Impacts of the Lowest Model Level Height on the Performance of Planetary Boundary Layer Parameterizations

Transcription

1 664 M O N T H L Y W E A T H E R R E V I E W VOLUME 140 Impacts of the Lowest Model Level Height on the Performance of Planetary Boundary Layer Parameterizations HYEYUM HAILEY SHIN AND SONG-YOU HONG Department of Atmospheric Sciences and Global Environment Laboratory, Yonsei University, Seoul, South Korea JIMY DUDHIA Mesoscale and Microscale Meteorology Division, NCAR, Boulder, Colorado (Manuscript received 2 February 2011, in final form 1 July 2011) ABSTRACT The lowest model level height z 1 is important in atmospheric numerical models, since surface layer similarity is applied to the height in most of the models. This indicates an implicit assumption that z 1 is within the surface layer. In this study, impacts of z 1 on the performance of planetary boundary layer (PBL) parameterizations are investigated. Three conceptually different schemes in the Weather Research and Forecasting (WRF) model are tested for one complete diurnal cycle: the nonlocal, first-order Yonsei University (YSU) and Asymmetric Convective Model version 2 (ACM2) schemes and the local, 1.5-order Mellor Yamada Janjić (MYJ) scheme. Surface variables are sensitive to z 1 in daytime when z 1 is below 12 m, even though the height is within the surface layer. Meanwhile during nighttime, the variables are systematically altered as z 1 becomes shallower from 40 m. PBL structures show the sensitivity in the similar manner, but weaker. The order of sensitivity among the three schemes is YSU, ACM2, and MYJ. The significant sensitivity of the YSU parameterization comes from the PBL height calculation. This is considerably alleviated by excluding the thermal excess term in determining the PBL height when z 1 is within the surface layer. The factor that specifies the ratio of nonlocal transport to total mixing is critical to the sensitivity of the ACM2 scheme. The MYJ scheme has no systematic sensitivity, since it is a local scheme. It is also noted that a numerical instability appears accompanying the unrealistic PBL structures when the grid spacing in the surface layer suddenly jumps. 1. Introduction The surface layer is defined as the region at the bottom 10% of the boundary layer where turbulent fluxes and stress vary by less than 10% of their magnitude (Stull 1988). According to this definition, the surface layer height is typically the order of 100 m in daytime convective boundary layers and the order of 1 10 m in nighttime stable boundary layers. In most atmospheric numerical models the lowest model level height (hereafter z 1 )is assumed to be within the surface layer height, and surface layer similarity is applied to z 1 whether or not the height is within a real surface layer. Based on this assumption and surface layer similarity, surface layer schemes in numerical models calculate surface momentum, heat, and Corresponding author address: Song-You Hong, Dept. of Atmospheric Sciences, College of Science, Yonsei University, Seoul , South Korea. shong@yonsei.ac.kr moisture fluxes using data at the surface and z 1.Whenthe models are coupled to a land surface model, the surface layer schemes calculate surface momentum flux and exchange coefficients, and surface heat and moisture fluxes are calculated by the land surface model. Surface fluxes from surface layer schemes and surface models serve as lower boundary conditions in planetary boundary layer (PBL) parameterizations for vertical transport of surface forcing (i.e., surface fluxes). In addition, some PBL parameterizations are designed to be strongly coupled with surface layer properties. In this context, the externally determined lowest model level height can influence the behavior of a PBL scheme, which in turn affects the performance of prediction skill for atmospheric states. The importance of the lowest model level height in atmospheric numerical models has recently been discussed by a few previous studies (Wei et al. 2001; Zängl et al. 2008; Aligo et al. 2009). Wei et al. (2001) examined how modifications of the height of the lowest model level can alter simulated surface heat fluxes and accompanying DOI: /MWR-D Ó 2012 American Meteorological Society

2 FEBRUARY 2012 S H I N E T A L. 665 snowmelt during a strong warm-advection snowmelt event. The surface layer is always stable in this environmental condition. Therefore, the frequently used height of the lowest model level in global and regional models several tens of meters is beyond the applicable range of surface layer similarity, and surface sensible and latent heat fluxes are large enough to be affected by the selections of z 1 under this environmental condition. Wei et al. concluded that sensible and latent heat fluxes are underestimated when z 1 is higher than the real surface layer depth, which in turn drives an underestimate of the simulated snowmelt. Zängl et al. (2008) showed that simulations of Alpine foehn are systematically dependent on the lowest model level height; the dependence on the height is larger and more systematic than the dependence on PBL parameterization selection. For quantitative precipitation forecasts over the Midwest, Aligo et al. (2009) demonstrated that precipitation forecasts are quantitatively improved when z 1 is lowered from 54 to 10 m. It is noted that during daytime convective initiation, the lower atmosphere is stabilized because of heavy cloud shading and wet surfaces. These previous studies commonly targeted stable surface layers where the commonly used z 1 of roughly m violates the surface layer assumption; z 1 is higher than the real surface layer height. These prior studies suggested the improvement of numerical simulations by lowering z 1 when the surface layer is stable. To the authors knowledge, there is no literature that examined impacts of z 1 on the resulting PBL structures when the environment is unstable. This kind of investigation is important because the lowest model level height is kept nearly constant during model integration regardless of environmental regime changes between unstable and stable conditions. In this study, impacts of the lowest model level height on the performance of PBL parameterizations are investigated for three PBL schemes in the Weather Research and Forecasting (WRF) model, for one complete diurnal cycle from the Cooperative Atmosphere Surface Exchange Study 1999 (CASES-99; Poulos et al. 2002) field experiment that contains both unstable and stable surface layer conditions. A brief review of PBL parameterizations and possible impacts of z 1 on the parameterizations is provided in section 2. Experimental setup and simulation results are given in sections 3 and 4, respectively. Conclusions follow in the final section. 2. Overviews of three PBL parameterizations and coupling to surface layer a. PBL parameterizations PBL parameterizations express effects of subgridscale turbulent motions to prognostic mean variables (C; u, y, u, q). The most frequently used relation is the vertical diffusion formula C t 52 z w9c9 5 C K z c z, (1) where K c is the diffusivity for the mean variable C. This approximation is commonly called K theory (Stull 1988). Three conceptually different parameterizations the Yonsei University (YSU; Hong et al. 2006; Hong 2010), the Asymmetric Convective Model version 2 (ACM2; Pleim 2007b), and the Mellor Yamada Janjić (MYJ; Janjić 1990) are selected for testing possible impacts of z 1 on modeled surface and PBL structures. The YSU and ACM2 schemes are nonlocal, first-order closure schemes. For the convective boundary layer (CBL) both use the K-profile approach, and they consider nonlocal mixing by large convective eddies. However, they are distinct from each other mainly in their nonlocal mixing formulations, as well as in their definitions of PBL height h and expressions of entrainment fluxes. The YSU PBL parameterization explicitly expresses nonlocal mixing of heat and momentum by adding a gradient adjustment term to the local gradient of each prognostic mean variable (Noh et al. 2003). The ACM2 PBL parameterization explicitly has a nonlocal upward transport from the surface and an asymmetrical layer-by-layer downward transport from the adjacent upper level (Pleim 2007a), for prognostic variables of heat, momentum, and moisture. For the stable boundary layer (SBL), the YSU scheme uses an enhanced vertical diffusion of Hong (2010), which is based on the bulk Richardson number between the surface layer and the top of the boundary layer. The ACM2 scheme uses a local mixing method in which the mixing coefficient is a function of the local Richardson number at a given model level. As a result of these differences, the YSU and ACM2 schemes produce divergent PBL structures (Shin and Hong 2011, hereafter SH11). Note that Hu et al. (2010) found the two schemes to be quite similar to each other for a different case: 4-km WRF simulations over Texas in July September The MYJ parameterization is classified as a local, 1.5-order closure [i.e., turbulent kinetic energy (TKE) closure] scheme, and it only treats local mixing for both CBL and SBL (i.e., a local scheme). The diffusion coefficient is a function of a prognostic TKE at a given model level. Only the MYJ scheme is tested in our study among the three local TKE closure schemes [i.e., the MYJ, the quasi-normal scale elimination (QNSE), and the Bougeault Lacarrére (BouLac)] in SH11, since the QNSE and BouLac schemes are also the local, 1.5- order closure schemes that have the same sort of linkage as the MYJ scheme to the surface layer (i.e., to z 1 ;

3 666 M O N T H L Y W E A T H E R R E V I E W VOLUME 140 cf. section 2b). Moreover, SH11 showed that behaviors of the three schemes are analogous to each other for the present simulation case. b. Surface flux formulations and their linkage to PBL parameterizations The fundamental role of the surface models and surface layer parameterizations in atmospheric numerical models is to calculate momentum, heat, and moisture fluxes from the surface to the atmosphere. In the current version of the WRF model, each PBL parameterization uses particular surface layer parameterizations (Skamarock et al. 2008): the fifth-generation Pennsylvania State University National Center for Atmospheric Research (PSU NCAR) Mesoscale Model (MM5) surface layer similarity (Zhang and Anthes 1982) for the YSU scheme, the Pleim Xiu (PX) (Pleim 2006) or MM5 surface layer similarity for the ACM2 scheme, and the Eta surface layer similarity (Janjić 1990) for the MYJ scheme. These schemes follow the Monin Obukhov similarity (Monin and Obukhov 1954). The surface momentum flux t is proportional to the surface friction velocity u * through the definition of u * : jtj 5 r[u9w9 s 2 1 y9w9s 2 ] 1/2 5 ru 2 *, u * 5 ku 1 ln(z 1 /z 0M ) 2 c M. (2a) (2b) In Eq. (2a), r is the air density; and u, y, andw are the horizontal and vertical velocity components, respectively. The prime designates the turbulent part of each variable, and the subscript s designates the surface. In Eq. (2b), U 1 is the wind speed at z 1, z 0M is the surface roughness length for momentum, and c M is the stability function for the momentum. In the surface layer schemes, the friction velocity is computed following similarity theory [Eq. (2b)], and then the momentum flux is calculated using Eq. (2a). In this study, the WRF model is coupled with the Noah land surface model (Chen and Dudhia 2001; Ek et al. 2003; cf. section 3b). Thus, the surface sensible heat flux H is calculated in the land surface model instead in the surface layer schemes, but using the exchange coefficient C H provided by the surface layer schemes: H 5 rc p u9w9 s 52rc p C H (u 1 2 u s ), C H 5 ku * ln(z 1 /z 0T ) 2 c H, (3a) (3b) where c p is the specific heat of air at constant pressure, and u s and u 1 are the potential temperatures at the surface and z 1,respectively.Herez 0T is the surface roughness length for heat, and c H is the stability function for the heat. Note that each surface layer scheme has some modifications in calculating u * and C H, while we only show the basic expressions. For the moisture flux, the latent heat flux (LH) isdetermined as LH 5 rl v q9w9 s 5 L v (E dir 1 E c 1 E t ), (4) where L v is the latent heat of vaporization, E dir is the direct evaporation from the bare soil, E c is the canopy reevaporation, and E t is the transpiration via canopy and roots (Chen and Dudhia 2001). The first equalities in Eqs. (3a) and (4) are always valid since they are the definitions of two fluxes, while the last equalities are based on empirical and physical hypotheses. Basically, the surface fluxes in Eqs. (2) (4) are calculated with the physical properties of the surface and z 1. In the YSU scheme, there are four parts that are directly linked to surface layer variables: surface fluxes (i.e., 2w9c9 s ) that are transported to the atmosphere; gradient adjustment terms g c that account for nonlocal mixing of PBL; the temperature excess term u T due to surface buoyancy flux and the temperature at z 1 that directly influence the PBL depth calculation; and vertical diffusivities proportional to the velocity scale w s, which is a function of surface friction velocity u * and nondimensional stability functions u valid in the surface layer. Refer to Eqs. (B6), (A3), (A12), and (A1) (A2) in Hong et al. (2006), respectively. The ACM2 scheme is also directly coupled with surface layer variables in these same four parts, even though the two schemes are different in expressing the nonlocal transport. In comparison with the YSU and ACM2 parameterizations, the MYJ scheme is more weakly linked with the surface layer. Only the surface fluxes, the lower boundary conditions in the scheme, directly affect near-surface vertical mixing. However, there are still indirect connections. For example, the TKE at the lowest model level that is directly influenced by the surface fluxes determines the eddy diffusivity, and the surface friction velocity affects the vertical wind speed gradients near the surface. 3. Experimental setup a. Synoptic conditions and boundary layer structures The CASES-99 main site is near Leon, Kansas (37.68N, 96.78W), and the location is relatively flat with lack of obstacles and covered by grassland (Poulos et al. 2002). The location is favored by a clear-sky and dry environment. Since SH11 already described the synoptic environment for the diurnal cycle, we briefly summarize the synoptic conditions. A high pressure system over the Texas Panhandle at 1200 UTC 23 October moved

4 FEBRUARY 2012 S H I N E T A L. 667 FIG. 1. Observed vertical profiles of (a) potential temperature (K), (b) wind speed (m s 21 ), and (c) vapor mixing ratio (g kg 21 ) from 1100 UTC 23 Oct (0600 LST 23 Oct) to 1100 UTC 24 Oct 1999, obtained from radiosonde soundings that were made at Leon, KS. In (b), near-surface wind speed profiles are discontinuous because of missing data. southeastward over the following 24 h, related to the movement of the 850-hPa ridge to the CASES-99 main site from the northwest (not shown). Figure 1 shows vertical profiles of temperature, wind speed, and moisture from 1100 UTC 23 October (0600 LST 23 October) to 1100 UTC 24 October 1999, provided by radiosonde soundings that were made at Leon, Kansas (see online at dss/id ). The temperature profile (Fig. 1a) at 1900 UTC 23 October shows a uniformly mixed daytime boundary layer with roughly 900-m depth. Van de Wiel et al. (2003) investigated that the turbulence in the night of October 1999 over the main site was weak and intermittent. This intermittent turbulence and the weak synoptic thermal advection made the high temperature of the daytime boundary layer remain until 0300 UTC 24 October, except near the surface where strong radiative cooling was present. However, the strong surface cooling and intermittent turbulence decoupled the boundary layer from the surface friction, and the low-level jet appeared at 0700 UTC 24 October (Fig. 1b). The strong shears due to the jet drove turbulent mixing; therefore, the stable layer between 100 and 1000 m appeared at the time. Since there was no source of moisture under the dry and weak synoptic forcing, the changes of moisture profiles were closely linked to the turbulent mixing (Fig. 1c). b. Model setup The Advanced Research WRF (ARW) numerical model version 3.2 is used, which has a fully compressible and nonhydrostatic dynamic core. The domain configuration and physics packages are identical to those used in SH11, which compared five PBL parameterizations in the WRF model including the YSU, ACM2, and MYJ PBL schemes for the same simulation period. The WRF model is run over spatial domains that consist of a parent domain and two nested domains centered on the location of the CASES-99 main site (37.68N, 96.78W) in the Lambert conformal space (Fig. 2); a 3-km grid-size domain (Do3, ) is nested inside a 9-km grid-size domain (Do2, ), which in turn is nested within a 27-km grid-size domain (Do1, ) using a one-way nesting method. Model integrations are conducted for 24 h from 1200 UTC 23 October (0700 LST 23 October) to 1200 UTC 24 October 1999, and the three domains are initialized by the National Centers for Environmental FIG. 2. Model domain for the 27-km horizontal grid-size experiment (Do1) with terrain heights contoured every 200 m. The two inner boxes represent domains for the 9-km (Do2) and 3-km (Do3) grid-size experiments, respectively. The crisscross symbol indicates the CASES-99 site.

5 668 M O N T H L Y W E A T H E R R E V I E W VOLUME 140 FIG. 3. A schematic diagram illustrating the lower vertical levels in the CTL, SL90, SL16, and SL04 experiments. Dotted and solid lines indicate full-s and half-s levels, respectively. Prediction (NCEP) Final Analysis (FNL) data on grids. Boundary conditions for the outmost 27-km domain are also forced by the NCEP FNL data every 12 h. Physics options for radiation and land surface processes are fixed for all simulations conducted: the Rapid Radiative Transfer Model for GCMs (RRTMG) longwave radiation (Mlawer et al. 1997) and the Goddard shortwave radiation (Chou and Suarez 1999) schemes, and the Noah land surface model (Chen and Dudhia 2001; Ek et al. 2003). Steeneveld et al. (2008) used an observation-based roughness length z 0 of 0.03 m that is valid at the CASES-99 main site, and this study adopts the value in all numerical simulations. The Kain Fritsch cumulus parameterization (Kain and Fritsch 1993) and the WRF Single-Moment 6-Class Microphysics scheme (WSM6; Hong et al. 2004; Hong and Lim 2006) are selected for cloud processes; the Kain Fritsch scheme is taken out in all 3-km grid-size experiments. No explicit horizontal diffusion is included, but sixth-order numerical diffusion is implicitly induced by the fifth-order horizontal advection scheme instead. c. Experimental design The experiments with the YSU, ACM2, and MYJ schemes are designated as the YSU, ACM2, and MYJ experiments, respectively. Sensitivities to the lowest model level height are analyzed for all three PBL schemes with the aim to compare reactions of these three PBL diffusion schemes to changes in z 1. The control run uses a vertical grid system of 28 full-s levels (i.e., 27 half-s levels or 27 layers) with the model top at 50 hpa, which is the default vertical grid system 1 in the WRF model. Here s is defined as s 5 (p p top )/(p sfc 2 p top ), where p is pressure, p sfc is pressure at the surface, and p top is pressure at the model top. In the WRF model, horizontal wind components and thermodynamic prognostic variables are 1 In this study, the term default vertical grid system refers to the vertical grid system that is given in the sample name list file for the WRF forecast execute program. allocated to the half-s levels, while vertical velocity, vertical turbulent fluxes, and eddy diffusivities are assigned to the full-s levels (cf. Fig. 3). In the control (CTL) simulation of each PBL scheme, the lowest (first) and second full-s levels above the ground are s and s , and the corresponding lowest half-s level height z 1 is roughly 40 m. Note that the lowest full-s level is the ground (i.e., s ). The lowest model level height is controlled by changing the value of s 2. For each PBL parameterization, 9 experiments with 9 different z 1 levels including the CTL experiment are conducted (Table 1): the SL90 (z 1 of roughly 90 m), SL64, CTL (or SL40), SL24, SL16, SL12, SL08, SL06, and SL04 experiments. To avoid an enormous jump in layer thickness, a full-s level of (i.e., s 2 of the CTL) is added between z 1 and a full-s level of (i.e., s 3 of the CTL) in the SL24, SL16, and SL12 vertical grid systems (cf. Fig. 3). In the SL08, SL06, and SL04 grid systems, two s levels at and are added between z 1 and the full-s level of It is noted that results will focus on the SL90, CTL (SL40), SL16, and SL04 experiments, because of their representativeness of the deep surface layer, frequently used z 1,and TABLE 1. A summary of numerical experiments. Vertical levels added below z 1 of the control (CTL) experiment (i.e., below the s level of 0.990) are underlined, and the number of vertical levels that is identical to the SL04 (CTL) experiment (i.e., 28 levels) are in boldface. Expt s 1 s 2 s 3 s 4 z 1 (m) No. of full-s levels SL SL SL40 (CTL) SL SL SL SL SL SL SL16_L SL04_L

6 FEBRUARY 2012 S H I N E T A L. 669 FIG. 4. (a) Surface energy budget of the YSU (black), ACM2 (red), and MYJ (green) SL40 experiments, with corresponding observations (gray): the sum of the surface sensible heat flux H, latent heat flux LH, and soil heat flux G (solid), and the net radiative flux (Rnet) (dotted). (b) Estimated surface-layer height (gray solid) derived by averaging values of 0.1h, where h is the PBL height that is calculated from the YSU (black dotted), ACM2 (red dotted), and MYJ (green dotted) PBL schemes. moderately shallow and extremely stable surface layer. In the SL90, CTL (SL40), SL16, and SL04 experiments, the heights of z 1 levels are 90, 40, 16, and 4 m, respectively. Information of the lower full-s levels, the lowest model level height z 1, and the number of vertical layers are summarized in Table 1. Figure 3 illustrates the vertical grid system of the lower vertical levels in the CTL (SL40), SL90, SL16, and SL04 experiments. 4. Results Here, we aim to answer two questions. First, how do the three schemes react to the changes in z 1? Second, how do the sensitivities change given the stratification of the boundary layer (i.e., in the convective regime of daylight hours vs the stable regime during nighttime)? Discussions are focused on the results of the 3-km grid-interval experiments. As reference observations, surface measurement data are provided by six 10-m towers surrounding the CASES-99 main site (see online at edu/isf/projects/cases99/isff.shtml), and vertical profiles are obtained from radiosonde soundings which were made at Leon, Kansas (37.48N, 96.48W, 436 m mean sea level; see online at a. Overview of the model performance Note that the simulated net surface radiation matches well with the observed one during the selected day (not shown), even though the modeled individual upward and downward longwave radiation fluxes deviate from those observed due to the warm bias in surface temperature. In the land surface model, the net radiation is in balance with the surface sensible heat flux, latent heat flux, and soil heat flux (the residual term is less than 5Wm 22 ; Fig. 4a). Meanwhile in the case of the observation, the sum of the sensible, latent, and soil heat fluxes is less than the net radiation flux by about 100 W m 22 around noon. In consequence, the simulated surface heat fluxes are larger than those observed owing to the imbalance in the observed energy budget, as well as due to the overestimated surface temperature. The closure of the observed surface energy budget is hard to be achieved because of the instrumentation error, surface heterogeneity, and theoretical assumptions in measuring systems (Brotzge and Crawford 2003). Oncley et al. (2007) mentioned that a possible source of the imbalance is the vertical flux divergence between the canopy top and flux measurement height, mainly due to the horizontal advection. For these reasons, discussions are focused on the differences in sensitivity experiments, rather than on an objective measure of performance against the observations. The temporal evolution of the surface layer height is estimated by averaging values of 0.1h (Fig. 4b); h is the PBL height that is calculated in each PBL scheme for each z 1. The surface layer height is compared with the various lowest model level heights that are labeled along the y axis. The surface layer height varies between 4 and

7 670 M O N T H L Y W E A T H E R R E V I E W VOLUME m during one complete diurnal cycle. It is apparent that none of the z 1 values are representative of the diurnal variations of the estimated surface layer depth, and this is because all tested s 2 values are constant and do not vary in time. The assumption that z 1 is within the surface layer is not valid in the stable regime for most of the z 1 values, and z 1 values of several tens of meters are not appropriate during the morning and evening transitions. b. Surface variables Figure 5 shows the sensitivities of temporal development of simulated sensible heat flux H, latent heat flux LH, and surface friction velocity u * to z 1 with the YSU, ACM2, and MYJ PBL schemes. The daytime time series show that the simulated H (Figs. 5a c) is slightly sensitive to changes in z 1. Even though the sensitivity of H is the most distinguishable at its peak time (inset), the fractional differences in H among different z 1 values remain small. The maximum value of H varies between 1.35% (ACM2) and 2.62% (MYJ) from the maximum of the corresponding CTL experiment. For stable surface layer conditions (i.e., in the nighttime), the ACM2 and MYJ schemes react to the lowest model level height in similar ways; the magnitude of H gets smaller as z 1 decreases from 40 to 4 m, whereas it gets larger in the YSU experiments. The increase in z 1 from 40 to 90 m does not result in the systematic sensitivity. In the Noah land surface model, the potential temperature difference in Eq. (3a) decreases as z 1 decreases. Since all z 1 values are expected to be within the real surface layer in the daytime (cf. Fig. 4b), the wind and temperature profiles at z 1 are logarithmic. On the other hand, C H is proportional to U 1 but inversely proportional to [ln(z 1 /z 0M ) 2 c M ] 3 [ln(z 1 /z 0T ) 2 c H ] [Eqs. (2b) and (3b)]; C H increases as z 1 decreases. Thus, a possible explanation for the slight decrease in the magnitude of H due to the reduction in z 1 is that the decrease in the temperature difference in Eq. (3a) overwhelms the increase in C H. The simulated latent heat flux (Figs. 5d f) is sensitive to changes in z 1 only during the daytime when the flux is large enough; the latent heat flux becomes larger as z 1 decreases. Since the latent heat flux is calculated in the land surface model and it is in balance with the sensible heat flux, the increase of LH is related to the energy budget balance in the land surface model consistent with the H reduction. In the case of the simulated friction velocity (Figs. 5g i), the momentum fluxes near the surface slightly increase as z 1 decreases through the daylight hours with all three PBL schemes. Here u * is directly calculated in surface layer schemes, and it is proportional to U 1, but inversely proportional to [ln(z 1 /z 0M ) 2 c M ] [Eq. (2b)]. As mentioned above, the wind profile at z 1 is also expected to be logarithmic. Thus, the impact of z 1 on the surface friction velocity is not significant. Under stable surface layer conditions, the ACM2 and MYJ parameterizations show a common dependency on the lowest level height; by and large, u * decreases as z 1 decreases from 40 down to 4 m. Unlike in unstable conditions, large z 1 values are beyond the real surface layer in stable conditions; the wind profile at z 1 (i.e., U 1 ) is no longer logarithmic for these large values, while [ln(z 1 /z 0M ) 2 c M ] is taken to be logarithmic because of the assumption that z 1 is within the surface layer. In this case, U 1 increases more rapidly than [ln(z 1 /z 0M ) 2 c M ] for the same z 1 increase. Therefore, u * increases [Eq. (2b)]. The YSU scheme shows an opposite behavior compared to the other two PBL schemes. Sensitivities of time series of simulated 2-m temperature T 2 and10-mwindspeedu 10 to z 1 are presented in Fig. 6. Note that T 2 and U 10 are diagnosed in the surface layer schemes; they are interpolated between z 1 and the surface using similarity theory. During the daytime, simulated temperatures of the YSU and MYJ schemes (Figs. 6a,c) slightly increase when z 1 is shallow, such as at 4 m (i.e., the SL04 experiments), reflecting the reduction in H. Note that the daytime changes in the surface heat fluxes are related to a resistance formulation of the fluxes (Stensrud 2007). In other words, the depth that responds to the sensible heat flux decreases as z 1 decreases, and then the layer responses more quickly to the same flux. This results in the higher 2-m air temperature, and decreases the lower temperature differences in Eq. (3a); the sensible heat flux eventually decreases. Nonetheless, it is found that the time step hardly changes the surface outcome of the experiments (not shown). The ACM2 and MYJ SL04/SL16 experiments produce more rapid surfacecooling rates during the day-to-night transition time. Therefore, with the ACM2 and MYJ schemes, the 2-m temperature becomes cooler during the nighttime as z 1 decreases. On the other hand, the YSU scheme shows an opposite sensitivity to these two schemes in modeling the nighttime 2-m air temperature, in accordance with the opposite sensitivity of H. The trend of sensitivities of the 10-m wind speed to the lowest level height resembles that of the surface friction velocity (cf. Figs. 6d f and 5g i). A noticeable difference between the sensitivities of U 10 and u * is the larger sensitivity of U 10 than u * in nighttime for the YSU scheme. Both U 1 and u 1 2 u s of the YSU PBL scheme decrease as z 1 gets closer to the surface, similar to the other two schemes (not shown). Hence, the opposite sensitivity of H and u * finversely proportional to [ln(z 1 /z 0T,M ) 2 c H,M ], Eqs. (2b) and (3)g from the YSU PBL in the stable regime is attributed to the stability function (c M or c H )ofthe MM5 surface layer scheme. The stability function has a bigger gap between the very stable regime [e.g., the bulk Richardson number (Rib) in the surface layer is larger

8 FEBRUARY 2012 S H I N E T A L. 671 FIG. 5. Time series of (a) (c) simulated sensible heat flux (W m 22 ), (d) (f) latent heat flux (W m 22 ), and (g) (i) surface friction velocity (m s 21 ) from experiments with the (left) YSU, (middle) ACM2, and (right) MYJ PBL schemes. For each PBL scheme, results from the SL90 (dot dashed), CTL (SL40) (solid), SL16 (dashed), and SL04 (dotted) experiments are presented. Observations are designated by gray lines with crisscross symbols. In (a) (c), each inset provides a closer look at the heat flux from 1600 UTC 23 Oct to 2000 UTC 23 Oct than 0.2] and the damped mechanical turbulent regime (0.0, Rib, 0.2), compared to the gap of the PX or Eta surface layer scheme. The magnitude of the stability function is larger in the very stable regime (cf. c M, 0in the stable regime). Since the wind profile almost does not vary in the vertical when z 1 is high (e.g., 90 m; cf. Fig. 10g), Rib in the surface layer is more likely to be above 0.2. On the other hand, Rib becomes smaller (i.e., enters the

9 672 M O N T H L Y W E A T H E R R E V I E W VOLUME 140 FIG. 6. As in Fig. 5, but for (a) (c) 2-m temperature (8C) and (d) (f) 10-m wind speed (m s 21 ). In (a) (c), each inset provides a closer look at the 2-m temperature from 1800 UTC 23 Oct to 0000 UTC 24 Oct mechanical turbulent regime) following the reduction in z 1, owing to the increased wind shear. In this case the surface layer is classified into the different regimes according to z 1 both H and u * are larger with the shallow z 1 in the mechanical turbulent case. Figure 7 summarizes the performance of the three PBL schemes according to the nine z 1 values in simulating surface parameters and PBL heights. In the daytime, variables are insensitive to increases in z 1 or they do not show systematic sensitivity when z 1 is higher than 12 m. However, the model results tend to gradually depend on z 1 when z 1 decreases below 12 m, even though the surface layer assumption is not violated. In the nighttime when most of z 1 values in this study are beyond the applicable range of the surface layer assumption, the simulations of most variables are systematically sensitive to z 1,asz 1 decreases from 40 m. The systematic sensitivities of the ACM2 and MYJ schemes show the same trend, while the YSU PBL scheme often shows the opposite behavior to the other two schemes. c. PBL structures Dependencies of the PBL height h on z 1 imply a deeper convective boundary layer in the YSU SL04 and SL16 experiments, while the ACM2 and MYJ PBL schemes are less sensitive to z 1 (Figs. 8a c). In the YSU scheme h is determined as the lowest level where the bulk Richardson number (Rib), between the lowest model level and z above z 1, reaches the critical Richardson number (Rib cr ; Hong et al. 2006): Rib(z) 5 gz[u v (z) 2 u s ] u va ju(z)j 2, (5)

10 FEBRUARY 2012 S H I N E T A L. 673 FIG. 7. Sensitivities to z 1 of (a) sensible heat flux (W m 22 ), (b) latent heat flux (W m 22 ), (c) surface friction velocity (m s 21 ), (d) 2-m temperature (8C), (e) 10-m wind speed (m s 21 ), and (f) PBL height (m) that are averaged over unstable regimes [i.e., 12 h from 1200 UTC 23 Oct (0700 LST 23 Oct) to 0000 UTC 24 Oct (1900 LST 23 Oct)] (circle marks) and over stable regimes [i.e., 12 h from 0000 UTC 24 Oct (1900 LST 23 Oct) to 1200 UTC 24 Oct (0700 LST 24 Oct)] (triangle marks) for the YSU (black), ACM2 (red), and MYJ (green) experiments. Observed values for the unstable and stable conditions are designated by gray solid lines and gray dashed lines, respectively. The axes on the right in (a) and (b) are for stable conditions. where g is the acceleration due to gravity, u va is the virtual potential temperature at z 1,andu s is the appropriate temperature near the ground. Here u v (z) andu(z) represent the virtual potential temperature and horizontal wind speed at z, respectively. The Rib cr is zero for CBL, whereas it is greater than zero for SBL (Hong 2010). The u s is defined as u s 5 u v (z 1 ) 1 u T 5b (w9u9 v ) 0, (6) w s where u T is the temperature excess of thermals, b is a proportional constant, and w s is the mixed-layer velocity scale. The u T is excluded in the SBL. Since u va and u s get warmer (cooler) as z 1 becomes closer to the surface in CBL (SBL), h becomes higher (lower) in the YSU experiments (Fig. 8a). The ACM2 scheme uses a similar method without the thermal excess term in stable conditions, but u va is defined as the average virtual potential temperature between z 1 and z [cf. Eq. (20) in Pleim (2007a)]. In unstable conditions, the mixed layer height z mix is first determined

11 674 M O N T H L Y W E A T H E R R E V I E W VOLUME 140 FIG. 8. As in Fig. 5, but for the PBL heights. where u v (z mix ) 5 u s. Then, the PBL height h is diagnosed similar to the YSU PBL, but with Rib defined between z mix and the heights above z mix (Pleim 2007a): Rib(z) 5 g(z 2 z mix )[u v (z) 2 u s ] u va ju(z) 2 U(z mix )j 2, (7) where u va is an average between u v (z) andu s.asz 1 decreases, z mix increases since u s gets warmer. Thus, both temperature gradient and wind shear between z mix and z decrease for a fixed z above z mix, then Rib and h are not as sensitive as in the YSU scheme (Fig. 8b). On the other hand, the MYJ algorithm determines the PBL height as the model height where the predicted TKE value reaches a sufficiently small background value (0.101 m 2 s 22 ). The MYJ parameterization is a local closure and is weakly linked with the surface layer properties. In the CBL TKE is generally large and the level where TKE becomes the background value is far from the surface. Thus, the surface layer quantities hardly affect the TKE at that level (Fig. 8c); h is not sensitive to z 1 as much as that of the YSU PBL. In the SBL of this study the prognostic TKE is generally small and below the background value (not shown), and h is usually equal to the height of the lowest full-s level above the ground (i.e., s 2 ). Therefore, h gradually increases as z 1 increases. The simulated potential temperature, vapor mixing ratio, and wind profiles corresponding to sounding measurements at 1900 UTC 23 October (1400 LST 23 October) are presented in Fig. 9. Under the SL04 configuration, the YSU scheme produces a deep mixed layer (Figs. 9a,d,g). Mixing becomes slightly weaker as z 1 increases from 16 to 90 m. On the other hand, the ACM2 scheme simulates a cooler and wetter PBL with the SL04 setting (Figs. 9b,e), whereas it is warmer and drier above the top of the PBL. In the ACM2 scheme, the contributions of the nonlocal transport and local mixing terms are determined by the variable f conv and (1 2 f conv ), respectively: K f conv 5 H g h, (8) u K H g h 2 K H z where g h is the countergradient term [cf. Eqs. (15) (19) in Pleim 2007a]. As z 1 decreases, the stronger mixing occurs during the early stage of the PBL development (not shown) due to larger local mixing (cf. Fig. 11b), and the PBL more quickly reaches a neutral state before 1900 UTC (1400 LST). However, the local mixing decreases in the neutral PBL, and then f conv increases. Pleim (2007a) showed that main effects of the nonlocal component are to stabilize (therefore, to cool) the lower 2 /3 of the PBL, and to lower the PBL height (cf. Fig. 2 in Pleim 2007a). The change of the temperature profiles according to the z 1 reduction can be interpreted as the effects of the increase in f conv [cf. Fig. 9b in this study and Fig. 2 in Pleim (2007a)]. The MYJ scheme is nearly insensitive to variations in z 1 (Figs. 9c,f,i). Figure 10 presents the simulated profiles at 0700 UTC 24 October (0200 LST 24 October). The strong SBL mixing of the YSU PBL is alleviated in the SL04 experiment (Fig. 10a). However, the q y profile indicates the presence of strongly mixed structures in the residual layer (roughly between 300 and 1300 m) in the SL04 framework (Fig. 10d). This is attributable to the excessive mixing throughout the whole PBL during the

12 FEBRUARY 2012 S H I N E T A L. 675 FIG. 9. Vertical profiles of the (a) (c) simulated potential temperature (K), (d) (f) vapor mixing ratio (g kg 21 ), and (g) (i) wind speed (m s 21 ) at 1900 UTC 23 Oct (1400 LST 23 Oct) 1999 from experiments with the (left) YSU, (middle) ACM2, and (right) MYJ PBL schemes and corresponding radiosonde soundings (gray lines). For each variable from each PBL scheme, results from the SL90 (dot dashed), CTL (SL40) (solid), SL16 (dashed), and SL04 (dotted) experiments are presented. daytime, as well as the nighttime local mixing (cf. Fig. 11d). The momentum mixing in the SBL decreases following the z 1 reduction (Fig. 10g), but it is not enough to simulate the low-level jet (LLJ). Note that all three schemes are not able to simulate the LLJ with proper intensity on this night. In the case of the ACM2 scheme (Figs. 10b,e,h), the lower atmosphere below 1000 m is still slightly cooler and wetter with the smaller z 1, because of

13 676 M O N T H L Y W E A T H E R R E V I E W VOLUME 140 FIG. 10. (a) (i) As in Fig. 9, but at 0700 UTC 24 Oct (0200 LST 24 Oct) In (g) (i), wind direction (8) is added. Note that near-surface wind speed profiles are discontinuous because of missing data [e.g., (g) (i)]. the daytime profiles. The ACM2 scheme produces a strongly mixed moisture profile in the nighttime (Fig. 10e). The mixing becomes weaker with the SL04 and SL16 vertical-grid configurations, but they are not enough to simulate a local minimum at 1000 m as small as in the other two schemes. The MYJ scheme shows almost no sensitivity to z 1 above the SBL (Figs. 10c,f,i), whereas z 1 affects the performance of the three PBL schemes below the top of the SBL. This is because temperature and wind profiles significantly change near the surface in the night

14 FEBRUARY 2012 S H I N E T A L. 677 FIG. 11. Eddy viscosity K M (m 2 s 21 ) averaged over 12 h (a) (c) from 1200 UTC 23 Oct to 0000 UTC 24 Oct (i.e., convective regime), and (d) (f) from 0000 UTC 24 Oct to 1200 UTC 24 Oct (i.e., stable regime) from experiments with the (left) YSU, (middle) ACM2, and (right) MYJ PBL schemes. For each PBL scheme, results from the SL90 (dot dashed), CTL (SL40) (solid), SL16 (dashed), and SL04 (dotted) experiments are presented. time, and the proportion of the SBL that z 1 accounts for varies considerably following z 1 : from several percent of thesl04toalmost50%ofthesl90. The K M (vertical diffusivity for momentum) averaged over unstable and stable regimes is displayed in Fig. 11. It is noted that the diffusivity K c (1 2 f conv ) is multiplied by the local gradient of the prognostic mean variable C to express local mixing in the ACM2 scheme [cf. Eqs. (10) and (11) in Pleim 2007a]. Thus, the diffusivity K c (1 2 f conv ) is depicted in the figure. In unstable regimes, as z 1 decreases from 90 to 4 m, the maximal magnitude of K M and mixing depth of the YSU scheme gradually increase (Fig. 11a). This supports the behavior of the simulated daytime profiles (Figs. 10a,d,g). The ACM2 scheme (Fig. 11b) shows a similar sensitivity to the YSU scheme from z 1 of 16 to 4 m, but it is not sensitive to the changes in z 1 from 90 to 16 m. The K M of the MYJ scheme does not reveal systematic sensitivity (Fig. 11c). The differences in z 1 sensitivity among the three PBL schemes can be explained by examining how the diffusivities are formulated in the schemes. In the YSU scheme, the diffusivity is specified based on the prescribed K-profile functions [refer to Eq. (A1) in Hong et al. 2006]: K M 5 kw s z 12 z h 2, (9) where k is the von Kármán constant, w s is the mixed-layer velocity scale, and h is the PBL height. According to this formula, the diffusivity profiles are limited below the PBL height, thus the PBL height is very critical in describing the K profiles. The PBL height gets higher as z 1 becomes smaller in the YSU scheme (cf. Fig. 8a), and it is consistent with the enhanced diffusivity within the PBL (Fig. 11a).

15 678 M O N T H L Y W E A T H E R R E V I E W VOLUME 140 In the ACM2 scheme, the larger of the K-profile value [Eq. (1) in Pleim 2007b] and a local K value [K is proportional to local wind shear and local Richardson number, Eq. (4) in Pleim 2007b] is applied in the CBL. The K-profile value is generally larger than the local K value in CBL, except near the top of the PBL. Thus, the ACM2 SL04 experiment shows larger diffusivity in the middle of the PBL than other ACM2 experiments as in the YSU SL04 experiment (cf. Figs. 11a,b). In the MYJ PBL scheme, the diffusivities are proportional to turbulent kinetic energy [i.e., e; refer to Eq. (3.4) in Janjić 1990]: pffiffi K c 5 l e Sc, (10) where l is the mixing length, e is the turbulent kinetic energy, and S c is the proportionality coefficient. The lowest model level height has a direct influence only on nearsurface heights in the MYJ scheme, while the local TKE and mixing length (therefore, the diffusivity) are large in middle of the PBL, which results in a less systematic sensitivity (Fig. 11c). Generally, K H (vertical diffusivity for heat and moisture) shows similar behaviors with K M according to z 1 changes (not shown), since K M and K H are linked to each other. In the YSU PBL algorithm, K M is calculated first, and K H is determined through multiplying K M by the Prandtl number. In the ACM2 method, K H is equal to K M. In stable regimes, the manners in which diffusivities change in accordance with z 1 differ among the PBL schemes (Figs. 11d,e,f). In the YSU scheme, the prescribed K-profile method [Eq. (9)] is used in stable regimes, unlike the local K method of the ACM2 and MYJ schemes. Therefore, the diffusivities gradually get smaller through lowering z 1 within the SBL (Fig. 11d), following the decrease in SBL height (cf. Fig. 8a). This explains the weaker mixing in the lower z 1 experiments (Figs. 10a,d,g). Meanwhile, the diffusivities above the SBL increase following the z 1 reduction in the SL04 experiment. The height of the larger K M of the SL04 experiment (i.e., between 500 and 1000 m above the ground) matches well with the height where the wind direction changes more with time compared to other vertical gridspacing experiments (not shown). The vertical gradient of the wind speed is also larger with height (e.g., Fig. 10g). Changes in inertial oscillations following the z 1 reduction seem to play a role in increasing the vertical wind shear in the nighttime. The diffusivities are proportional to the local wind shear above the SBL [cf. Eq. (A15) in Hong et al. 2006], and this explains the increases of K c above the SBL. The ACM2 experiments show that diffusivities increase when z 1 is between 90 and 40 m (Fig. 11e; i.e., from SL90 to SL64, and then to SL40); however, they decrease when the height is lowered from 40 down to 4 m. It is noted that the diffusivities are set as the background value when the local Richardson number exceeds 0.25 in the ACM2 PBL scheme: K Dz (m 2 s 21 ). A very stable near-surface profile is produced when z 1 is low, and the diffusivities are set to K 0 near the surface with a large local Richardson number. The diffusivities of the MYJ scheme tend to decrease as z 1 decreases down to 24 m, and they are almost invariable when z 1 is below 24 m (Fig. 11f). Synthesizing the above, the two nonlocal, K-profile PBL parameterizations the YSU and ACM2 schemes are more sensitive to the lowest model level height than the local PBL scheme. However, the sensitivities of the two schemes are different (sometimes, opposite) to each other, according to the dissimilarities in the definition of the PBL height, the determination of the diffusivity in the entrainment zone, and the nonlocal mixing formula. The local MYJ scheme is nearly insensitive to the height of the lowest model level, except for the stable regime. Since we use a one-way nesting method between the 27-, 9-, and 3-km grid spacing domains (cf. section 3b), we checked whether the z 1 sensitivity depends on the horizontal resolution (not shown). The impacts of z 1 of the 3-km grid-size experiments are kept at the 9-km grid size. WRF simulations with the 27-km grid spacing also show the similar sensitivity to z 1 to the 3-km grid spacing simulations, except for surface wind variables during the morning transition; the magnitude of the surface friction velocity and 10-m wind speed suddenly decreases during the transition unlike the 9- and 3-km experiments. Another issue is the impact of evening transition simulations on the z 1 sensitivity for stable conditions, since the WRF simulations in our study are begun in early morning. It is well known that simulating the evening transition from a CBL to an SBL is a common deficiency of many atmospheric numerical models (Edwards et al. 2006). A second set of experiments, which are initiated at 0000 UTC 24 (1900 LST 23) October 1999, showed that the z 1 sensitivities of the three PBL schemes are generally kept whether the evening transition is simulated by the WRF model or provided from the NCEP FNL data (not shown). However, for vertical profiles, the strongly mixed moisture profiles resulting from the excessive daytime mixing in the two nonlocal schemes (Figs. 10d,e) are removed when the simulations are started in early evening (not shown); the PBL structures are insensitive to the lowest model level height above the SBL. d. Importance of vertical grid spacing in surface layer In the experiments with z 1 below 40 m, the vertical grid spacing in surface layer becomes finer as z 1 decreases (cf.

16 FEBRUARY 2012 S H I N E T A L. 679 FIG. 12. (a) Vertical profiles of the simulated vapor mixing ratio (g kg 21 ) at (a) (c) 1900 UTC 23 Oct and (d) (f) 0700 UTC 24 Oct 1999, from experiments with the (left) YSU, (middle) ACM2, and (right) MYJ PBL schemes. Results from the SL90 (dot dashed black), CTL (SL40) (solid black), SL16_L28 (dashed red), and SL04_L28 (dotted red) experiments are presented, with corresponding radiosonde soundings (gray lines). Fig. 3 and Table 1). Increasing the number of the vertical levels is done to avoid a sudden jump in layer thickness between the first and second layers, but this also results in a refined vertical grid resolution in the surface layer. To discuss the importance of vertical grid spacing in surface layer, SL16_L28 and SL04_L28 experiments are conducted. In these cases, we lower z 1 without adding vertical layers (i.e., with 28 full-s levels; Table 1); the z 2 values of the two experiments are 100 and 90 m, respectively. In section 4b, it is mentioned that the surface and 2-m air temperatures increase through lowering z 1,consistent with the resistance formulation of the fluxes. On the other hand, the second vertical layer is excessively deeper than z 1 in the SL04_L28 experiments. Then, the second layer responds more slowly to the heated first layer in comparison with the SL04 experiments; the heat from the surface is accumulated in the lower layer. On account of this, the maximum surface and 2-m air are warmer by about 2 (YSU) to 4 K (ACM2) than the SL04 experiments (not shown). Owing to this increased near-surface temperature, the YSU and ACM2 SL04_L28 experiments produce an overly deep mixed layer, and the moisture profiles are significantly deteriorated (Figs. 12a,b). These degraded structures remain in the residual layer in the nighttime (Figs. 12d,e). Opposite to the two schemes, the MYJ SL04_L28 experiment shows a shallower mixing in the CBL (Fig. 12c). This is attributed to the accumulation of the TKE at the first layer and the decrease in TKE above (not shown), leading to the decrease in the diffusivity in the PBL [cf. Eq. (10)].