m22 for Tianjin, Hekou, and Longkou, respectively, whereas the RMSE between CRE and FRR is decreased to 29.05, 7.61, and 19.76 W m22, which is 68.9%, 35.9%, and 48.8% of that between CRA and FRR in each city, respectively (Table 4), at about a mean of one-half of the RMSE between CRA and FRR (51.2%). For the latent heat flux, CRE exhibits much more obvious improvement than CRA. As shown in Fig. 7, relative to FRR, the pronounced feature is that CRA usually

overestimates the latent heat flux much more than CRE does during daytime. The RMSE between CRE and FRR is 16.06, 4.08, and 7.21 W m22 for Tianjin, Hekou, and Longkou, respectively. However, it is as large as 36.15, 14.13, and 22.53 W m22 between CRA and FRR (Table 4), which is about 2.25, 3.46, and 3.12 times (with a mean of 2.94 times) of that between CRE and FRR, respectively. It has been pointed out that the surface heterogeneity would impact the boundary layer dynamics via energy balance partitioning, such as sensible heat flux and latent heat flux (Brunsell et al. 2011), and the insufficiency in describing the surface heterogeneity with more homogeneous surface will lead to an underestimation of sensible heat flux and overestimation of the latent heat flux (Huang et al. 2008; Brunsell et al. 2011). The comparisons for heat flux between CRA and CRE show that AS underestimates sensible heat flux (Fig. 6) and overestimates latent heat flux (Fig. 7) for more cases than ZS in those coastal cities with a mixture of city buildings, rural land, and water bodies, and a great horizontal gradient for surface aerodynamic parameters. They also show great heterogeneity and large differences of the simulated heat fluxes (Figs. 4c,f), which suggests that the effect of surface heterogeneity cannot be described by AS completely.

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FIG. 11. Distributions of (a),(b) air temperature at 2 m (8C) and (c),(d) specific humidity at 2 m (g kg21) averaged between 1000 and 1400 LST on 24, 25, and 26 May for (left) CRA and (right) CRE.

One of the most important parameters in the atmospheric surface layer is the friction velocity u* related to the momentum flux or turbulent stress, which is related to the simulated atmospheric boundary layer structure (Zhang et al. 2011b). The temporal variations of u* for FRR, CRA, and CRE are shown in Fig. 8, which is calculated from the square root of the mean friction velocity u2* over grid points in each selected city area. Though the improvement of u* in CRE calculated from the simulated momentum flux and sensible heat flux is not so significant relative to that in CRA, the RMSE of CRE with respect to FRR is still less than that of CRA with respect to FRR in all three selected coastal city eff from ZS, areas (Table 4). Moreover, with the zeff 0 and d the underestimation of u* in CRA is ameliorated distinctively in Hekou. As a very important model variable in the atmospheric surface layer directly affected by land–atmosphere interaction heat fluxes, as well as by the surface wind speed associated with temperature advection, the air temperature at 2 m T2 was also reproduced better with ZS than with AS (Fig. 9, Table 4). The most obvious improvement of T2 with ZS is in Tianjin, where

both CRA and CRE give weaker daily temperature variations than FRR (Figs. 9a,b), whereas CRE has a lower RMSE of T2 versus CRA, with an RMSE of 1.138C for CRE versus 1.958C for CRA (Table 4). The RMSE of T2 for CRE in Longkou is of 1.188C against that for CRA of 1.738C (Table 4). However, the improvement for surface temperature in Hekou is not so clear, though the simulated sensible heat flux and latent heat flux by CRE show better performance there, due to heat fluxes being compensated by the temperature advection, which will cause the temperature variation in other areas just like the upstream effect of urban heat island (Zhang et al. 2011a). As a result, the surface air temperature shows less sensitivity to local surface heterogeneity in some areas, where the heterogeneity may maximize convective heat fluxes through modifying and maintaining local temperature gradients (Brunsell et al. 2011). As evidence that the horizontal advection induced by sea–land breeze would have a significant influence on the transportation of physical quantities, the simulated temporal variations of zonal surface wind speed (at 10 m) along 398N and meridional surface wind speed along 1208E and

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ZHONG ET AL. TABLE 5. As in Table 4, but for bias. 21

u10 (m s )

Tianjin Hekou Longkou

SH (W m22)

LH (W m22)

BAF

BEF

BAF

BEF

BAF

BEF

20.16 20.12 0.08

20.08 20.08 0.14

231.23 213.13 232.88

215.09 21.90 213.85

15.35 11.28 17.27

24.05 1.53 5.62

the distributions of air temperature at 2 m averaged for 1200 LST on 24, 25, and 26 May during the simulation period, are plotted in Figs. 10 and 11, respectively. In Fig. 10, it can be seen that the persistent westerly component greater than 4 m s21 eastward from Tianjin was dominant in the Bohai Sea before 1200 LST 26 May for CRA and CRE (Figs. 10a,b), while for the temporal variations of meridional wind speed along 1208E, there appears to be significant daily variation of wind direction of sea– land breeze (Figs. 10c,d), which provides the dynamic conditions for the heat exchange between coastal regions and sea surface by horizontal advection. In addition, the large air temperature and humidity contrast between coastal regions and sea surface (Fig. 11) would make the horizontal advection more effective, which will neutralize the effect of aerodynamic parameters on heat fluxes over coastal heterogeneous areas. In brief, the simulation with the surface aerodynamic parameters determined by ZS performs better than that by AS in representing the underlying surface heterogeneity according to the comparison of RMSE of atmospheric surface layer variables between the coarse- and fine-resolution runs. Meanwhile, the superiority of ZS is also exhibited in the bias between the simulation runs, except for the friction velocity in Tianjin (Table 5). Specifically, the underestimation of sensible heat flux and overestimation of latent heat flux in simulating land–atmosphere interaction over heterogeneous coastal regions could be improved with ZS.

5. Concluding remarks For a sea–land breeze case in the coastal area of Bohai Gulf of China, the WRF Model is used to evaluate the performance of the scheme for effective roughness length eff proposed by zeff 0 and effective zero-plane displacement d Zhong et al. (2011), in representing the effect of surface heterogeneity. As a sensitivity comparison experiment, the widely used approximate area-weighted logarithmic avavg erage scheme for zeff 0 (i.e., z0 ) and the area-weighted linear average scheme for deff (i.e., davg ) are also employed. For the representation of the effect of heterogeneous eff from ZS in the limited-area model surface, zeff 0 and d gave a better performance through improving the simulated variables and parameters in the atmospheric

u* (m s21) BAF BEF 20.015 20.079 0.026

20.042 20.031 0.000

T2 (8C) BAF

BEF

21.68 20.72 21.70

20.90 20.38 21.46

surface layer, including the surface wind speed, sensible heat flux, latent heat flux, friction velocity, and surface air temperature, among others. Such an improvement is very important for quantitative calculations of land– atmosphere interaction in numerical models and is expected to benefit the circulation simulation aloft in weather and climate models. From the statistics for the coastal city areas, where the city buildings, water body, and croplands make the land surface exhibit great heterogeneity, relative to the highresolution run, the numerical model is sensitive to the aerodynamic parameter scheme. The experiment with ZS can reduce the simulation errors for heat fluxes sufficiently, at about one-half of sensible heat flux error and one-third of latent heat flux error against that with AS, which underestimates the sensible heat flux and overestimates the latent heat flux over the heterogeneity surface, for its insufficiency in describing the surface heterogeneity, as pointed out by Huang et al. (2008) and Brunsell et al. (2011); specifically, the contributions of roughness step and rough-portion zero-plane and deff were not taken into displacement to zeff 0 consideration. There is no doubt that more work is needed to better represent the effective aerodynamic parameters associated with various aspects of land–atmosphere interaction, especially in climate models at coarser resolution. Our future studies will focus on the availability of ZS in representing the heterogeneity for the longterm simulations. Acknowledgments. The authors thank two reviewers for their comments and suggestions, which helped to improve the quality of this work. This work is sponsored by the National Natural Science Foundation of China (41475083, 41475063) and R&D Special Fund for Public Welfare Industry (Meteorology) under Grant GYHY201306025. REFERENCES Albertson, J. D., and M. B. Parlange, 1999: Surface length scales and shear stress: Implications for land–atmosphere interaction over complex terrain. Water Resour. Res., 35, 2121–2132, doi:10.1029/1999WR900094.

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