1. Introduction
The objectives of this paper are to evaluate the heights of significant nocturnal boundary layer (NBL) features using observed and model profiles and then use them to evaluate four planetary boundary layer (PBL) schemes in high-resolution (1-km innermost grid) simulations using the Advanced Research version of the Weather Research and Forecasting Model (ARW-WRF, hereafter referred to as WRF). As in its companion paper, LeMone et al. (2013), which examined the convective boundary layer (CBL), we focus on the Yonsei University (YSU; Hong et al. 2006), Mellor–Yamada–Janjić (MYJ; Janjić 2001), Bougeault–LaCarrere (BouLac; Bougeault and LaCarrere 1989), and quasi-normal scale elimination (QNSE; Sukoriansky and Galperin 2008; Sukoriansky et al. 2005) and use data from three fair-weather nights with mostly moderate winds during the April–May 1997 Kansas-based Cooperative Atmosphere–Surface Exchange Study (CASES-97; LeMone et al. 2000) field program. After identifying a good criterion for objectively determining NBL depth h, we explore PBL-scheme strengths and shortcomings by comparing the behavior and magnitudes of h, hTvmax, and hSmax, respectively the heights of the virtual temperature Tυ and wind speed S maxima, to observations.
While the CBL has a well-defined mixed-layer top, the NBL h can be difficult to identify. Numerous methods have been tried (Table 1). Diagnosis of h using mean or instantaneous vertical profiles has had mixed success. Using Doppler lidar data, Pichugina and Banta (2010) found a strong correspondence of hSmax to h as defined by profiles of the variance of the radial velocity for a subset of wind profiles (one maximum, wind in lowest 200 m greater than 5 m s−1), with minimum curvature in the S profiles yielding even better results. However, in a large-eddy simulation (LES) of a weakly stable NBL (Obukhov length L > 100 m) by Kosovic and Curry (2000), hSmax and hTvmax coincided with h only under steady-state conditions, after about one inertial period of simulation. Similarly, observations show that hTvmax does not necessarily coincide with hSmax or h in moderately to very stable conditions (e.g., Figs. 6 and 7 of Mahrt and Vickers 2006). Indeed, as illustrated in Banta et al. (2007) and Sun et al. (2004) and elsewhere, the NBL often has a complex structure that varies with time.
Selected potential criteria for NBL depth h from vertical profiles.
Bulk Richardson numbers (e.g., Vogelezang and Holtslag 1996) and more complex formulations (e.g., Vickers and Mahrt 2004; Steeneveld et al. 2007) have also been used, with varying degrees of success. A significant shortcoming of such approaches is that radiosonde data need to be smoothed for reliable estimates. Also, magnitudes of criteria using vertical gradients, including Richardson numbers, tend to vary with the vertical spacing used.
When turbulence data are available, the height at which a second-moment variable decreases to a specific fraction of its surface or near-surface maximum provides a useful estimate of h. Examples of such parameters are buoyancy flux (Caughey et al. 1979), vertical velocity variance (Vickers and Mahrt 2004), vertical flux of the component of the horizontal momentum along the surface wind direction (Kosovic and Curry 2000), and the turbulence kinetic energy (TKE; Lenschow et al. 1988). Fortunately, such parameters tend to be internally consistent, at least for weakly stable NBLs [e.g., see LES of Kosovic and Curry (2000), Basu and Porte-Agel (2006), and simulations summarized in Beare et al. (2006); compare to http://gabls.metoffice.com/variance_625.html and follow the menu for profiles of fluxes and means].
Since TKE profiles are available from WRF runs, we use them to determine subjective h (hsubj) for BouLac, MYJ, and QNSE and use the profiles and resulting hsubj to judge the model h metrics in Table 1. For YSU, we use the eddy exchange coefficient K, noting its relationship to TKE (Shin et al. 2013). The LES-generated TKE profiles of Kosovic and Curry (2000) and Basu and Porte-Agel (2006) in Fig. 1 illustrate what we can expect for weakly stable conditions. The two profiles in the figure have weakly concave-up, almost linear shapes, with a maximum at the lowest grid level (10 m). The authors found h by dividing by 0.95 the height at which 
Steady-state LES TKE profiles for the weakly stable (L > 100 m) Arctic SBL. Black refers to Kosovic and Curry (2000), red refers to Basu and Porte-Agel (2006), and SGS is the subgrid scale.
Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1
Here, we estimate h, hTvmax, and hSmax for observed NBLs that are deep enough for analysis using radiosondes, radar wind profilers, and minisodars, perform the same exercise for corresponding model profiles, and use model–observation comparisons to evaluate the behavior of the four PBL schemes. Observations, data analysis, and stability regimes are described in section 2. In section 3, we describe the model setup and PBL schemes and then explain how model TKE profiles are used to select from Table 1 the best h criterion for comparison to observations. In section 4, we evaluate the PBL schemes in terms of how well they replicate observed NBL evolution patterns and how predicted and modeled heights compare from day to day and make suggestions for future improvements, and we compare surface fluxes and discuss the origins and implications of their differences. We summarize the results and suggest future work in section 5.
a. The observational array
A major objective of CASES-97 was to examine the diurnal evolution of the fair-weather PBL. Radiosondes, released at 90-min intervals for four 24-h periods (1100 to 0930 UTC the following day), radar wind profilers (RWP), and minisodars (MS) at Beaumont (BEA), Whitewater (WHI), and Oxford (OXF) provided PBL profiles (Fig. 2). We used the “blended” RWP + MS data, which are simply combined from the two sources (R. Coulter, Argonne National Laboratory, 2014, personal communication). Surface mean and flux data from the sites numbered from 1 to 8 were used for comparison and defining stability. (The radiosonde data are available from http://data.eol.ucar.edu/codiac/ds_proj?CASES-97, the RWP and MS data are available from http://gonzalo.er.anl.gov/ABLE/, and the surface data are available from http://www.eol.ucar.edu/isf/projects/cases97/asciiDownload30min.jsp.)
CASES-97 observational array. Numbers indicate surface flux sites. At the vertices of the triangle lie 915-MHz RWP/MS sites BEA (elevation 478 m), OXF (360 m), and WHI (430 m), with collocated radiosonde releases. Solid lines indicate flight tracks. Terrain contour interval is 20 m.
Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1
Comparisons to radiosonde data indicated that the MS winds were good (MS data at Whitewater were only available for 10 and 20 May). As for the RWP, Beaumont winds were of good quality for all four nights, with Whitewater data totally absent on 29 April, of poor quality on 5 May, good for 10–11 and 20–21 May, and Oxford winds were of marginal quality. Radiosonde data were missing after 0500 UTC at Whitewater on 11 May (see Fig. 7).
b. Determination of NBL depth from observations
Figure 3 illustrates how the heights of the NBL features listed in Table 1 are identified subjectively from observations. Temperature T profiles were smooth enough to make hTmax 
Illustration of how hSmax, hTmax, hRiloc, h1wsonde, and h2wsonde are estimated from radiosonde data.
Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1
In the final technique, h is based on the rapid decrease in sonde vertical velocity wsonde as the balloon travels from turbulent to nonturbulent air (Johansson and Bergstrom 2005), which results from an increase in drag on the balloon once it enters laminar flow (MacCready 1965; Gallice et al. 2011; Wang et al. 2009). This method is appealing because it directly relates to our TKE-based NBL definition. In contrast to the one PBL depth chosen by Johannson and Bergstrom, we used two depths, h1wsonde and h2wsonde, to identify the lower and upper limits of the height interval through which wsonde falls from its “turbulent” to “nonturbulent” value. A low bias for hwsonde of up to 30 m results from the fact that the balloon responds to the turbulence, while the sonde, which collects the data, is attached to the balloon by a 30-m string. The angle of the string to the vertical is unknown, so we do not correct for this bias.
It was not possible to estimate h from wsonde if the NBL was much less than ~100 m deep. It takes time for the sonde to unreel from the balloon and for the balloon–sonde system to accelerate to a typical speed of ~5 m s−1, and there were typically only 3–4 points below 100 m at the 10-s data rate. Given the general association of deeper NBLs with larger 
c. NBL classification
The data used for this study were gathered in rolling terrain (Fig. 2) with varying land cover (Table 2); both cause wind and turbulence to vary horizontally. Indeed, according to Acevedo and Fitzjarrald (2001), Fiebrich and Crawford (2001), Van de Wiel et al. (2002), and others, the turbulent near-surface flow sometimes detaches from the surface, especially in lower-lying areas. With this in mind, we characterize the NBL in a regional sense.
Conditions for days examined (time in UTC). B is Beaumont (open grassland), O is Oxford (some trees), and W is Whitewater (grassland). Figure 2 shows site locations. Italics indicate data that are from the radiosonde.
According to LeMone et al. (2003), NBLs regionally vary from being continuously turbulent and fully coupled to the surface, with air trajectories following the terrain along the synoptic wind direction, to having only weak turbulence driven by drainage winds. In the former case, the 2-m T changes with the elevation, T2m,el ~ −9.8 K km−1, following the adiabatic lapse rate, while T2m,el > +40 K km−1 for the latter case (their Fig. 5), with a magnitude that increases with the vertical T gradient; low-lying locations where radiative cooling is not offset by downslope winds or turbulent mixing also increase T2m,el. From Table 2, T2m,el = −11 K km−1 (based on a least squares straight line for T2m as a function of elevation for sites 1–8), and the wind direction varies little spatially, indicating that the synoptic flow on 4–5 May is continuously coupled to the surface at 0930 UTC. On the other hand, intermediate T2m,el and more variation in wind direction on the nights of 10–11 May and 20–21 May suggest some influence by drainage flow, with possible occasional decoupling and associated cooling, especially for the low-lying stations.
A similar picture emerges from the local classification scheme of Van de Wiel et al. (2003), who use net radiation Rnet and 
Following Van de Wiel et al. (2012) and Sun et al. (2012), classifying the days according to whether the wind speed at a given height is capable of sustaining turbulence beneath also reveals a similar picture. Based on Cabauw data, Van de Wiel et al. found that continuous turbulence is maintained when the wind at 40 m exceeds ~5 m s−1, with the threshold increasing with |Rnet|. Using data from the 55-m CASES-99 tower, Sun et al. found that threshold speeds increase with height, with values of ~7 m s−1 at 40 m and ~8 m s−1 at 50 m. The CASES-99 thresholds are larger than for Cabauw at least partially because of larger |Rnet| [cf. Fig. 4 of Van de Wiel et al. (2012) for Cabauw to Table 2 of Van de Wiel et al. (2003) for CASES-99]. Since |Rnet| in our Table 3 is close to that during CASES-99, 7.5–8 m s−1 is a good threshold speed at 48 m for CASES-97 as well as CASES-99. Based on this criterion, turbulence below 48 m can be sustained on 4–5 May, at Beaumont and Whitewater at 0930 UTC 10–11 May, for Beaumont on 20–21 May, and for Oxford at 0930 UTC 21 May.
Net radiation (W m−2) at surface flux sites 1–8.
2. Model setup and analysis
a. WRF runs
The model results analyzed are from WRF version 3.2 runs described in LeMone et al. (2013) for 4–5 May, 10–11 May, and 20–21 May, with an additional set performed using WRF version 3.4 with YSU version 3.4.1. Each simulation was run for 24 h, starting at 1200 UTC (0600 LST), using four two-way interacting nested grids with spacing of 27, 9, 3, and 1 km, respectively. The 2128 × 2547 km2 outer domain (Fig. 4; LeMone et al. 2013) extends across most of the continental United States, and the inner 127 × 107 km2 grid is centered on the CASES array. The vertical grid has 44 sigma levels, with the lowest half model level just below 5 m, spacing increasing with height (e.g., Fig. 4), and the top level at about 16 km. Initial and boundary conditions for WRF are from the 3-h North American Regional Reanalysis (NARR; http://rda.ucar.edu/datasets/ds608.0/) data on a 32-km grid.
Comparison of PBL scheme h (solid lines) for MYJ, QNSE, and YSU to subjective values based on TKE or Kh profiles (dashed lines). No h value is defined for BouLac in stable conditions. Squares are the full grid levels (zf) for MYJ, QNSE, and YSU and half grid levels (zh) for BouLac.
Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1
The physical parameterizations include the Noah land surface model (Chen and Dudhia 2001a,b; Ek et al. 2003), the Rapid Radiative Transfer Model (RRTM) long-wave parameterization scheme (Mlawer et al. 1997), the Dudhia (1989) shortwave radiation scheme, and the Lin et al. (1983) bulk microphysics scheme. Three PBL schemes (described in more detail in the next section) were linked to their default surface layer options (option 1 for YSU, option 2 for MYJ, and option 4 for QNSE); BouLac uses the same option as MYJ. Surface characteristics are based on the Moderate Resolution Imaging Spectroradiometer (MODIS) VEGPARM Table version 3.1.1, with modified surface roughness values zo (see Table 3; LeMone et al. 2013). Land use types over the CASES-97 array are mainly crop- and grassland, with the latter increasing eastward. All three grassland sites used for model observation comparisons (Beaumont, site 1, and site 2) correspond to grassland grid cells in WRF.
b. PBL schemes in stable conditions
Characteristics of PBL schemes for stable conditions. N is the Brunt−Väisälä frequency. TKE units are m2 s−2.
c. Evaluation of model NBL depth and selection of the 5% 
The candidate h criteria based on the mean profiles and Richardson numbers are listed in Table 1. Note that the altitude at which the vertical gradient of virtual potential temperature Θυ,z = 10 K km−1 is within ~10 m of hTvmax. This is not surprising, as can be shown by subtracting the adiabatic lapse rate 
All thresholds are examined moving upward until their value is bracketed and interpolation can take place to determine the corresponding h.
The eight candidate h indicators were plotted on TKE (or for YSU, K) profiles for each night and location for subjective assessment, as illustrated in Fig. 5.2 The TKE only slightly above the background (0.1 m2 s−2) in the upper part of the profiles at 0000 and 0200 UTC is associated with decaying CBL turbulence. After 0200 UTC, the two hRi are close to or slightly higher than hsubj, the top of the enhanced TKE profile. The TKE-based criteria 5, 7, and 8 do well through the night, but hTKE from criterion 6 (TKE = 0.101 m2 s−2) is initially greater than hsubj by two grid points, changing to one grid point later on. Finally, hTvmax and hSmax are different from one another and from hsubj at the beginning of the night, but converge by 0500 UTC, after which they correspond to within one grid point.
For MYJ at Beaumont on 5 May 1997, the evaluation of h criteria based on TKE profiles (shifted 2 m2 s−2 each 2 h); “1M” in upper left of the first panel indicates that criterion 1 failed to identify h. Sunset was around 0130 UTC (1930 CST).
Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1
Figure 6 summarizes the height comparisons for Beaumont. From the figure, criteria 7 or 8 were closest to hsubj. Comparing results from all three profiler sites, we chose criterion 7, which we will call the 5% 
For Beaumont, evaluation of eight potential h criteria based on comparisons to series of TKE profiles like those in Fig. 5 for nights of 4–5, 10–11, and 20–21 May. Labels refer to dates in UTC and M signifies May.
Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1
The 5% 
d. Uncertainty in heights of NBL features in WRF output
Our analysis is limited by relatively coarse vertical grid spacing compared to h, which varied from ~100 m (resolved by 5 grid points) to ~500 m (resolved by 10 grid points). In addition, maps of 1-km domain w at 270 m (a “typical” NBL depth) indicate weak but noticeable resolved wave structures, which could displace h, hSmax, and hTvmax vertically. While their impact appears to be minor for the weaker wind nights, the structures reach an amplitude of ~0.1 m s−1 by 0900 UTC 5 May. With a northwest–southeast orientation and a 30-km wavelength along the north–south wind (20 m s−1) this translates to a worst-case displacement of features of up to ~24 m.
3. Comparison to observations
a. Relationship among observed NBL profile features
Since our sample is small, we look for repeatable behavior of hSmax, hTvmax, h1wsonde, and h2wsonde before comparison to model results. The observations are summarized in Fig. 7. Though there are considerable differences among the three heights for some of the cases, there is a close match between hTmax and hSmax by 0800 UTC (0200 LST), just as for the model results in Figs. 5 and 6. Note that Beaumont had the fewest clear estimates of h1wsonde and h2wsonde, perhaps due to air currents associated with nearby terrain.
Observed NBL features: hTmax (red circles), hSmax (blue circles for radiosondes, green squares for RWP + MS), h1wsonde (tan upside down triangles), and h2wsonde (tan triangles). Heights of minimum wind profile curvature (if it differs from hSmax sometime during the night): radiosonde (small turquoise dots) and RWP + MS (small light green squares). For Whitewater 5 May, smaller dots and the dashed blue line indicate heights of secondary maxima in Tυ and S.
Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1
The composited data (Fig. 8) show convergence of hTmax and hSmax with time, with hTmax starting out lower than hSmax but increasing fast enough to catch up with it by around 0800 UTC, at which time both lie within the h range bracketed by minimum h1wsonde and maximum h2wsonde. Composite time series of each height were estimated using its value at 0930 UTC. For example, for each night and location, (i) the time series hTmax(t) was divided by hTmax(t = 0930 UTC), (ii) the hTmax(t = 0930 UTC) values were averaged (for all cases in Fig. 7 except for 11 May/Whitewater, when soundings ended before 0930 UTC), and (iii) the normalized heights were multiplied by the average 0930 UTC value to obtain its composite value. The procedure was similar for hSmax, h1wsonde, and h2wsonde.
Time series of radiosonde depths of NBL features Smax and Tmax (symbols), minimum h1wsonde, and maximum h2wsonde (lines) after compositing using values at 0930 UTC as described in text. For the few times that minimum curvature in the wind profile did not correspond to Smax (see Fig. 7) the corresponding height was used rather than the height of Smax. Symbols represent location: Beaumont (squares), Whitewater (upside down triangles), and Oxford (circles).
Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1
Time convergence of hTmax and hSmax is supported by the closeness of average hTmax at 0930 UTC (279 m) to average hSmax from radiosondes (264 m) and blended RWP + MS data (265 m), using the four cases with good data from both sources (Fig. 7). Taking the seven cases for which 0930 UTC values can be determined without extrapolation, average hTmax = 377 m and average hSmax = 354 m, close to average h2wsonde (333–363 m) but greater than average h1wsonde (212–242 m), where the first number is the sonde height and the second number accounts for the maximum possible correction for the balloon–sonde separation.
b. Relationship among modeled NBL profile features and comparison to observations
Figure 9 shows four types of modeled behavior for hTvmax, hSmax, and h. The pattern in the top panel, that is, converging of hTvmax, hSmax, and hTKE with time, is most consistent with observations (Figs. 7, 8). In this case hMYJ overlaps with the heights of the two maxima, while 
(left) Four patterns in hSmax and hTvmax evolution, along with h estimates 
Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1
To trace the origins of the pathologies in Fig. 9, we plot their frequency as a function of stability (Obukhov length L) for three types of hTvmax behavior: “increasing,” “too low,” and “too high” in Figs. 10 and 11. Individual points were counted. Thus, all the hTvmax points showing an increase toward hSmax with time were counted in the increasing pattern; points for which hTvmax < 50 m were counted as too low, and points for which hTmax exceeds hSmax by more than a grid point were counted as too high. Thus, for example, BouLac 11 May in Fig. 9 has five increasing points and six too-low points. Similarly, only the last three points for the YSU 3.4.1 case on 5 May fall in the too-high category.
For the three TKE schemes, frequency of times for which hTvmax increases with time, until it follows hSmax as observed, compared to too-low hTvmax (<50 m AGL) and too-high hTvmax (more than a grid point higher than hSmax) leading to patterns in Fig. 9.
Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1
As in Fig. 10, but for YSU 3.2 and YSU 3.4.1. Number of samples are in parentheses.
Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1
From Figs. 10 and 11, the behavior of hTvmax varies with PBL scheme, with MYJ reproducing the observed increasing pattern most often (89% of the samples). YSU 3.2 (67%) and BouLac (55%) show too-low hTvmax most often and MYJ (7%) the least. The too-high values are the least common, with a few examples for YSU 3.4.1 (7%) and MYJ (4%). Both too-low and too-high hTvmax occurred more often for more near-neutral situations (larger L), although the association is not perfect. The lack of a sharp distinction is likely related to horizontal variation of wind, temperature, and L; so, any relationship reflects upstream as well as local behavior. Also, the TKE schemes from (1) respond to vertical gradients (and for QNSE, the bulk Richardson number; see Table 4) more directly than the surface flux–determined L.
The origins of too-low hTvmax become apparent when we examine the results for Beaumont on 5 May, the windiest night, in Fig. 12. In the time series (left side), MYJ and YSU 3.4.1 replicate observed hTmax to within about a grid interval until at least 0800 UTC, while BouLac, QNSE, and YSU 3.2 show hTvmax < 50 m AGL. The vertical profiles (right side) reveal the explanation: too-strong vertical mixing produces deep near-neutral layers for BouLac and YSU 3.2 and a more modestly well-mixed layer for QNSE; all result in low-level Tυ maxima. (The lower secondary maximum in the observed Tυ profile does not persist.) For the BouLac and YSU 3.2 wind profiles, a height of minimum curvature below 100 m and an hSmax much greater than observed roughly bracket the well-mixed thermal layer, while hSmax for QNSE, MYJ, and YSU 3.4.1 is close to the observed value.
For a case of too-low hTvmax at Beaumont, 4–5 May 1997. (left) Evolution of hTvmax and hSmax. (right) Profiles of Θυ − 0.0098z (same shape as Tυ) and S at 0500 UTC.
Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1
From Fig. 13, the excessive mixing for YSU 3.2 and BouLac can be traced to their K (=KH = KM) being much larger than for the other three PBL schemes. In the case of YSU 3.2, large KH results from setting the scaling velocity ws to its neutral stratification value 
As in Fig. 12, but for turbulence variables for BouLac, QNSE, YSU 3.2, YSU 3.4.1, MYJ, and MYJ2 (MYJ rerun to extract KM but on a different computer). (top left) KH and (top right) KM; (bottom left) TKE, and (bottom right) Lmix. MYJ2 denoted by dashed line.
Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1
The differences between QNSE and MYJ are related to differences in their Pr values. Figure 14 (top) compares Pr−1 = KH/KM for hourly profiles at Beaumont for the same night as Figs. 12 and 13. While KH/KM = 1.4 for QNSE [consistent with Sukoriansky et al. (2006)] near the surface where Riloc is closest to neutral, KH/KM = 1.0 for MYJ, a consequence of (A8) in Janjić (2001). If one accepts Pr = 1 for the surface layer (e.g., Kaimal and Finnigan 1994, their Fig. 1.8), the MYJ Prandtl number is closer to correct near the surface. Further, when Pr−1 is plotted against Riloc (Fig. 14, bottom), the MYJ points fit the Monti et al. (2002) data at least as well as the QNSE points [though Grachev et al. (2007) suggest that the relationship in such plots is contaminated by self-correlation and that Pr might actually increase with Riloc if self-correlation is eliminated]. Note that Riloc < 0.5 for all MYJ NBL output examined.4 However, Pr = 1 when TKE = 0.1 m2 s−2, its background value.
(top) For 5 May Beaumont, inverse Prandtl number KH/KM as a function of height for hourly profiles from 0200 to 1000 UTC. (bottom) Relationship between KH/KM and local Richardson number, superposed on plot from Monti et al. (2002). For the bottom plot, the field data were collected in nocturnal downslope flows during the Vertical Transport and Mixing Experiment. Laboratory data are from Strang and Fernando (2001). The dashed line extending QNSE to higher Riloc is based on Fig. 4 of Sukoriansky et al. (2006).
Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1
c. Collapse of the NBL
A final behavior, “collapse” of h to near-zero values, occurs only for the most stable NBL encountered, on 21 May at Whitewater (Fig. 15), with hMYJ < 10 m for 11 h. For QNSE, 
For 21 May Whitewater, observed and modeled time series of NBL profile features. Observations: Red with hSmax from both radiosondes (circles) and RWP + MS (squares), and h zone based on h1wsonde (upside down triangles) and h2wsonde (triangles). For PBL schemes: BouLac (green), MYJ (turquoise), QNSE (blue), and YSU 3.4.1 (purple). For BouLac, QNSE, and MYJ, h = 
Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1
Figure 16 indicates that small hMYJ is associated with TKE hitting its lowest-allowed value, 0.1 m2 s−2 at the surface; 
For Whitewater 0800 UTC 21 May, profiles of observed and modeled mean and turbulence parameters. Red and oranges represent observations. For PBL schemes, green is BouLac, turquoise is MYJ, blue is QNSE, and purple is YSU 3.4.1.
Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1
d. Daily model bias in depth of NBL profile features
Figure 17 compares modeled and observed hTvmax, hSmax, and h. The green-shaded cells, which indicate model heights within about one grid point of observed heights, show that the number of successful predictions so defined is about the same for MYJ (using 
Comparison of modeled to observed hTvmax, hSmax, and h. Model hTvmax represented by h(Θυ,z = 10 K km−1); observed hTvmax represented by hTmax. For the model, h = 
Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1
The assumption that KH = KM for z < hYSU does not seem to have had a negative impact on YSU 3.4.1. Why is this? As illustrated by Fig. 18, Riloc (and thus Pr, see Fig. 14, bottom) reaches a maximum above the height of the K maximum, keeping Pr closer to 1 where K is the largest. Furthermore, NBL Riloc reaches only ~0.5–1 in windy conditions. However, it should be noted that Pr > 1 for z > hYSU.
For YSU 3.4.1, profiles of K and Riloc. (top) Weaker wind night and (bottom) stronger wind night and time corresponding to Figs. 12 and 13.
Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1
Although 
e. Surface fluxes
Since surface fluxes influence NBL evolution, we compare model 
Figure 19 shows variation among model 
Observed (sites 1 and 2) and modeled (Beaumont) time series of 
Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1
As in Fig. 19, but comparing modeled fluxes using MYJ at Beaumont, site 1, and site 2 to observations at sites 1 and 2.
Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1
Nor does the 
Though the largest 
In addition, MYJ 10-m winds are consistent with observations on all 3 days (Fig. 21). Based on averages of sites 1 and 2 between 0200 and 1100 UTC, the observed speed exceeds the linearly interpolated model results by 0.48, 0.14, and 0.58 m s−1 for 5, 11, and 21 May, respectively. Interpolation assuming a logarithmic profile reduces the differences by up to 0.2 m s−1, based on calculations for the day with the strongest winds (5 May). Thus, model underestimates are ~2%–3% for this day.
As in Fig. 20, but for 10-m wind speed, with model wind interpolated linearly between level 1 (~5 m) and level 2 (~14 m).
Citation: Monthly Weather Review 142, 8; 10.1175/MWR-D-13-00358.1
Estimates of Richardson et al. (2013) constant α in (7) at Beaumont. For observations, Ric from (6) with h and lowest level above surface; L based on sites 1 and 2.
4. Conclusions
Radiosonde, minisodar, radar wind profiler, and surface observations and WRF simulations for three moderately windy fair-weather nights during the CASES-97 field program are used to identify NBL depth h and the heights of maxima in wind speed hSmax and virtual temperature hTvmax, which are then used to evaluate four PBL schemes: BouLac, MYJ, QNSE, and YSU. Rather than simply focus on biases, we determine the observed coevolution pattern of h, hTmax ~ hTvmax, and hSmax and then evaluate the success of the four schemes in reproducing that pattern as a function of environmental conditions, as defined by the Obukhov length L.
To find h for BouLac, MYJ, and QNSE, we compared eight objectively determined h criteria (four TKE-based criteria, two Richardson number criteria, hTvmax, and hSmax; Table 1) to subjectively based values (hsubj) on plots of the model TKE profiles. Based on this comparison, we chose a threshold equal to 5% of the maximum TKE excess from its background value, where the maximum was found for the lowest kilometer. Fortuitously, the height so derived, 
The observed TKE-based h was based on a decrease in balloon rise rate from ~5 to ~3 m s−1 going from turbulent to nonturbulent air (Johansson and Bergstrom 2005). Taking the heights at which the deceleration started (h1wsonde) and ended (h2wsonde) yielded reasonable bounds for h, given proper balloon launch procedure, the absence of large air vertical velocities, and h > ~100 m. This method worked least reliably at Beaumont, perhaps because of the currents associated with nearby terrain.
Summary plots of composite h1wsonde, h2wsonde, hSmax, and hTvmax revealed a general pattern: hTvmax increases gradually through the night, hSmax and hTvmax converge, and the two approach the h zone based on wsonde after several hours, after which all three occupy roughly the same altitude range until surface heating starts to form the CBL. On many nights hSmax followed h through most of the night to such a degree that hSmax was a good secondary measure of h, in agreement with the work of Banta et al. (2003) and Pichugina and Banta (2010). Kosovic and Curry (2000) produced such an evolution using LES, although they cautioned that it took an inertial period (about 20 h at this latitude) for the three heights to correspond.
The observed coevolution pattern provided metrics against which the NBL schemes could be judged. Of the PBL schemes examined, MYJ, QNSE, and YSU version 3.4.1 mostly reproduced the observed converging of hTvmax, hSmax, and h with time. However, BouLac (55% of the time) and YSU version 3.2 (67% of the time) produced unrealistically low hTvmax, a sign of too much vertical mixing. In both cases, hSmax tended to be too high compared to observations. The low hTvmax behavior occurred with intermediate frequency for QNSE (33%) and seemed to be associated with too low a Prandtl number (too large a KH) since QNSE wind profiles were simulated far better (KM about right). The low hTvmax behavior occurred least frequently for MYJ (7%) and YSU 3.4.1 (8%). In most cases, the excessive vertical mixing was associated with larger values of L (windier nights). However, the L dependence was not a clean one: a bulk Richardson number could be a better parameter, and upstream as well as local forcing determines the profiles of resolved parameters.
A final behavior, the collapse of the NBL (hMYJ ~ 0 for several hours; 
There was a large mismatch between observed and modeled friction velocity 
The conclusions should be generalized with caution. Because of data limitations, we limited ourselves to windier nights, during which we would expect deeper NBLs and more continuous coupling of the atmosphere to the surface. The 108 h and three locations analyzed thus mostly represent less stable conditions [intermittent to continuous turbulence regimes of Van de Wiel et al. (2003)]. Further, the TKE did not always simply decrease with height, sometimes reaching a maximum (or two maxima) above the surface. Finally, resolved mesoscale NBL structures could influence the results slightly.
The small number of nights sampled is compensated for by the completeness of the dataset, which along with the WRF runs, allows the examination of the impacts of upstream and surface conditions on the evolution of the NBL. This case study approach draws on the strengths of the simulations and observations to examine the coevolution of observed and modeled NBL profile features and TKE values, terrain effects on the flow, and vertical surface fluxes. Though we cannot quantify model biases, we can explore their sources.
As to PBL scheme improvements, the results suggest the following:
for BouLac, allowing for stability in converting TKE to vertical velocity in the expression for estimating Lmix, which could mitigate too much mixing at night [already recognized as a shortcoming by Therry and LaCarrere (1983)];
modifying QNSE to mitigate apparent excess mixing of the temperature profile;
using the stability-dependent form for ws in YSU (i.e., use YSU 3.4.1 rather than 3.2); and
including the advection of TKE by resolved winds.
As to the observations, the results suggest designing field measurements to better measure the relevant parameters in NBL evolution or using datasets that include a useful subset (e.g., CASES-99; Poulos et al. 2002):
For NBL depth, this would include radiosonde releases optimized to find h using balloon rise rate. Collocated tethersonde, tower, and lidar data could enable sampling a broader range of NBLs as well as comparison of techniques for determining h.
This would also involve designing flux measurements to include “regional” as well as “local” fluxes by adding measurements from a taller tower and/or aircraft or unmanned aerial vehicles to a traditional flux tower network. Analysis would include examination of averaging times.
Acknowledgments
The surface meteorology, surface flux, and radiosonde data were collected, processed, and archived by NCAR’s Earth Observations Laboratory and the RWP/MS data were collected, processed, and archived by the Argonne National Laboratory’s former Argonne Boundary Layer Experiments Facility. The authors are indebted to Tom Horst and Steven Oncley of NCAR and Richard Coulter of Argonne National Laboratory for help in data interpretation as needed. Valuable help in interpreting the PBL schemes was provided by Alberto Martilli (BouLac), Zavisa Janjić (MYJ), Esa-Matti Tastula (QNSE), and Songyu Hong (YSU). Xubin Zeng, Jeff Weil, Sukanta Basu, Jielun Sun, and Wayne Angevine provided useful insights, with the last two also helping to clarify figures. Finally, suggestions by Jun Zhang and an anonymous reviewer helped us clarify several points and improve the figures. This work was supported by the Air Force Weather Agency, the NCAR Water System Program, and NCAR base funding from the National Science Foundation.
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Both vertical divergence terms are much smaller than the other terms in (1), with the pressure transport contribution close to zero in the Kosovic and Curry (2000) LES of a weakly stable NBL.
Odd hours are omitted for readability.
A persistent (3 h) shallow S maximum occurs at ~50–100 m, which is sometimes linked to a Tυ maximum on 5 May at Whitewater (Fig. 7). A check of other observed sounding sequences showed this behavior to be unique.
This is consistent with Janjic (2001, p. 13) as well as our choice of Riloc = 0.5 as a potential NBL depth criterion (Table 1). On nights when it failed for MYJ, hRiloc > h.
The criterion of Richardson et al. is an improvement over a critical Richardson number for both model and observations: values of α vary far less than values of Ric, with time or between days.
