Although most of the planetary boundary layer (PBL) parameterizations have demonstrated the capability to reproduce many meteorological phenomena in the lowest few kilometers, little attention has been paid to the prediction of the diurnal cycles of surface wind speed (VSFC) in relation to surface temperature (TSFC). In this study, the performance of five widely used PBL parameterizations in reproducing the diurnal cycles of VSFC and TSFC is evaluated using the 3-day mesoscale simulations of summertime weak-gradient flows over the central United States where little organized convection and topographical forcing were present. The time series of area-averaged VSFC and TSFC, as well as the vertical wind and thermal profiles from the five sensitivity simulations, are compared with hourly surface observations and other available data. The hourly surface observations reveal that the diurnal cycles of VSFC are in phase (but surface wind directions are 5–6 h out of phase) with those of TSFC. It is shown that both VSFC and TSFC are very sensitive to the PBL parameterizations, given the identical conditions for all of the other model parameters. It is found that all five of the PBL schemes can reproduce the diurnal phases of TSFC (and wind directions), albeit with different amplitudes. However, all of the schemes underestimate the strength of VSFC during the daytime, and most of them overestimate it at night. Moreover, some PBL schemes produce pronounced phase errors in VSFC or substantially weak VSFC all of the time, despite their well-simulated diurnal cycle of TSFC. The results indicate that a perfect simulation of the diurnal TSFC cycle (and the thermal structures above) does not guarantee the reproduction of the diurnal cycles of VSFC. The final outcome would depend on how various physical processes, such as the vertical turbulent exchanges of the mass and momentum under different stability conditions, are parameterized. Because the upper portion of the PBL flow is often nearly opposite in phase to VSFC under weak-gradient conditions, the results have significant implications for the predictability of diurnal precipitation and the studies of air quality, wind energy, and other environmental problems.
The planetary boundary layer (PBL) over land generally undergoes significant diurnal cycles,1 especially on calm, clear-sky days. The daytime PBL begins when the net surface heat flux is directed upward after sunrise. As more solar energy is absorbed by the earth's surface, free convective eddies become active in transporting sensible heat (moisture) upward to warm (moisten) the air above and momentum downward to accelerate the flow below. Meanwhile, the rising eddies, with their roots in the surface layer, penetrate into the capped inversion and mix heat, moisture, and kinetic energy with their environments—a countergradient heat transport process referred to as entrainment. The mass and wind fields in this mixed layer adjust quickly to produce a state of slowly evolving equilibrium until the PBL reaches its maximum depth in the late afternoon. Near sunset, rapid radiative heat losses occur at the ground so that a second temperature inversion starts to grow from the bottom surface. As a result, horizontal winds above the surface layer begin to decouple from the surface friction, sometimes leading to the formation of a nocturnal low-level jet (LLJ) near the top of the nocturnal inversion layer (Blackadar 1957).
During the past 30–40 yr, considerable progress has been made in the development and improvement of the PBL parameterizations (e.g., Mellor and Yamada 1974; Blackadar 1976, 1979; Zhang and Anthes 1982; Burk and Thompson 1989; Janjić 1994; Hong and Pan 1996) and land surface parameterizations (Xue et al. 1991; Chen and Dudhia 2001) in order to obtain realistically the above-mentioned flow properties in the PBL and the collective effects of the PBL on the free atmospheric circulation with numerical weather prediction (NWP) and climate models. For example, one-dimensional (1D) PBL schemes have advanced from the early first-order, local K theory to 1.5-order and higher-order turbulent kinetic energy (TKE) closures, and 3D atmospheric models have progressed from the bulk, mixed-layer treatment to higher resolution and to the large-eddy-simulation models (Holt and Raman 1988; Moeng 1984). Because the PBL behaves differently in unstable and stable stratifications, various nonlocal closures have been developed to treat the daytime PBL development (e.g., see the appendix). However, most of the previous 3D modeling studies focused on the diurnal cycles of surface temperature (TSFC) and the spatial structures of the mass and wind fields in the PBL in relation to clouds and precipitation (Burk and Thompson 1989; Hong and Pan 1996; Braun and Tao 2000). Little attention has been paid to the model's capability to capture the diurnal cycles of surface and PBL winds. This omission is due partly to some uncertainties in parameterizing the vertical momentum transport and pressure diffusion in the PBL and partly to the misconception that the convective development is associated more with the vertical transport of sensible and latent heat fluxes than with momentum fluxes. Sometimes the PBL winds (and divergence) are considered simply as a dynamical response to the thermal gradient generated by differential (radiative) heating or cooling (e.g., sea breezes). For the convenience of subsequent discussions, we will hereinafter distinguish the surface wind speed (VSFC) from the wind speed above in the PBL (VPBL).
Similarly, only a limited number of observational studies have been performed to examine the diurnal variations of VSFC and VPBL over tropical islands (Aspliden 1977), open oceans (Deser 1994), and coastal and mountainous regions (Hering and Borden 1962; Reiter and Tang 1984; Savijarvi 1997). These earlier studies related the diurnal wind changes to the atmospheric tidal variations in surface pressure and to differential solar heating associated with topography, land–water contrasts, and cloudiness. Based on 3-hourly global observations of VSFC during 1976–97, Dai and Deser (1999) suggested that diurnal variations of VSFC are caused by diurnal changes in vertical momentum fluxes and surface pressure tides. They found that (a) the diurnal harmonics of continental VSFC are approximately in phase with those of TSFC and (b) the mean daily variations of surface divergence are closely related to those of VSFC. In another study, Dai et al. (1999) observed significant diurnal anomalies of precipitation during the summer months over the contiguous United States, which were also supported by the radar-based climatological description of warm-season precipitation episodes by Carbone et al. (2002). This observation led Dai et al. (1999) to suggest that the diurnal variations of divergence could be a major factor controlling the timing of summer convective precipitation. To test this hypothesis, they examined the sensitivity of the model-simulated precipitation in the summer of 1993 to several convective parameterizations. They found that the regional climate simulations tend to produce too much cloudiness, thereby reducing surface solar radiation and weakening the subsequent development of the PBL, including VSFC and VPBL. As a consequence, the simulations overestimate precipitation frequency and underestimate precipitation intensity as compared with the observations. Because of the pronounced convective forcing and its nonlinear interaction with other physical processes, it was not possible to identify the parameters that influence the simulated diurnal variations of VSFC and VPBL.
It is obvious that obtaining realistic diurnal cycles of VSFC and VPBL is important, not only for NWP and climate research, but also for studies of air quality, wind energy, visibility (haze, fog, and low clouds), engineering (construction), and other environment-related problems. However, it still remains unclear to what extent such diurnal cycles could be reasonably reproduced by current numerical models despite the above-mentioned advances in PBL modeling. This issue could be addressed by testing the performance of various PBL parameterizations that are being used in today's numerical models.
Therefore, we are motivated to conduct a comparative numerical modeling study of limited-area boundary layer flows with five widely used PBL parameterization schemes in the fifth-generation Pennsylvania State University (PSU)–National Center for Atmospheric Research (NCAR) Mesoscale Model (MM5; Dudhia 1993; Grell et al. 1995). To minimize the impact of deep convection, land–water contrast, and topography on the diurnal cycles of VSFC and VPBL, a 72-h dry period (i.e., from 1200 UTC 12 July to 1200 UTC 15 July 1997) of weak-gradient atmospheric flows over the central United States is selected for this study. Although the land surface processes may contribute to the development of the PBL through vertical fluxes of heat, moisture, and momentum in the surface layer, they generally play a role in determining the amplitude, rather than the phase, of the diurnal variations of TSFC and VSFC as compared with the other PBL processes.
The next section provides a brief description of the case study and shows the observational evidence of the diurnal cycles of VSFC in relation to TSFC. Section 3 outlines the basic physical options used for the MM5 simulations, and the appendix presents the major characteristics of the five PBL parameterization schemes being tested in the study. Section 4 compares the diurnal cycles of VSFC simulated with the five different PBL schemes with the observed cycle. The simulated vertical PBL structures will also be studied in relation to the diurnal variations of VSFC and TSFC. A summary and concluding remarks are given in the final section.
Figure 1 shows the distribution of 3-day-averaged geopotential height and temperature at 850 hPa during the period of 12–15 July 1997. The large-scale flow over the area of interest, that is, the central United States, was dominated by a subtropical high pressure system over the southern states, with a weak-gradient westerly flow to the north. A topographically generated warm tongue with pronounced thermal gradients extended from the Rocky Mountains into the western portion of the central United States. However, these thermal gradients diminished rapidly with height and became insignificant at 700 hPa and above (not shown). Few significant disturbances passed over the region during the 3-day period (not shown), and so there was little organized convective activity except for a few isolated afternoon convective events. Thus, the weak large-scale flow, little convective influence, and little topographical forcing over the region provide a reasonable test bed to isolate the impact of surface radiative forcing on the diurnal variations of the surface and PBL properties. Nevertheless, Dai and Deser (1999) and others have shown that diurnal variations of VSFC could account for 50%–70% of the total daily variance over land during all seasons.
To reduce the influences of locally generated meteorological disturbances (associated with terrain, inhomogeneities in the land use, etc.) and errors in the observed VSFC, it is meaningful and statistically significant to examine the area-averaged properties rather than individual single-station observations; similar logic holds for the model-simulated fields. Thus, all of the observed and simulated data used in this study are spatially averaged over an area of 9° lat × 9° lon in the central U.S. regions (see Fig. 1). The zonal migrating effect of solar radiation, which is equivalent to ±18 min, is neglected in generating the time series of the area-averaged surface properties. On average, there were about 105 surface stations over the area that reported hourly temperature, winds, and other meteorological variables; they were extracted from the National Oceanic and Atmospheric Administration (NOAA)'s Technical Development Laboratory U.S. and Canada Surface Hourly Observations archived at NCAR (available online at http://dss.ucar.edu/datasets/ds472.0/).
Figure 2 shows the diurnal variations of the area-averaged hourly VSFC (speed and direction) and TSFC during the 3-day period. Note that, in this study, VSFC and TSFC are defined, following meteorological convention, at the altitudes of 10 and 2 m, respectively. The (nearly sinusoidal) diurnal cycles of TSFC were clearly evident, with the amplitudes varying from the minimums (TMIN) of 20°–23°C at 1100 UTC (or 0600 LST) to the peaks (TMAX) of 31°–32°C at 2100 UTC (or 1600 LST) during the 3-day period (Fig. 2a). The continued increases in TMAX and the mean temperature on each day were consistent with the daily progression toward the middle summer. Note that, for each diurnal cycle, TSFC always increased more rapidly during the first 3–5 h of the daytime development because of the existence of shallow PBL depth with increasing energy input and decreased at slower rates as it approached TMIN as a result of the reduced net radiative heat losses.
Of particular relevance for this study is the fact that the diurnal cycles of VSFC were in phase with those of TSFC (Fig. 2a). That is, the strongest surface wind occurred 2–3 h before sunset when the surface air was hottest, whereas the weakest flow occurred near sunrise when the surface layer was coldest. Of significance is that even the trends of changes in wind speed at some periods were similar to those of TSFC. This phase relationship is as expected, based on the concept described at the beginning of section 1, assuming that the horizontal winds increase monotonically with height. We may speculate that the amplitude of such diurnal cycles would be greater in the cases of stronger vertical wind shear and deeper PBL developments. Note, however, that the surface wind speeds oscillate, following the rapid acceleration during the early morning hours on the first 2 days. This oscillating feature appears to be attributable to the interaction of the PBL development with the LLJ layers developed in the previous evenings, based on the model simulations to be shown in section 4 (see Fig. 9). It took 4–6 h for the surface-based turbulent eddies to penetrate into the layers above the LLJ layer, before the PBL was fully developed with the strongest VSFC. The daytime variations of VSFC on the third day appear to differ from the previous 2 days, indicating that certain changes might have occurred in the free atmosphere; this possibility will be further discussed in section 4 (in relation to Fig. 9). To our knowledge, such diurnal cycles of VSFC have not been previously examined in detail, particularly by numerical modeling studies.
The time series of surface wind direction is given in Fig. 2b, which exhibits a steady directional shift (>90°) from the southerly to westerly mean flow associated with the movement of the subtropical high. Of interest is that there also appears to be some diurnal variations (in the range of 0°–30°) in wind direction, but about 5–6 h out of phase with VSFC. The momentary peak wind direction coincides closely with the initiation of the above-mentioned VSFC oscillations, suggesting the likely penetration of the surface-based turbulent eddies into the LLJ layer in which the jet flow under inertial oscillation is out of phase with the mean flow above and the frictional flow below. The surface wind direction subsequently becomes more consistent with the mean flow above, as more upper-level momentum is transferred downward. Nevertheless, because the amplitude of diurnal variations in surface wind direction was much smaller than that of directional changes associated with larger-scale disturbances, we will hereinafter focus only on the diurnal changes of surface wind speed (VSFC), unless otherwise mentioned. To minimize the subsequent digression from the focus of this study, Fig. 2b also compares the surface wind directions simulated by five different PBL schemes to those of the observed. It is obvious that all of the PBL schemes reproduce reasonably well the time evolution of the observed surface wind directions, with little difference among them except for the final 6-h simulations.
The fundamental features of MM5 used for this study include (i) the simultaneous use of the newest version of the Kain–Fritsch (1993) convective parameterization, which contains the parameterized shallow convective effects (Deng et al. 2003) and an explicit moisture scheme that contains prognostic equations for cloud water (ice) and rainwater (snow) (Hsie et al. 1984; Dudhia 1989; Zhang 1989), (ii) a multilayer soil model to predict land surface temperatures by using the surface energy budget equation, (iii) a simple radiative cooling scheme, and (iv) the specification of the outermost coarse-mesh lateral boundary conditions by linearly interpolating National Centers for Environment Prediction (NCEP) 6-hourly Eta Model analyses at the resolution of 40 km on the Advanced Weather Interactive Processing System 212 grid as in Perkey and Kreitzberg (1976).
The above-mentioned model features are identical for all five of the sensitivity experiments, except for the PBL parameterization schemes and their associated surface flux calculations. The five PBL schemes to be tested are the (i) Blackadar (BLK; Zhang and Anthes 1982), (ii) Gayno–Seaman (GS; Shafran et al. 2000), (iii) Medium-Range Forecasts (MRF; Hong and Pan 1996), (iv) Miller–Yamada–Janjić (MYJ; Janjić 1994), and (v) Burke and Thompson (1989; BT) parameterizations. These PBL schemes are currently being used in MM5, NCEP's operational MRF and NWP models, and the U.S. Navy's Coupled Ocean–Atmosphere Mesoscale Prediction System. As described in the appendix, all of the schemes contain nonlocal treatments of the unstable PBL developments, which include TKE closures (e.g., GS, MYJ, BT), countergradient heat fluxes (MRF), and a buoyant plume model with roots in the surface layer (i.e., BLK).
The model domain has (x, y) dimensions of 123 × 109 with a uniform spacing of 36 km. A total of 26 σ levels in the vertical direction are used, with the model top at 50 hPa. These full σ levels are 0.0, 0.025, 0.075, 0.125, 0.175, 0.225, 0.275, 0.325, 0.375, 0.425, 0.475, 0.525, 0.575, 0.625, 0.675, 0.725, 0.770, 0.815, 0.860, 0.900, 0.935, 0.96, 0.98, 0.99, 0.9974, and 1, which give 25 half-σ layers. The height of the lowest model layer, at which all of the surface variables except vertical velocity are defined, is about 10 m in order to be comparable with the altimeter-level observations of VSFC. To facilitate the TSFC comparisons, the model-simulated TSFC at the altitude of 2 m is diagnosed from the ground temperature (TG) and the surface temperature in the lowest model (z = 10 m) layer (TA), namely, TSFC = 0.45TG + 0.55TA. All sensitivity simulations are initialized at 1200 UTC 12 July 1997 with NCEP's Eta Model analysis as a first guess, which is then enhanced by upper-air and surface observations. They are integrated for 72 h, ending at 1200 UTC 15 July 1997. Hourly model outputs are used to show the time evolution of various surface and PBL features.
Numerical sensitivity simulations
In this section, we examine to what extent the observed diurnal cycles of VSFC, described in section 2, could be reproduced by the above-mentioned five different PBL schemes. First, it is desirable to examine how well the five PBL schemes can reproduce the diurnal cycles of TSFC because of its strong correlation with those of VSFC (see Fig. 2a). It is evident from Fig. 3 that all five of the schemes reproduce the diurnal phases of TSFC, including the characteristic time rates of change during the different stages of the PBL development as discussed in section 2. It is clear that this phase reproduction results from the dominant radiative cycle in the surface energy budget. However, the amplitudes of the simulated diurnal cycles of TSFC differ significantly from those of the observed, for example, from 2.5°C at TMIN to 4.5°C at TMAX because of the different treatments of the surface fluxes of sensible and latent heat and of the energy exchange with the air above in the five PBL schemes.
It is obvious that almost all of the PBL schemes underestimate the magnitude of TMIN, albeit to different degrees, and the two similar schemes (i.e., MYJ and BT, see the appendix) underestimate markedly the magnitudes of TMAX. The MYJ and BT schemes also generate similar vertical profiles of the potential temperature θ during both the daytime and nocturnal periods (see Figs. 4a,b). Like TSFC, their mixed layers are colder and shallower than those generated by the other three schemes (Fig. 4b), due partly to less upward transfer of the net surface heat flux and partly to underestimation of the countergradient heat flux from the capped inversion (D. Stauffer 2003, personal communication). In fact, the BT scheme tends to transfer more surface moisture upward, according to Braun and Tao (2000), thus causing more evaporative cooling and explaining the weakest amplitude in the diurnal cycles of TSFC. In a similar way, the air in the lowest 1 km remains colder than that in the other three schemes during the nocturnal period (Fig. 4a). The two schemes also appear to be more efficient in transferring the sensible heat flux downward under the stable conditions, as indicated by the linear-shaped θ profiles in the lowest 1.5 km.
In contrast, the GS, MRF, and BLK schemes reproduce better the observed time series of TSFC, in that order. This result could be attributed partly to the use of nearly identical surface flux (θ and water vapor q) representations between the MRF and BLK (and GS) schemes [see appendix B in Braun and Tao (2000)]. Of interest is that, despite the use of different closures, their daytime and nocturnal PBL structures are also similar to each other (Figs. 4a,b). Moreover, the lowest 500-m layers produced by the three schemes at TMIN are more statically stable than those of the BT and MYJ schemes (see Fig. 4a).
Despite the above-mentioned considerably different results among the five PBL schemes, the amplitudes in the diurnal cycles of TSFC and the PBL warmth are of little concern in this study of the diurnal cycles of VSFC because all of the surface parameters in the BT, MYJ, and MRF schemes that determine the energy input into the atmosphere above were “tuned” along with their “mother” models and PBL schemes. In other words, some parameters should have been tuned when their associated PBL schemes were incorporated into MM5. In fact, as will be seen in the next paragraph, a higher TSFC or a deeper PBL does not always imply the generation of a stronger VSFC in some PBL schemes. At issue here is to what extent the different PBL schemes can reproduce the strong correlation between VSFC and TSFC that is shown in Fig. 2, given the realistic diurnal radiative cycle at the earth's surface.
A comparison of the simulated diurnal cycles of VSFC with the observed cycles (Fig. 5) shows that all of the PBL schemes underestimate the observed VSFC during the daytime. In relative terms, the daytime phases and amplitude of VSFC are better simulated by the BLK, BT, and MYJ schemes, even though the latter two schemes produce colder TSFC and PBL. The peak VSFC generated by the MRF scheme occurs 6 h ahead of the observed peak and is about 50% of the observed peak, despite the well-simulated diurnal cycles of TSFC. This result is likely caused by the use of a prescribed K profile with too-small momentum diffusivity in the surface layer (see the appendix); its vertical coupling of horizontal momentum is also questionable, as compared with its nonlocal treatment of heat fluxes. Of interest is that the time series of VSFC generated by the GS scheme exhibits a decrease in wind speed during the early morning hours, followed by a rapid increase until it reaches its peak 3–4 h later than the observed peak. This result is to a certain extent unexpected, given the more realistic simulation of TSFC, the more physically sound TKE closure, and the reasonable VSFC evolution of the other two TKE-based schemes. This result clearly must have something to do with the vertical momentum diffusivity Km [see Eq. (A2) in the appendix] and the large amplitude of the nocturnal LLJ (shown below) simulated by the GS scheme. Nonetheless, the results indicate that even a perfect diurnal TSFC (radiative) cycle does not guarantee a reasonable outcome of the diurnal cycles of VSFC. The latter appears to depend highly on how the horizontal momentum above is transferred downward to the surface layer by the PBL processes. The phase correlation between TSFC and VSFC during the daytime, as shown in Fig. 2a, requires the rapid vertical exchanges (or strong coupling) of horizontal momentum between the surface layer and the layers above in the PBL. This characteristic appears to be reproduced well by the BLK, BT, and MYJ schemes, in which nonlocal closures are adopted. On the other hand, any local K treatment would tend to transport the momentum fluxes slowly downward, making the daytime variations of VSFC out of phase with the observed.
Although there are significant differences in the simulated VSFC (and TSFC and the vertical θ profiles), the vertical profiles of wind speed taken at the time of the peak TSFC (i.e., at 1600 LST) show similar vertical distributions, with relatively strong winds above z = 10–50 m, particularly for the three TKE-based schemes (Fig. 6b); the BLK and MRF schemes produce relatively weaker and well-mixed wind profiles. The simulated stronger VPBL but weaker VSFC indicate that VSFC in some PBL schemes is not realistically coupled with VPBL (cf. Figs. 5 and 6b). In this regard, the BLK scheme produces an entrainment layer (i.e., 1000–1400 m), a nearly uniform flow layer (100–1000 m), and a convective root layer below, with more momentum transferred downward to accelerate the surface flow, leading to the generation of strong VSFC during the daytime. This vertical wind profile in the PBL is very similar to that discussed by Santoso and Stull (1998).
It is of interest that all of the TKE-based schemes overestimate the nocturnal minimum VSFC (Fig. 5)—the worst overestimate of 40%–50% is generated by the GS scheme, whereas the BLK and MRF schemes tend to underestimate it slightly. The GS scheme also produces important phase errors during the nocturnal period. The pronounced errors in amplitude and phase during the nocturnal period are somewhat disturbing because the stable PBL over a near-homogeneous surface has been claimed to be understood much better and parameterized more realistically. Most PBL schemes, including those used in this study, use a local K theory to treat the vertical transfers of heat, moisture, and momentum under stable conditions. The prognostic TKE equation(s) in the MYJ, GS, and BT schemes is just used to provide more “realistic” magnitudes for the eddy exchange coefficients K.
Despite the different daytime developments, the nocturnal wind profiles all show the development of a local wind maximum, loosely defined herein as the LLJ, with the range of 7–9 m s−1 near the altitude of 300 m (see Fig. 6a). This altitude is close to the top of the low-level nocturnal thermal inversion (cf. Figs. 6a and 4a), which is consistent with that discussed by Blackadar (1957). The similar wind profiles produced by the five PBL schemes are understandable because of their similar depths of the surface-based inversion (Fig. 4a) and the use of similar local K treatments for turbulent transfers. On the other hand, the generation of too-strong nocturnal VSFC by all of the TKE-based schemes is likely caused by too much downward transport of horizontal momentum associated with the too-strong LLJ generated (cf. Figs. 5 and 6a). In nature, the flows above are decoupled with VSFC and a substantial reduction in eddy viscosity should occur below the inversion, as parameterized in the BLK scheme.
Overall, the BLK scheme produces the best diurnal cycles of VSFC, whereas the GS scheme generates the worst results, with its diurnal cycles being about 12 h out of phase with the observed cycles (see Fig. 5). The daytime VSFC produced by the MYJ and BT schemes are comparable to those of the BLK scheme, but their nocturnal VSFC are too strong and have opposite time rates of change. By comparison, the MRF scheme yields systematically the weakest VSFC at all of the times, with some unsmoothed transitions and phase errors.
Note that the nocturnal time series of VSFC simulated with the BLK scheme in the previous version of MM5 is similar to that from the MYJ and BT schemes, mainly because of the use of virtual potential temperature θυ to estimate the bulk Richardson number (Rb) and the Richardson number (Ri) and secondarily because of the use of a relatively large background K0 (i.e., 1 m2 s−1) coefficient in the (thin) surface layer. The inclusion of moisture in calculating Ri and Rb tends to make the atmosphere less stable, producing larger K coefficients and stronger downward transfers of horizontal momentum, especially from the LLJs (see Fig. 6). In particular, Fig. 4a shows that the lowest 300 m is very stable (i.e., Rb ≥ 0.2) so that little turbulence should be expected (Zhang and Anthes 1982). Thus, in this study we used the potential temperature θ to estimate Ri and Rb as in the original BLK scheme (Zhang and Anthes 1982) and set K0 = CkΔZ, where Ck = 10−3 m s−1 and ΔZ is the depth of the model layer (m), as described in the appendix.
Although the vertical profiles of the potential temperature and horizontal winds shown in Figs. 4 and 6 are useful for understanding the correlation between the surface properties and those above, it is not possible to validate whether the two extreme PBL developments are realistically simulated. However, there were six conventional upper-air stations located within the area of interest (see their locations in Fig. 1) that could be utilized to verify indirectly the above-mentioned features, because the two synoptic times of 1200 and 0000 UTC were only about 1 and 3 h later than those of TMIN and TMAX, respectively. Nevertheless, the six soundings were too few to sample the mean atmospheric states over the region. Thus, the observed wind profiles at the two synoptic times are averaged both spatially and temporally and likewise for the simulated profiles for verification purposes (see Fig. 7). In general, the simulated wind profiles by all of the PBL schemes compare favorably to those of the observed at both times. They all exhibit nearly constant wind speeds above 300 m at 0000 UTC (Fig. 7b), and local wind maxima between 300 and 500 m at 1200 UTC (Fig. 7a). Of course, some differences could also be noted. For example, the simulated wind speeds in the lowest 1.5 km at 0000 UTC are 1–2 m s−1 stronger than those of the observed (Fig. 7b), whereas the opposite is true at 1200 UTC (Fig. 7a). A close examination of Figs. 7a and 7b reveals that the BLK and GS schemes produce the least differences in the vertical wind profiles from the observed profiles at 0000 and 1200 UTC, respectively, except that the GS nocturnal wind maximum appears to be too strong. The result indicates that all of the PBL schemes produce similar vertical distributions and magnitudes of VPBL, which are comparable to those of the observed, in contrast to their marked variations and differences in VSFC. The simulated vertical profiles of the potential temperature θ at the two synoptic times are also similar to those in Fig. 4, except for some evolutions in the lowest 100–200-m layer (not shown). Again, like the wind profiles, the vertical θ profiles of the GS and BLK schemes resemble better those of the observed (not shown).
To gain further insight into the relationship between VSFC and VPBL, Fig. 8 shows the time series of the simulated horizontal wind speeds in the second and fourth model layers from the bottom surface (i.e., at z = 50, 243 m) in relation to the observed VSFC. Of interest is that VPBL in each layer also exhibits the diurnal cycle, more significantly near the level of the LLJs, but it is nearly opposite in phase with (i.e., 2–3 h lagging behind) the observed VSFC. That is, VPBL (VSFC) begins to weaken (intensify) 1–2 h before (after) sunrise, whereas VPBL (VSFC) commences its acceleration (deceleration) in early (late) afternoon. In general, the differences in the simulated VPBL among the five PBL schemes become smaller with height, except for the GS scheme, the magnitude of which increases more rapidly as it approaches the level of the LLJs. Note the more pronounced asymmetries in the time series of VPBL as compared with those of VSFC. This result is apparently because the variations of VPBL are affected not only by the surface forcing but also by the inertial oscillations and the large-scale forcing.
Figure 9 compares the time–height cross sections of horizontal wind speeds produced by the BLK and GS schemes to see their different relationships between VPBL and VSFC. Some common features include the diurnal cycles of VPBL, which negatively correlated with those of VSFC, the development of the nocturnal LLJs with strong vertical shear below, and the weak VPBL with relatively weak shear during the daytime. Because of the strong vertical coupling during the daytime, the time series of VSFC reflects, to a certain degree, the flow structures above in the PBL, as discussed in section 2. On the third day when a weak baroclinic disturbance passes by, the daytime VSFC becomes stronger than before (Fig. 5) and the nocturnal LLJ turns out to be much less evident. In this case, the deeper the PBL is, the stronger is the daytime VSFC. Based on the simulated colder TSFC (Fig. 3) and stronger VPBL aloft (Fig. 9), we may speculate that the MYJ, BT, and BLK schemes could make the daytime VSFC closer to that of the observed (see Fig. 5) if a deeper PBL with warmer TSFC were simulated. Some errors (e.g., 1 m s−1; see Fig. 7) in the large-scale flows may also explain the underestimation of the peak VSFC by these PBL schemes.
A comparison of Figs. 9a and 9b reveals that the BLK-generated vertical shear in the lowest 100–200 m during the nighttime (daytime) is greater (weaker) than that by the GS scheme, even though the opposite is true for the intensity of the LLJs. This result indicates that VPBL in the former case is more decoupled with VSFC because of the reduced downward momentum transport from the LLJs. In general, the BLK-produced VPBL, particularly for the lowest 100–200 m, shows more pronounced diurnal variations and a more rapid transition between the stable and unstable regimes than that of the GS scheme (and the other three schemes). It is evident from Fig. 9 that use of the high vertical resolution in the PBL is essential not only for resolving the LLJs and its associated large vertical shear, but also for ensuring smooth transitions in the vertical turbulent mixing between the unstable and stable turbulence regimes.
Summary and conclusions
In this study, the performance of five widely used PBL parameterization schemes in reproducing the diurnal cycles of surface wind speed in relation to surface temperature is evaluated using 3-day regional simulations of summertime weak-gradient flows over the central United States with the PSU–NCAR MM5. This case was also characterized by little organized deep convection and little topographical forcing. The area-averaged hourly time series of VSFC and TSFC, as well as their vertical structures in the PBL from the five sensitivity simulations, are compared with hourly surface observations and some upper-air measurements at the two synoptic times.
The hourly surface observations show that the diurnal variations of VSFC are in phase with the diurnal cycles of TSFC. Although surface wind directions also exhibit diurnal variations but 5–6 h out of phase with VSFC and TSFC, their amplitudes, reasonably simulated by the five PBL schemes, are much weaker than the directional changes associated with larger-scale disturbances. So, the diurnal cycles of surface wind directions are not examined in detail in this study. The numerical simulations show that both TSFC and VSFC are sensitive to the PBL parameterizations, given the identical conditions for all of the other model parameters. It is found that the five PBL schemes all reproduce the diurnal phase of TSFC because of the dominant radiative forcing; three of them reproduce very well the diurnal cycles of TSFC in both magnitude and phase. However, all of the PBL schemes tend to underestimate the magnitudes of VSFC during the daytime, and three schemes overestimate them substantially at night. Moreover, some PBL schemes produce pronounced phase errors in the diurnal cycles of VSFC or substantially weak VSFC all of the time despite their well-simulated diurnal cycles of TSFC. The results suggest that even a perfect simulation of diurnal TSFC cycles does not always guarantee the reproduction of the diurnal cycles of VSFC. Furthermore, even with the realistically simulated vertical thermal structures in the PBL, the diurnal cycles of VSFC may not be reasonably obtained if certain physical processes, such as the strong vertical coupling in daytime and the vertically decoupled flows at night, are not properly parameterized.
The numerical simulations also show the significant diurnal cycles of VPBL, but in opposite phase with VSFC, that is, with the development of weak VPBL during the day and LLJs at night. Such a phase relationship indicates the necessity to use a thin surface layer to reduce possible errors in simulating the lower-level flows and to use high vertical resolution to resolve the surface-based inversion, its associated LLJs, and stability transitions. It is shown that the vertical distributions and magnitudes of VPBL simulated by the five PBL schemes are, on average, similar to each other, and they are all comparable to those observed at the two synoptic times. Based on these results, we conclude that the diurnal cycles of VSFC simulated with some PBL schemes do not depend on how well the horizontal winds and mass in the PBL and TSFC are reproduced, although these variables are all interrelated in nature. To reproduce the observed diurnal cycles of VSFC, it appears to be essential to incorporate realistically certain physical processes in the PBL schemes, such as the nonlocal closures, including the countergradient transport, which could provide a strong coupling between VSFC and VPBL under unstable conditions, and the Richardson number–based closures, which could distinguish various stable regimes for the generation of different vertical fluxes of the mass and momentum in the surface layer.
In this regard, the BLK scheme is shown to perform the best among the five tested PBL schemes in reproducing the diurnal cycles of VSFC for this particular case study. This is because (a) the BLK scheme allows direct mass and momentum exchanges between the surface layer and the layer above in the unstable PBL, with the entrainment effects included, and (b) it treats the nocturnal module with three different stability regimes based on the bulk Richardson number, which yield more reasonable magnitudes of the vertical heat and momentum fluxes in the surface layer. The use of more stability regimes also permits reasonable simulations of the transitions between a wide range of turbulent mixing regimes. It is evident that some of the above features, such as the treatment of the nocturnal module, could easily be implemented into the other PBL schemes.
It should be mentioned, however, that the results presented herein do not imply the capability of the BLK scheme to reproduce many other important PBL features. It is clear that more case studies of this kind over different geographical regions and under different surface (e.g., topographical, water) and large-scale forcing conditions should be done to generalize our findings. Furthermore, it is highly desirable to obtain 3D high-resolution observations in order to examine more realistically the model's capability to reproduce the correlations among VSFC, VPBL, TSFC, and the vertical thermal structures in the PBL, especially around the time of TMIN and TMAX.
We gratefully acknowledge Drs. Gopal Sistla and Mike Ku of the New York State Department of Environmental Conservation who noted the significant phase errors in the MM5-simulated surface winds after their careful analyses of our earlier datasets. Their keen interest in the use of surface winds provided the impetus for us to launch this study. We wish to thank Drs. Zavisa Janjić and Hua-Lu Pan of NCEP for their helpful comments on our earlier results. Many thanks also go to our colleagues in the UMD-MDE Regional Atmospheric Measurement Modeling and Prediction Program (RAMMPP) for their enthusiastic support and to Dr. Nelson Seaman of The Pennsylvania State University for his encouragement during the course of this study. This work was supported by Maryland's Department of Environment and NOAA's Grant NA96GP0277.
The Planetary Boundary Layer Parameterization Schemes
To help to understand the characteristics of the simulated surface winds shown in section 4, some pertinent features of the five PBL schemes tested in this study are summarized below. They include calculations of the surface fluxes and the treatment of vertical turbulent mixing for the mass and wind fields under stable and unstable conditions. Most variables given below, if not defined, would assume their usual meteorological meaning.
The Blackadar PBL scheme
The Blackadar PBL scheme (Blackadar 1976, 1979; Zhang and Anthes 1982) consists of a nocturnal (stable) and a free convection (unstable) module of turbulent mixings. In the nocturnal module, local K theory is used and the eddy viscosity K is calculated as a function of the Richardson number Ri,
where K0 = Ck ΔZ is a background value that depends on the vertical resolution ΔZ and Ck = 10−3 m s−1, k is the von Kármán constant, ℓ = kz(1 + kz/λ)−1 is the mixing length (Blackadar 1962), and f(Ri) denotes a functional dependence of K on the Richardson number Ri (Holtslag and Boville 1993). For unstable conditions (Ri < 0), we use
and, for stable conditions (Ri > 0),
To help to reproduce the smooth transition of a wide range of turbulent mixing, the nocturnal module is subdivided into three stability regimes, depending on the bulk Richardson number Rb. When Rb ≥ 0.2, the surface layer is assumed to be so stable that little turbulence exists and all fluxes at its top are set to their minimum values by assuming K = K0. When 0 < Rb < 0.2, the surface layer is assumed to be driven by damped mechanical turbulence. When Rb ≤ 0 and |H/L| ≤ 1.5, where L is the Monin–Obukhov length and H is the height of the PBL, a marginally unstable state of forced convection is assumed.
In the free convection module, Rb ≤ 0 and |H/L| > 1.5, the vertical transfers of heat, moisture, and momentum are explicitly calculated using a nonlocal mixing model in which buoyant plumes from the surface layer mix directly with all other layers within the PBL. The intensity of the mixing is determined by the ratio of the heat flux at the top of the surface layer to the vertically integrated potential temperature θ difference between the surface layer and the layers in the PBL. Above the PBL (i.e., z > H), vertical mixing is calculated with K theory as in the stable module.
The Gayno–Seaman PBL scheme
The Gayno–Seaman scheme (Shafran et al. 2000) is a Mellor–Yamada (1974) 1.5-order closure model in which a prognostic equation for turbulent kinetic energy (TKE) is included. It uses the liquid water potential temperature, θL = θ(1 − LqL/cpT), as the two fundamental mass variables (Betts 1973), where qL is the liquid water mixing ratio, and the total water mixing ratio qT = q + qL. Vertical turbulent transfers of the mass and wind fields are calculated using nonlocal K theory, but the eddy diffusivities for the mass (Kh) and momentum (Km) fields are determined by TKE or E, according to
where the mixing-length scales ℓh and ℓm are defined by Ballard et al. (1991), and N is the moist buoyancy frequency. Under unstable conditions, a nonlocal K approach is adopted by adding a countergradient θL flux term γc to the local gradient transport, that is,
for the layers of z < 1.2H. In this scheme, the PBL depth is diagnosed from the TKE profile as the level at which the surface-based mixed-layer TKE decreases to 0.1 m2 s−2 in strongly convective situations (i.e., when the maximum PBL TKE > 0.2 m2 s−2) or to 50% of the maximum TKE in weakly convective situations (i.e., when the maximum PBL TKE < 0.2 m2 s−2). The surface fluxes are calculated in the same way as those in the BLK scheme (Zhang and Anthes 1982).
The PBL scheme in the Medium-Range Forecast model
The MRF scheme (Hong and Pan 1996) is a nonlocal K scheme in which the countergradient transports of temperature and moisture under unstable conditions are added to the local gradient transports in a form similar to that given in Eq. (A6). In this situation, the PBL height H is estimated by
where Rbc is the critical bulk Richardson number, θυ is the virtual potential temperature, and z = za and z = H represent, respectively, the surface layer and the top of the PBL at which θυ, θ, and V are involved in the calculation. The eddy diffusivity for the wind field Km is obtained from a prescribed profile shape, similar to that of O'Brien (1970), as a function of H, the height from the surface z, and some surface scaling parameters, whereas the eddy diffusivities for the mass field are computed from Km by using a Prandtl-number relationship.
Under stable conditions, including the layers above the PBL, the local K approach is utilized for all prognostic variables, in which the eddy diffusivity Kz is calculated as a function of the mixing length, Ri, and ∂|V|/∂z. The value of Kz is limited between 1 and 1000 m2 s−1 for all possible atmospheric conditions.
The vertical diffusivities so obtained also apply to the surface layer under both stable and unstable conditions.
The Miller–Yamada–Janjić PBL scheme
The Miller–Yamada–Janjić (Janjić 1990, 1994) scheme is a Mellor–Yamada (1982) level-2.5 scheme, or a variant of 1.5-order closure model that includes a prognostic equation of the TKE. Like all of the TKE closures, the nonlocal K approach is used, which has a form similar to that given in Eqs. (A4) and (A5) but as complex algebraic functions of the mixing length, TKE, vertical wind shear, and static stability. The mixing length is diagnosed as a function of the height from the surface, which is large under unstable conditions. In these situations, certain constraints are imposed to avoid the development of too-large K.
The surface layer is treated using a Mellor–Yamada (1982) level-2 closure with the logarithmic extension. The magnitudes of surface eddy exchange coefficients depend on the mixing length, vertical shear, and static stability.
The Burk–Thompson PBL scheme
The Burk–Thompson (1989) PBL scheme is a Mellor–Yamada (1982) level-2.5 scheme, or a variant of 1.5-order closure model with many features similar to those in the MYJ scheme. Unlike the formulations described in Burk and Thompson (1989), the scheme in MM5 does not include the countergradient θυ and moisture flux terms.
Corresponding author address: Dr. Da-Lin Zhang, Department of Meteorology, University of Maryland at College Park, College Park, MD 20742-2425. firstname.lastname@example.org
The diurnal cycle of the PBL used to be viewed in terms of surface radiative forcing and low-level temperature variations. In this study, it also includes the surface winds and the winds above in the PBL.