Experimental data from four field campaigns are used to explore the
variability of the bulk Richardson number of the entire planetary boundary
layer (PBL),

The planetary boundary layer (PBL), or the atmospheric boundary layer, is
the lowest part of the atmosphere that is directly influenced by earth's
surface and has significant impacts on weather, climate, and the hydrologic
cycle (Stull, 1988; Garratt, 1992; Seidel et al., 2010). The height of the
PBL (PBLH) is typically on the order of

The PBL is characterized by the presence of continuous turbulence, while turbulence is lacking or sporadic above the PBL. Therefore, the PBLH can be viewed as the level where continuous turbulence stops (Wang et al., 1999; Seibert et al., 2000). Using high-frequency turbulence measurements (e.g., collected from ultrasonic anemometers on aircraft), the PBLH can be readily determined. This is known as the turbulence (Tur) method. It is highly reliable, but the instruments required by this method are costly. A more economic option is to determine the PBLH through analyzing temperature and wind profiles measured from radio soundings. In this method, the PBLs are broadly classified as strongly stable boundary layers (type I SBLs), weakly stable boundary layers (type II SBLs), or unstable boundary layers (UBLs) (Holtslag and Boville, 1993; Vogelezang and Holtslag, 1996). They are defined using the surface heat flux and the potential temperature profile, as shall be seen later.

For strongly stable boundary layers or type I SBLs, there is a strong
inversion in the potential temperature profile and the PBLH is usually
defined as the top of the inversion where the potential temperature gradient
(PTG) first becomes smaller than a certain threshold

For an atmosphere with discernible characteristics (i.e., a strongly stable
potential temperature profile for the type I SBL, a strong LLJ for the
type II SBL, and a capping inversion layer for the UBL), the three methods
generally show good performance (e.g., Mahrt et al., 1979; Liu and Liang,
2010; Dai et al., 2011). However, for an atmosphere without these discernible
characteristics, large errors can be introduced by these methods. As such,
these methods are usually used in experimental studies but not in numerical
models since numerical models need to determine the PBLH automatically.
Instead, the bulk Richardson number (

The objective of this study is to examine the variation of

The study is organized in the following way: Sect. 2 describes the
observational data used in this study; Sect. 3 compares estimates of PBLH
from different methods that are widely used to determine the PBLH from
measurements; Sect. 4 focuses on the bulk Richardson number method and
describes the search for a best choice of

Observational data from four field campaigns that were conducted under different surface and atmospheric conditions are used in this study. These field campaigns are the Litang experiment, the Atmospheric Radiation Measurement (ARM) experiment, the Surface Heat Budget of the Arctic Ocean (SHEBA) experiment, and the Cooperative Atmosphere–Surface Exchange Study (CASES) in 1999 (CASES99). Each of these four field campaigns is briefly described as follows.

The Litang site is located over a plateau meadow in the southeast of the
Tibetan Plateau. The campaign provides 105 effective radio soundings of wind
and temperature in three observational periods (7–16 March, 13–22 May, and
7–16 July, 2008), with a typical 6 h interval (about 00:30, 06:30, 12:30,
and 18:30 LST, local standard time). The 30 min averaged wind and temperature at 3

The ARM experiment was carried out over a plain farmland in Shouxian, China,
from 14 May to 28 December 2008. During the campaign, soundings were
collected every 6

The SHEBA site is located around the Canadian icebreaker

The CASES99 is the second experiment of CASES conducted in Kansas, USA.
The terrain is relatively flat (the average slope is about
0.5

In postprocessing, a 20 m moving-window average is used for all the soundings from all the sites (except the turbulence measurements by aircraft in CASES99) to remove the measurement noise.

Examples of vertical profiles of the type I SBL (upper panels) and
the type II SBL (lower panels) from CASES99 aircraft measurements:

As mentioned in the introduction, the PBLs during a typical diurnal cycle are
categorized into three types: type I SBLs (i.e., strongly stable boundary
layers at night), type II SBLs (i.e., weakly stable boundary layers at early
morning/night), and UBLs (i.e., unstable boundary layers during the daytime).
The PTG method, the LLJ method, and the modified parcel method are usually
used to determine the PBLH for type I SBLs, type II SBLs, and UBLs,
respectively. Based on previous studies (e.g., Holtslag and Boville, 1993;
Vogelezang and Holtslag, 1996), they are classified using the surface heat
flux

Note that cases with

For any of the three types of PBLs, the Tur method is the most direct and
accurate approach for the PBLH estimation because it measures the turbulence
intensity directly. Figure 1 shows vertical profiles of potential
temperature, mean wind velocity, bulk Richardson number, and wind velocity
perturbations from CASES99 for a type I SBL (a1–d1) and a type II SBL
(a2–d2). The wind velocity perturbations (

Figure 1 further shows the PBLHs determined with the PTG method (see the red solid line on a1) and the LLJ method (see the red solid line on b2) for type I and type II SBLs, respectively. It is clear that the estimates of PBLHs with these two methods are comparable to the PBLHs determined from the Tur method, suggesting that the PTG method and the LLJ method work well for type I and type II SBLs, respectively.

Figure 2 shows the sounding profiles taken from Litang on 9 July 2008 and the
PBLHs estimated by the PTG, LLJ, and modified parcel methods for the three
different PBLs, respectively. At midnight (00:35 LST), the PBL was very
stable due to radiative cooling from the surface and is classified as a
type I SBL. According to the PTG method, the PBLH was found at the top of the
strong inversion (125

However, for a PBL without these discernible characteristics, these methods
may introduce large biases (see Fig. 3 and e.g., Russell et
al., 1974; Martin et al., 1988; Balsley et al., 2006; Meillier et al., 2008).
For type I SBLs, when the underlying inversion is not strong, it will be
difficult to determine the PBLH by the PTG method due to the fact that the
maximum PTG can be less than the threshold

Although these special cases do not always exist, they limit the applications
of the three methods. The accuracy of the determined PBLH can be improved
with additional information, as have been demonstrated before. The following
sums up the procedures that are used in this study for estimating PBLH by
using these four methods. First, whenever turbulence measurements are
available, the Tur method is used to determine the PBLH. Second, for type I
SBL cases with a relatively weak inversion (the local PTG maximum is

Typical profiles of potential temperature (blue), wind speed (red),
and

The “observed” PBLH and the stability parameter at four observational sites.

Examples of vertical profiles in type I SBLs (upper panels), type II
SBLs (middle panels), and UBLs (lower panels):

The PTG method, the LLJ method, and the modified parcel method are usually
used to determine the PBLH in observational data. However, they do not work
well when the PBL has no distinct features that are required by these
methods. Instead, the bulk Richardson number method with a prescribed

To avoid overestimating the shear production in Eq. (1) for relatively high
wind speeds (i.e., in type II SBL) and to account for turbulence generated
by surface friction under neutral conditions, Vogelezang and Holtslag (1996)
proposed an updated formulation, which is employed in the Community
Atmosphere Model version 4 (CAM4), written as

Under unstable conditions, the virtual potential temperature at the lower
boundary

In this study, the virtual potential temperature is estimated as the potential temperature in the calculation because the former can lead to significant fluctuations in the estimated PBLH due to inaccurate humidity measurements (Liu and Liang, 2010).

After

Because each profile provides a

The representative

Linear fitting method inferred

The inferred

For UBLs, the height

Linear fitting method inferred

Linear fitting method inferred

Comparisons of the heights of UBL at different sites determined by
the bulk Richardson number method with

It is seen that the linear fitting method yields small correlation
coefficients under unstable conditions. Under stable conditions, the linear
fitting method also has some disadvantages. For example, the inferred
value of

The correlation coefficient, bias, SEE, and NSEE with different values of

Compared to type I SBLs, the correlation coefficients are smaller and errors are
larger for type II SBLs (Fig. 9), again indicating that the PBLH for weakly
stable boundary layers is more difficult to determine. However, the maximum
correlation coefficient, minimum bias, SEE and NSEE, and the range of optimal

Comparison between estimated PBLH using the bulk Richardson number
method with

Comparison between estimated PBLHs using the bulk Richardson number
method with

Comparison between estimated PBLHs using the bulk Richardson number
method with

For UBLs, Fig. 10 shows that the maximum correlation coefficient is larger,
the minimum bias, SEE, and NSEE are smaller, and the values of optimal

Through the above statistical error minimization methods, the optimal

Inferred bulk Richardson number of the entire PBL,

Comparison between estimated PBLH using the bulk Richardson number
method and observed PBLHs for all types of PBLs. The correlation
coefficient

Comparisons between observed and estimated PBLHs with a single

With the above analyses, the best choices of

To further investigate the improvements in estimating PBLHs with the new,
variable

Comparison of observed and simulated PBLHs using CAM4 with the
default and new

The PBLH is an important parameter in boundary-layer research and accurate estimates of the PBLH are vital for many environmental applications. In this study, we investigated several methods for computing the PBLH under different stratification conditions. The Tur method is considered as the most accurate approach for any atmospheric stratification due to its direct measurement of turbulence intensity. However, such a method is expensive and thus cannot be widely applied. However, determining of the PBLH with radio soundings through the PTG, LLJ, and modified parcel methods is more affordable. These methods usually work well when the PBL has certain unique features but may fail under special conditions (e.g., a weak underlying inversion for strongly stable boundary layers, multiple wind maxima for weakly stable boundary layers, and no clear maximum of vertical gradient of potential temperature for unstable boundary layers). With corrections made for these special cases, we used the Tur, PTG, LLJ, and modified parcel methods to determine PBLHs from Litang, ARM Shouxian, SHEBA, and CASES99 field experiments. The estimated PBLHs using these methods are treated as observed PBLHs.

The bulk Richardson number method is more commonly used in numerical models
due to its reliability for all atmospheric stratification conditions, which
requires a specified value of the bulk Richardson number for the entire PBL,
or

This study is supported by the China Meteorological Administration under grant GYHY201006024, the National Program on Key Basic Research Project of China (973) under grants 2012CB417203 and 2011CB403501, the National Natural Science Foundation of China under grant 41275022, and the CAS Strategic Priority Research Program, grant 5 XDA05110101. We are grateful to two anonymous reviewers for their careful review and valuable comments, which led to a substantial improvement of this manuscript. Edited by: A. Colette