The states of coupling between clouds and
surface or boundary layer have been investigated much more extensively for
marine stratocumulus clouds than for continental low clouds, partly due to
more complex thermodynamic structures over land. A manifestation is a lack
of robust remote sensing methods to identify coupled and decoupled clouds
over land. Following the idea for determining cloud coupling over the ocean,
we have generalized the concept of coupling and decoupling to low clouds
over land, based on potential temperature profiles. Furthermore, by using
ample measurements from lidar and a suite of surface meteorological
instruments at the U.S. Department of Energy's Atmospheric Radiation
Measurement Program's Southern Great Plains site from 1998 to 2019, we have
developed a method to simultaneously retrieve the planetary boundary layer
(PBL) height (PBLH) and coupled states under cloudy conditions during the
daytime. The new lidar-based method relies on the PBLH, the lifted
condensation level, and the cloud base to diagnose the cloud coupling. The
coupled states derived from this method are highly consistent with those
derived from radiosondes. Retrieving the PBLH under cloudy conditions, which
has been a persistent problem in lidar remote sensing, is resolved in this
study. Our method can lead to high-quality retrievals of the PBLH under
cloudy conditions and the determination of cloud coupling states. With the
new method, we find that coupled clouds are sensitive to changes in the PBL
with a strong diurnal cycle, whereas decoupled clouds and the PBL are weakly
related. Since coupled and decoupled clouds have distinct features, our new
method offers an advanced tool to separately investigate them in climate
systems.
Introduction
A large fraction of low clouds is driven by surface fluxes through the
conduits of the planetary boundary layer (PBL) over land (e.g., Betts, 2009;
Ek and Holtslag, 2004; Golaz et al., 2002; Teixeira and Hogan, 2002; Zheng
et al., 2020; Wei et al., 2020; Santanello et al., 2018). This is a coupled
cloud–surface system (Cheruy et al., 2014; Zheng and Rosenfeld, 2015; Wu et
al., 1998). However, not all low clouds respond to surface forcing. Those
clouds without close interactions with the local surface are considered to
be in a decoupled state. Given that the PBL is, by definition, the lowest
atmospheric layer influenced by the underlying surface (Stull, 1988), to
what degree the PBL top overlaps with cloud bases becomes a good criterion
to separate coupled and decoupled low clouds.
Conventionally, the “coupled state” of a cloud-topped marine boundary
layer implies that the moist conserved variables are vertically well mixed
within the PBL (Bretherton and Wyant, 1997; Dong et al., 2015; Zheng and Li,
2019; Zheng et al., 2018, 2021). However, such a definition
cannot be simply applied to clouds over land since the definition and the
determination methods of the PBL over land differ from those over ocean
(Garratt, 1994; Vogelezang and Holtslag, 1996). The concept of coupled and
decoupled states is typically used to characterize marine stratocumulus
clouds due to their large-scale coverages (Nicholls, 1984). Since
stratocumulus only constitutes a relatively small portion of continental
clouds (Warren et al., 1986), we attempt to extend the concept of coupling
and decoupling to characterize low clouds over land. Due to the relatively
complex thermodynamics, the moisture conserved variables (e.g., total water
mixing ratio and liquid potential temperature) may not be a constant in the
coupled sub-cloud layer (Driedonks, 1982; Stull, 1988).
Following parcel theory, the lifted condensation level (LCL) has been used
to diagnose a coupled cloud, based on the distance between the LCL and the
cloud base (e.g., Dong et al., 2015; Glenn et al., 2020; Zheng and
Rosenfeld, 2015; Zheng et al., 2020). When potential temperature and
humidity are uniformly distributed in the vertical, the LCL should be
consistent with the cloud base for coupled cases. However, the cloud base
for coupled cases can considerably differ from the LCL over land because
potential temperature and humidity have large variabilities in the vertical
scale within the PBL over land (Driedonks, 1982; Guo et al., 2016, 2021;
Stull, 1988; Su et al., 2017a). To address the limitation in the LCL method,
we attempt to develop a remote sensing method to distinguish coupled and
decoupled clouds over land.
Since the PBL height (PBLH) is the maximum height directly influenced by
surface fluxes, we consider coupling with the PBL equivalent to coupling
with the land surface. Thus, we use the PBLH as a critical parameter to
diagnose the coupling between clouds and the land surface. The degree of
coupling may thus be gauged in terms of quantitative differences between the
cloud base and the PBL top. Such differences can be determined in a height
coordinate system or in a potential temperature coordinate system (Kasahara,
1974). For this purpose, ground-based lidar has great potential because it
can continuously track the development of the PBL (Demoz et al., 2006;
Hageli et al., 2000; Sawyer and Li, 2013; Su et al., 2017b, 2018) and clouds
(Clothiaux et al., 2000; Platt et al., 1994; Zhao et al., 2014) at high
temporal and vertical resolutions.
By jointly using lidar measurements and meteorological data from the U.S.
Department of Energy's Atmospheric Radiation Measurement (ARM) Southern
Great Plains (SGP) site (36.6∘ N, 97.48∘ W), we attempt to identify
coupled and decoupled low clouds during the daytime. Unlike previous studies
that use the LCL or radiosonde (RS) data to diagnose coupled clouds (e.g.,
Dong et al., 2015; Zheng and Rosenfeld, 2015), this study developed a
lidar-based method to determine the status of cloud coupling over land at a
high temporal resolution.
The paper is organized as follows. Section 2 describes the measurements and
data. Section 3 describes the new methodology in terms of the definition and
implementation. The performance of the method is demonstrated in Sect. 4,
and a summary is presented in Sect. 5.
Data descriptionsRadiosonde
RS launches took place at least four times per day at the ARM SGP site,
usually at 00:30, 06:30, 12:30, and 18:30 local time (LT). Holdridge et al. (2011) provide technical details about the ARM RS (https://www.arm.gov/capabilities/instruments/sonde, last access: 2 December 2021). In this study, we consistently use daylight saving time (coordinated universal time -5 h) as
local time throughout the year to avoid inconsistencies between summer and
winter. Besides the routine measurements, there are fewer but still
considerable numbers of RS data obtained at other times of the day (e.g.,
09:30, 12:00, 13:00, 15:30, and 19:00 LT). These supplemental RS samples at other
times comprise ∼ 10 % of the total number of cases. RS data
from 06:30–19:00 LT are utilized in this study. The vertical resolution of RS
data varies according to the rising rate of the balloon, but measurements
are generally taken ∼ 10 m apart. We further vertically
average the RS data to achieve a vertical resolution of 5 hPa.
There are several methods to determine PBLH from RS-measured potential temperature (θ),
pressure, and humidity profiles. They include, among others, the parcel
method (Holzworth, 1964), the gradient methods (Stull, 1988; Seidel et al.,
2010), and the Richardson number method (Vogelezang and Holtslag, 1996).
After examining the previous methods, Liu and Liang (2010) proposed a
different approach to determine the PBLH that is valid under different
thermodynamic conditions. The robust performance was demonstrated over the
SGP site and in other major field campaign sites around the world (Liu and
Liang, 2010). Thus, we adopted this method to calculate PBLH from RS data in
this study. By using the water vapor mixing ratio (WVMR), the potential temperature is corrected as the virtual potential
temperature, θv (θv=θ(1+0.61 WVMR)). The virtual potential temperature does not include
a correction for the liquid water content profile, as this is challenging to
measure in many conditions. Therefore, the virtual potential temperature is
not conserved during moist convection. Since we mainly focus on the
sub-cloud atmosphere, this is not a serious problem. Moreover, for available datasets, we use scaled
RS moisture profiles normalized by the total precipitable water vapor
derived from the microwave radiometer (https://www.arm.gov/capabilities/vaps/lssonde, last access: 2 December 2021, Revercomb et al., 2003).
Micropulse lidar (MPL) system
MPL backscatter profiles were collected at the SGP site from September 1998
to July 2019 with high continuity (Campbell et al., 2002). Technical details and data availability can be found at the website https://www.arm.gov/capabilities/instruments/mpl, last access: 1 December 2021. The backscatter profiles
have a vertical resolution of 30 m. MPL signals have an initial temporal
resolution of 10–30 s and are averaged every 10 min for this study. Due to
the inherent problem of lidar observations, there is a ∼ 0.2 km near-surface blind zone. Following the standard lidar-data
processing, background subtraction, signal saturation and overlapping, and
after-pulse and range corrections are applied to the raw MPL data (Campbell
et al., 2002, 2003). Questionable data are excluded based on the
quality-control flags.
Cloud product
The MPL can be used to detect cloud layers based on signal gradients (Platt
et al., 1994). Lidar-based methods are accurate for determining the
cloud-base height (CBH) but may miss information about the cloud top due to
the signal saturation within an optically thick cloud (Clothiaux et al.,
2000). Under this condition, the cloud radar provides a better estimation of
the cloud-top height (CTH). In this study, we directly use an existing
quality-controlled cloud product, CLDTYPE/ARSCL (https://www.arm.gov/capabilities/vaps/cldtype, last access: 1 December 2021), which combines information
from the MPL, ceilometer, and cloud radar to determine the vertical
boundaries of clouds (ARM Data Center, 2021; Flynn et al., 2017). For the
lowest cloud base, the best estimation from laser-based techniques (i.e.,
MPL and ceilometer) is used. The original temporal resolution of the
CLDTYPE/ARSCL product is 1 min, averaged to a 10 min temporal resolution. To
avoid averaging jumps in signal between different clouds, a cloud is
considered to be continuous if its base height varies less than 0.25 km
between two consecutive profiles.
MethodologyDefinition of coupled and decoupled clouds based on thermodynamics
The definition of the state of cloud–surface coupling over land is a
critical question. For marine stratocumulus, coupled clouds are identified
when the liquid water potential temperature varies less than a certain
threshold (i.e., 0.5 K) below the cloud base (Jones et al., 2011). We try to
extend the concept of coupling and decoupling to clouds over land. The PBL
over land is typically buoyancy driven and controlled by surface fluxes
during the daytime. We consider a cloud is in the coupled state when it
strongly interacts with the buoyancy fluxes within the PBL.
Figure 1 presents the idealized vertical profiles of virtual potential
temperature (θv) under the clear sky, coupled cloud, and
decoupled cloud. A superadiabatic surface layer exchanges the heat fluxes
between the surface and PBL. The outer layer and entrainment zone are
turbulently coupled with the surface and, thus, are considered as the
coupled regime. Meanwhile, the free atmosphere is considered as the
decoupled regime. Theoretically, θv is constant in the outer
layer and follows the wet adiabatic lapse rate in the cloud layer. Although
the profiles of θv in the real atmosphere can largely differ from
the idealized profiles, the relative position between the cloud layer and
capping inversion of entrainment zone is clear. For the coupled cases, the
cloud base is below the capping inversion of entrainment zone. For the
decoupled cases, the cloud base is above the capping inversion. Based on
this feature, we can use the profiles of virtual potential temperature
(θv) in the sub-cloud layer to determine the coupling state of
continental clouds. It should be noted that the virtual potential
temperature is not conserved in a moist adiabatic process and thus would
decrease within a cloud layer. On the other hand, the liquid potential
temperature remains a near-constant within the stratocumulus. Since we use
the profiles of potential temperature in the sub-cloud layer to diagnose the
cloud coupling, there is no difference in the identification results by
using the virtual potential temperature.
Idealized vertical profiles of virtual potential
temperature (θv) under the clear sky, coupled cloud, and
decoupled cloud over land. The surface layer, outer layer entrainment zone,
and free atmosphere are divided by the dashed blue lines. The cloudy layer is
marked as the shaded area, and PBLH is marked as the pink point. Red and
green zones indicate the coupled and decoupled regime, respectively.
Elements (e.g., turbulence, heat fluxes, cloud) in the coupled regime are
directly affected by the PBL processes, while these elements are not
directly affected by the PBL processes in the decoupled regime. For the
coupled cases, the cloud base is below the capping inversion of entrainment
zone. For the decoupled cases, the cloud base is above the capping
inversion.
Following the previous studies (Jones et al., 2011; Dong et al., 2015), we
attempt to use the variations in the potential temperature within the
sub-cloud layer to diagnose the cloud coupling. For determining a suitable
threshold, we first look at several examples of profiles of θv
and WVMR from the RS (Fig. 2). If the CBH is lower than the PBLH, the
cloud is affected by turbulence and buoyancy fluxes in the PBL, such as the
cases shown in Fig. 2a. Note that the PBLH is not an absolute boundary
limiting turbulence and buoyancy fluxes. Due to the overshooting of rising
air parcels, we use a range to screen the condition of coupled clouds. As
shown in Fig. 2b, even when the CBH is slightly above the PBLH, WVMR and
θv are still relatively consistent between the cloud layer and
the PBL and show large step signals at the cloud top.
Figure 2c–d show a clear inversion layer between the cloud base and the PBL
top, and the difference in θv between the CBH and the PBLH
(Δθv) is relatively large. Such a notable
inversion layer prevents the buoyancy fluxes within the PBL from reaching
the cloud base, leading to the decoupling between the cloud and the PBL.
Overall, we consider Δθv as the key
factor to determine cloud coupling. In Fig. 2, Δθv for coupled cases (a–c) is -0.32 and 0.31 K,
respectively, and Δθv for decoupled cases
(d–e) is 1.47 and 5.0 K, respectively.
Virtual potential temperature (θv, blue lines)
and water vapor mixing ratio (WVMR, red lines) profiles from radiosonde (RS)
over the Southern Great Plains site for different cases. The differences in
virtual potential temperature between the cloud base and the planetary
boundary layer (PBL) top are expressed as Δθv(θvCBH-θvPBLH). The time of each radiosonde
launch is marked in each panel as “YYYYMMDDHH”, where YYYY, MM, DD, and HH
indicate the year, month, day, and local time, respectively. Green regions
are cloud layers, and dashed green lines indicate their boundaries. The
cloud layer is obtained from the CLDTYPE/ARSCL data. PBLHs is derived from
RS data and is marked as dashed pink lines.
Therefore, instead of giving a height range to limit the differences between
CBH and PBLH, we consider using the differences in θv between CBH
and PBLH to determine the threshold for distinguishing coupled and decoupled
clouds. For convenience, we use Δθv to
refer to the difference in θv between the CBH and the PBLH
(Δθv=θvCBH-θvPBLH). For decoupled cases, the cloud base is
above the capping inversion of the entrainment zone. There is a notable
inversion in θv between PBL top and decoupled cloud base. Thus,
we identify the cases satisfying Δθv>δs as being in a decoupled state. Correspondingly, we
identify the cases satisfying Δθv<δs as being in a coupled state. We set the range of CBH to between 0 and
4 km and excluded cases of deep convection (i.e., CBH < 4 km and CTH > 6.5 km). In the previous studies for marine clouds, the
difference in the potential temperature between the CBH and the near surface
is used as the criterion (Jones et al., 2011; Dong et al., 2015). However,
we use the potential temperature at the PBL top instead of the potential
temperature near the surface. This change is due to the relatively complex
thermodynamic structure over the land. The large variation in the potential
temperature within the surface layer would notably affect the result. Hence,
we use the potential temperature above the PBL top to replace those values
near the surface.
As the basic framework of PBL, the slab model assumes that θv is constant within the PBL (Wallace and Hobbs, 2006). Under this
assumption, δs can be set as 0. However, there are certain
variations in θv within the PBL, which can cause
inversions with relatively small magnitudes between the cloud base and PBL
top. Figure 3a presents the inversion strength in θv
within PBL during the daytime. Specifically, inversions represent the layers
with continuously increased structures of θv. For an inversion
layer, the inversion strength is calculated as the differences in θv between the top and bottom of the layer. The inversions near the surface
or across the PBL top are excluded. Besides the capping inversion and
surface inversion, the inversion strength within PBL is typically below 1 K.
Therefore, we set δs as 1 K, which is the same as the criterion
for determining stable or convective conditions (Liu and Liang, 2010).
Furthermore, we demonstrate the probability density function (PDF) of
Δθv for the low-cloud cases. Coupled and
decoupled clouds are classified by the threshold of δs (1 K).
Through the development of PBL, boundary layer clouds frequently occur in
the entrainment zone and form a coupled cloud–PBL system. For such coupled
systems, θv at cloud top and PBL top is highly
consistent for the majority of cases. Thus, the PDF of Δθv shows significantly high values for the range of -2
to 0.5 K in the coupled regime. Meanwhile, the PDF of Δθv is evenly distributed in the decoupled regime. Since
we only analyze low clouds, the PDF of Δθv slowly decreases when Δθv is above
10 K.
Based on the variations in θv within the PBL, we set δs as 1 K. However, it should be noted that it is not an absolute value. A
similar threshold of 0.5 K has been used for marine stratocumulus (Jones et
al., 2011; Dong et al., 2015). Comparing to the marine condition,
θv shows greater variabilities over land. Hence, the
threshold is correspondingly larger. On the other hand, since the threshold
of 1 K is in the low PDF regime (Fig. 3b), the small changes in this value
would not notably affect the identifications. Specifically, a 0.1 K
difference in δs will lead to a 0.5 % difference in the
identification of coupled cloud.
(a) Blue bars represent the inversion strength of
θv within the PBL. The inversion strength is derived
from the radiosonde during daytime (08:00–19:00 LT). The inversions near
the surface or across PBL top are excluded. The solid black line represents
the cumulative frequency. (b) Pink area represents the probability density
function (PDF) of the differences in the virtual potential temperature
between cloud-base height (CBH) and PBLH (Δθv=θvCBH-θvPBLH). By using a threshold of Δθv<δs (1 K), we can identify the
coupled cloud regime.
Similar to the previous studies (Jones et al., 2010; Dong et al., 2015; Zheng
and Rosenfeld, 2015), we identified the coupled clouds as the thermodynamics
coupling between surface and cloud base. However, it is an open question
whether the entire cloud layer is coupled for coupled cases. It depends on
whether the liquid water potential temperature is conserved within the cloud
layer, which represents a moisture adiabatic process. This issue is closely
related to the cloud types. In the cloud parameterizations, the entire
stratocumulus layer is considered to be well-mixed, while the cumulus-capped
layer is usually partially mixed (Lock, 2000). For stratocumulus clouds, the
entire cloud layer and PBL are typically fully coupled with surface, when
the cloud base is coupled with surface. For the cumulus-capped PBL, the
entire cloud layer may not be completely coupled, despite the coupling
between cloud base and surface. The well-established parameterizations are
supported by many observational studies (e.g., Betts, 1986; Storer et al.,
2015; Berkes et al., 2016; de Roode and Wang. 2006; Ott et al., 2009).
Lidar-based method to identify coupled and decoupled cloudsMethod description
Given the rapid change in clouds over land, RS observations have limitations
when it comes to tracking cloud development due to the coarse temporal
resolution and drifting of the balloon. We thus further developed a
lidar-based method to identify the coupled states of clouds based on our new
algorithm for retrieving the PBLH that can better track the diurnal
variations in PBLH than conventional lidar-based approaches (Su et al.,
2020). We adapted this algorithm for retrieving the PBLH and developed a new
scheme to deal with cloudy conditions. Following the original method (Su et
al., 2020), the rainy cases are eliminated in the quality-control
process. The principles behind the PBLH algorithm are stated next
for completeness.
List of parameters in the flowchart of DTDS (Fig. 4).
Our new PBLH algorithm can retrieve the PBL variability from the MPL under
different thermodynamic stability (thus named the DTDS algorithm)
conditions, taking into account the vertical coherence and temporal
continuity of the PBLH. First, we identify the local maximum positions
(LMPs; range: 0.25–4 km) in profiles of the wavelet covariance transform
function derived from lidar backscatter (Brooks, 2003). These LMPs are the
potential positions of the PBLH. We can use the PBLH derived from morning RS
soundings as the starting point. Without morning RS soundings, the algorithm
can still work well, with the lowest LMPs selected as the starting point,
which reduces by 0.02–0.05 the correlation coefficient between MPL-derived
and RS-derived PBLHs (Su et al., 2020).
To ensure good continuity, we select the closest LMP to the earlier position
of the PBLH. Different stages of PBL development are considered.
DTDS-derived PBLHs likely increase during the growth stage and decrease
during the decaying stage, but the algorithm is also able to identify
decreases during the growth stage or increases during the decaying stage
based on the selection scheme described by Su et al. (2020). There are
multiple step signals in the backscatter profiles when complex aerosol
structures (e.g., the residual layer) are present, leading to multiple LMPs.
Based on temporal continuity, we select the appropriate LMP as the position
of the PBL top. However, PBLH retrievals still suffer from relatively low
accuracies under stable conditions because of the weak vertical mixing and
residual layer.
Clouds induce strong step signals in the lidar backscatter, further
considerably affecting PBLH retrievals. Su et al. (2020) only considered
cases where the low cloud top coincided with the previous PBL top, excluding
other low-cloud cases (> 60 % of all low-cloud cases). Here, we
specifically consider coupled and decoupled states of low clouds. Due to the
MPL's ∼ 0.2 km blind zone, we only analyze the PBLH and CBH
above 0.2 km. Figure 4 presents the flowchart describing the updated DTDS
algorithm. In particular, we jointly use PBL development and the LCL to
diagnose the states of coupling or decoupling. In ideal situations, LCL,
PBLH, and CBH are highly consistent with each other for coupled clouds. But
for real conditions, we only require that either the LCL or the PBLH
coincides with the CBH for identifying coupled cases, with another parameter
serving as an additional constraint. Specifically, a coupled cloud needs to
occur within a certain range of LCL and the previous position of the PBL
top.
The flowchart of the updated DTDS algorithm. In this
diagram, H(i) is the retrieved planetary boundary layer height (PBLH) at
time i. CBH and CTH represent the base and top heights, respectively, of the
lowest cloud at time i. The PBLH part for selecting the suitable local
maximum position (LMP) follows Su et al. (2020), and a detailed scheme for
identifying a coupled cloud is added to the DTDS algorithm. LCL stands for
lifted condensation level. Five empirical parameters (A1, A2,
A3, A4, and A5) are set as 0.7, 0.2, 0.15, 1.35, and 1.1,
respectively.
For the DTDS algorithm, five empirical parameters are used, including
A1, A2, A3, A4, and A5. As listed in the Table 1,
A1–A5 are set as 0.7, 0.2, 0.15, 1.35, and 1.1, respectively. A
cloud at time i is identified as being in the coupled state if the CBH is
less than [H(i-1)+0.2 km (A2)] and [LCL +0.7 km (A1)]. This
step moves 39.5 % of low-cloud cases to the category of decoupled
clouds. A cloud is also considered to be in a coupled state if the
CBH is coincident with the LCL within 0.15 km (A3),
and the CBH is less than [H(i-1)+0.7 km (A1)], where H(i-1) represents the
PBLH at time (i-1). This step further moves 17.8 % of the remaining
cases to the category of decoupled clouds.
The LCL is calculated from surface meteorological data (relative humidity,
temperature, pressure) at the SGP site based on an exact expression (Romps,
2017). Specifically, Romps (2017) proposed an exact, explicit, analytic
expression for LCL as a function of surface meteorology. Compared to the
previous approximate expressions, some of which may have an uncertainty in
the order of hundreds of meters, the Romps expression can be considered as
the precise value. The uncertainty of empirical vapor pressure data may lead
to a bias of ∼ 5 m (Romps, 2017), which may be neglected in
the analyses.
After determining the coupling or decoupling state of a cloud, we retrieve
H(i) (i.e., PBLH at time i) based on the cloud state. For
decoupled cases, we use the same strategy for a clear sky to retrieve the
PBLH. Based on the selection scheme in the DTDS algorithm, the LMP
below the CBH is selected as H(i). For coupled cases, we
jointly use CBH and CTH to determine PBLH. During the warm season, active
cumulus often occurs in the upper part of the PBL with strong surface
heating, so the CBH can be generally regarded as the PBLH (Stull, 1988;
Wallace and Hobbs, 2006). Under this condition, the CBH coincides with the
previous PBL top. Therefore, if [CTH≥PBLH30min+0.2 km (A2)], we set H(i)=A5CBH,
where PBLH30min is the average value of the PBLH within 30 min of the prior time i. Hence, A5 would be a critical parameter for the PBLH
estimation. On the other hand, if [CTH<PBLH30min+0.2 km (A2)], we set H(i) equal to the minimum between CTH and
the product A4× CBH. This step is designed for thin clouds or some
stratiform clouds. In particular, A5× CBH can be notably larger than the CTH
for a thin cloud. Under this situation, we tend to use CTH to denote the PBL
top. This step has little impact on the detection of surface–cloud coupling
but can ensure that the CTH of the coupled cloud is always higher than the
retrieved PBLH to fit the real situation.
After retrieving H(i), we consider that the cloud above the
PBLH is still coupled if [CBH<H(i)+0.2 km (A2)]. Moreover, we added an upper limit for all PBLH
retrievals. If [H(i)>LCL+0.7 km (A1)], we adjust H(i) as the maximum LMP below the LCL.
The new DTDS method combines lidar measurements and surface meteorological
observations and can simultaneously retrieve the PBLH and cloud states.
Selection of empirical parameters
The states of coupling and decoupling are diagnostic parameters rather than
explicit expressions. Similar to the other methods for retrieving PBLH
(e.g., Brooks, 2003; Liu and Liang, 2010), multiple empirical parameters are
used to determine PBLH. Table 1 lists the five empirical parameters in the
algorithm. These parameters are related with three factors, including LCL,
PBLH, and CBH. The sensitivity to the selection of these parameters is
presented. The detailed impacts of variations in these parameters on the
retrievals of cloud coupling and PBLH will be discussed in this section.
Note that we used the CTH and A4× CBH as the upper limits for PBLH
retrievals in the DTDS algorithm. For coupled cases, these two limits are
generally close to or above the position of the PBL top. Only 2 % (3 %)
of total cases meet the condition that the RS-derived PBLH is 0.25 km higher
than the CTH (A4× CBH). Section 4 presents the detailed relationships
between CBH, CTH, and PBLH. In the DTDS method, CTH serves as the upper
limit for PBLH under the condition of coupled shallow cumulus.
Similar to previous studies, we can also use the LCL as the standard to
identify coupled clouds (Dong et al., 2015; Zheng and Rosenfeld, 2015). We
assume a cloud is coupled if CBH-LCL<Δh. By using ∼ 7500 RS profiles, the cloud coupling state
derived from the virtual potential temperature method (Sect. 3.1) is
considered as the ground truth for evaluation. Figure 5a shows the
commission errors and omission errors for different criteria. Here, the
commission error is calculated as the percentage of decoupled clouds
misidentified as coupled clouds. The commission error can also be called a
“false positive”, as the former is a common term for describing the nature
of an error in identification. The omission error is calculated as the
percentage of coupled clouds that have not been identified under this
criterion. By using the LCL, we can obtain a relatively low commission error
if the criterion is less than 0.15 km and a relatively low omission error if
the criterion is greater than 0.7 km. Thus, we set A1 and A3 as
0.7 and 0.15 in the DTDS method to exclude and to select cases of coupled
clouds. We can also use the RS-derived PBLH as the criterion (Fig. 5b).
Commission errors and omission errors of coupled cloud
identifications (a) for different criteria for the lifted condensation level
(LCL) and (b) for different criteria for the planetary boundary layer height
(PBLH). “Criteria for LCL” means coupled clouds are identified if CBH-LCL< criteria for LCL. Similarly, “Criteria
for RS PBLH” means coupled clouds are identified if CBH - RS
PBLH < criteria for RS PBLH. The dashed red and blue lines indicate
the commission and omission errors, respectively, for the DTDS algorithm.
CBH stands for cloud-base height, and RS stands for radiosonde. By using
∼ 7500 RS profiles, the cloud coupling state derived from the
virtual potential temperature method (Sect. 3.1) is considered as the
ground truth for evaluation.
Despite the coarse temporal resolution, the RS-derived PBLH can be a good
criterion to use to distinguish between coupling and decoupling. If we
consider a coupled cloud as a cloud where CBH < RS-derived PBLH + 0.2 km, both commission and omission errors are ∼ 5 %.
Therefore, we primarily use [PBLH + 0.2 km (A2)] in the DTDS method to
identify coupled and decoupled regimes. As cloud can considerably
affect with lidar backscattering and generate large signal variations, we
jointly use lidar backscattering, the previous position of PBL top, and LCL
to determine the surface–cloud coupling and PBLH. In particular, the LCL
constraint in the algorithm notably reduces the absolute biases in PBLH
retrievals under cloudy conditions by 9.3 %.
Moreover, we test the sensitivity of selecting these empirical parameters.
Figure 6 presents the commission errors and omission errors in the
identifications of coupled clouds for selecting different values of
empirical parameters. Among these parameters, A2 is the critical one,
which would notably affect the identification results. In general, A2
determines the maximum differences between PBLH and CBH for coupled cases. If
[CBH - PBLH >A2], we consider the cloud is under the
decoupled state. Thus, the identification method is quite sensitive to
A2. Selecting a low value of A2 would neglect many coupled cases,
which leads to a high omission error. Meanwhile, selecting a high value of
A2 would misclassify many coupled cases, which leads to a high
commission error. After a trail and error, A2 is set as 0.2 km to
balance the omission and commission errors. The selections for other
parameters are not sensitive for the coupled cloud identifications. We can
choose them from a reasonable range.
Commission errors (red line) and omission errors (blue
line) of coupled cloud identifications for selecting different values of
empirical parameters (A1, A2, A3, A4, A5) in the
DTDS algorithm. Dashed black lines indicate the default values. For each test,
one parameter is variable, while other parameters are set as default values.
For identifications of cloud coupling, A2 is the critical parameter.
As a by-product of this method, we also pay attention to the PBLH
retrievals under cloudy conditions. Figure 7 presents the mean absolute
biases and correlation coefficients between PBLH derived from lidar and
radiosonde for selecting different values of empirical parameters. To match
the scope of this study, we only analyze the low-cloud conditions. For
retrieving PBLH under cloudy conditions, A2 is the critical parameter.
The variations in correlation coefficients under different values of
empirical parameters are small with a range of 0.81–0.82. However, the
absolute biases can considerably differ under different values of A5.
In general, A5 represents the ratio between CBH and PBLH under coupled
conditions. If A5 is above 1.1, PBLH retrievals under cloudy conditions
are overestimated. We set A5 as 1.1 to achieve a relatively low bias
and a relatively high correlation coefficient at the same time. For other
parameters, the selections from reasonable ranges would not notably affect
the PBLH retrievals.
Red lines indicate the mean absolute biases between PBLH
derived from lidar and radiosonde for selecting different values of
empirical parameters (A1, A2, A3, A4, A5) in the
DTDS algorithm. Here, we only analyze the low-cloud cases. Blue lines
indicate the corresponding correlation coefficients between PBLH derived
from lidar and radiosonde. Dashed black lines indicate the default values. For
each test, one parameter is variable, while other parameters are set as
default values. For PBLH retrievals under cloudy conditions, A5 is the
critical parameter.
In short, selections of these empirical parameters are based on the overall
relationship between cloud and PBL under the coupled and decoupled states.
In our method, the selection of A2 is critical for the identifications
of coupled clouds, while the selection of A5 is critical for the PBLH
retrievals under cloudy conditions. The selections of other parameters are
not sensitive.
Results
Figure 8 illustrates four examples of PBLH retrievals and cloud states
derived from the DTDS algorithm for 27 October 2011, 31 July 2002, 19 March 2000, and 1 May 2012. Figure 8a depicts coupled shallow cumulus occurring at
noontime at the PBL top. With a weak surface flux of ∼ 200 W m-2, this shallow cumulus cloud appeared for less than an hour. Figure 8b shows a developed coupled cumulus cloud. With a strong surface flux of
∼ 500 W m-2, this coupled cloud continuously developed
during the daytime. Figure 8c presents the case of a daylong coupled cloud.
After the passage of a frontal system that day, stratocumulus occurred
during the morning with a cloud thickness of 0.5 km. Through the development
of the PBL, the thick stratocumulus cloud was broken up by the strong
turbulences, transforming into shallow cumulus clouds. Figure 8d shows the
case of an active coupled cloud, which is generally associated with a large
amount of convective available potential energy. Even though coupled clouds
can differ in appearance and variability throughout the day, the common
feature is the coherent variation between the cloud base and the PBL top.
The LCL is a relevant parameter and can differ from the PBLH and the CBH for
some coupled cases (e.g., Fig. 8b–c).
Daily backscatter profiles: (a) short-lived coupled
cloud, (b) developed coupled cloud, (c) daylong coupled cloud, and (d) active coupled cloud. Backscatter is normalized to a range of 0–1 in
arbitrary units. Red dots and blue dots indicate cloud-top heights (CTHs)
and cloud-base heights (CBHs) of coupled clouds. Grey dots mark CBHs for
decoupled clouds. Black lines and green stars mark the planetary boundary
layer height (PBLH) retrieved from the DTDS algorithm and from radiosonde
(RS) soundings, respectively. Dashed white lines represent lifted
condensation levels (LCLs).
The identification accuracy, or disparity between different methods, is
evaluated in terms of the selected criteria, for which the identification
method based on Δθv is regarded as the
“truth”, as described in Sect. 3.1. Hereafter, all results are analyzed
for the period of 10:00–19:00 LT, so early-morning data are not used. The
commission error is 10.1 %, and the omission error is 6.8 % for the DTDS
method. Note that lidar-based PBLH methods generally suffer from relatively
low accuracy under stable atmospheric conditions. Following Liu and Liang (2010), we identified stable PBLs from RS measurements. Since coupled clouds
are driven by relatively strong buoyancy fluxes, only 1 % of total cases
of coupled clouds occurred under stable PBL conditions during the study
period (07:00–19:00 LT). Therefore, the relatively low accuracy for stable
PBLs is not a major problem in this study.
Figure 5 also compares the accuracy between the DTDS and LCL methods. Based
on the LCL alone, we cannot choose an appropriate criterion to achieve a
lower commission error and omission error simultaneously. Thus, we do not
use the LCL as the single standard to detect the coupling and decoupling of
low clouds in our study. As diagnostic parameters, different methods
inevitably produce different results regarding coupling and decoupling.
Although we consider the method based on Δθv as the standard, it still suffers from uncertainties arising from
balloon drifting. From this perspective, it is hard to conclude which method
is the best. Since it determines the PBLH based on aerosol backscattering,
the lidar-based method may be more representative of the coupling between a
cloud and the aerosol layer near the surface when clear skies occur, at
least during a short window of time.
Figure 9a–b present the occurrence frequencies of the CBH and the CTH at
different heights. Despite the same variation ranges, clouds are mostly
coupled if the CBH is lower than 1 km, while decoupled clouds dominate if
the CBH is higher than 3 km. Figure 9c–d show the changes in the coupled
fraction (ratio of coupled cases to total cases) with different CBHs and
CTHs. The coupled fraction is about 90 % if the CBH is lower than 1 km and
decreases to 2 % for CBHs above 3 km. Although the CBHs for coupled cases
are generally less than 3 km, CTHs for coupled cases can be much higher.
Coupled clouds still account for around 10 % of the cases with CTHs above
6 km.
The height-dependent occurrence frequencies of (a) the
cloud-base height (CBH) and (b) the cloud-top height (CTH) for coupled
clouds (red bars) and decoupled clouds (grey bars). The relative occurrence
frequencies of (c) the CBH and (d) the CTH for coupled clouds (red area) and decoupled clouds (grey area).
The relationships between (a) LCL and CBH, (b) CBH and
RS-derived PBLH, (c) CTH and RS-derived PBLH for coupled clouds, and (d) DTDS-derived PBLH and RS-derived PBLH. Panels (e)–(h) are similar to panels
(a)–(d) but for decoupled clouds. Black lines represent the linear
regressions. The linear fitting functions, correlation coefficients (R), and
sampling numbers (N) are given in each panel.
Figure 10 shows scatter plots between CBH, CTH, PBLH, and LCL for coupled
and decoupled clouds. For coupled clouds, there is a generally strong
correlation between CBH, LCL, and PBLH, contrary to the weak relationships
of decoupled cases. The relationship between CTH and RS-derived PBLH is
complicated. For shallow cumulus clouds, their tops can be considered as PBL
tops for the coupled state, while the cloud top is considerably above the
position of the PBL top for active cumulus clouds. We also note that the
accuracy of CTH retrievals is generally lower than the accuracy of CBH
retrievals (Clothiaux et al., 2000). As CTH is not a criterion for cloud
coupling, the accuracy of CTH would not affect the identification of coupled
cloud but may affect the PBLH retrievals for the coupled cloud cases.
Meanwhile, despite the laser-based detection of CBH being considered the
standard method (Platt et al., 1994; Clothiaux et al., 2000; Lim et al.,
2019), the CBH retrievals from ceilometer or lidar still bear some
uncertainties, which can potentially lead to a mean bias of 0.1 km (Silber et
al., 2018). In our method, a systematic increase of 0.1 km in the CBH can
lead to an increase of 2.1 % in omission errors and a decrease of 1 % in
commission errors.
After identifying the coupling state of clouds, it is feasible to retrieve
the PBLH under cloudy conditions. In particular, the DTDS-derived PBLH needs
to resort to the cloud position for coupled cloud cases. For decoupled cloud
cases, on the other hand, the PBLH below clouds is sought to avoid cloud
interference. For coupled clouds, DTDS-derived PBLHs show a strong
correlation with RS-derived PBLHs with a correlation coefficient (R) of
∼ 0.9 (Fig. 10d). For decoupled cases, the correlation
between DTDS-derived PBLHs and RS-derived PBLHs is generally good (R=0.73) but worse than the correlation for coupled cases (Fig. 10h). As
pointed out in previous studies (Chu et al., 2019; Hageli et al., 2000;
Lewis et al., 2013; Su et al., 2017b), it has been a persistent problem to
retrieve the PBLH under cloudy conditions since the strong backscattering
and step signals from cloud interference would be excluded to avoid
interfering with the retrievals. The PBLH determined by our method under a
cloudy condition is much more reasonable. Moreover, due to the
different definitions of the PBLH and aerosol stratification within the PBL,
there are always considerable differences between lidar- and RS-derived
PBLHs, which cannot be eliminated by a specific algorithm (Chu et al., 2019;
Su et al., 2020).
Summary
In this study, we proposed a novel method for distinguishing between coupled
and decoupled low clouds over land. Based on the understanding of PBL
processes and quantitative analyses, we developed a lidar-based method
(DTDS) to identify the coupling state of low clouds over the SGP site. In
practice, we identified a coupled cloud when the position of the cloud base
was generally close to or lower than the previous position of the PBL top,
with the LCL serving as an additional restriction. Compared to using the LCL
alone, the coupled states identified by the DTDS method show better
consistency with the results derived from radiosondes, with about 10 %
differences between the lidar-based retrievals and radiosonde results.
Not only the coupled state but also the PBLH under
cloudy conditions is retrieved by the method. A long-lasting problem with lidar retrieval of PBLH is
either incapability of retrieval or large uncertainties induced by the
occurrence of low clouds (e.g., Chu et al., 2019; Hageli et al., 2000; Lewis
et al., 2013); we address this issue by separately considering the coupled
and decoupled state of low clouds. Specifically, in coupled conditions, the
position of the coupled cloud serves as a good reference for identifying the
PBLH. In decoupled conditions, the large backscatter and step signals from
clouds would be excluded to avoid interfering with the retrievals. With our
method, cloudy conditions are well handled.
With the new method, we study the difference of cloud–PBL interactions in
coupled and decoupled conditions. In contrast to the sensitive responses of
coupled clouds to changes in the PBLH and buoyancy, the decoupled clouds and
the PBLH are weakly related. Due to their different relationships with the
PBL, a robust differentiation between the coupled and decoupled low clouds
is critical for further investigating the coupled land–atmosphere system and
aerosol–cloud interactions. Our methodology paves a solid ground for such
pursuits.
Data availability
All these datasets are publicly available at the ARM archive https://adc.arm.gov/discovery/#/results/site_code::sgp (ARM Data Center, 2021).
The products developed in this study, i.e., cloud states and the PBLH, are
currently available upon request from the lead author (tianning@umd.edu) and are expected to be added to the ARM archive in the
near future.
Author contributions
TS, YZ, and ZL conceptualized this study. TS carried out the
analysis, with comments from other co-authors. TS, YZ, and ZL
interpreted the data and wrote the manuscript.
Competing interests
The contact author has declared that neither they nor their co-authors have any competing interests.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
We acknowledge the provision of radiosonde, MPL data, surface
meteorological data, and cloud products by the U.S. Department of Energy's
ARM program. We thank the two anonymous reviewers for their comments.
Financial support
This research has been supported by the U.S. Department of Energy (grant no. DE-SC0018996) and the National Science Foundation (grant nos. AGS2126098 and AGS1837811).
Review statement
This paper was edited by Yun Qian and reviewed by Xiquan Dong and two anonymous referees.
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