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**Atmospheric Measurement Techniques**
An interactive open-access journal of the European Geosciences Union

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**Research article**
21 Dec 2020

**Research article** | 21 Dec 2020

Integrated System for Atmospheric Boundary Layer Height Estimation (ISABLE) using a ceilometer and microwave radiometer

^{1}Research Center for Atmospheric Environment, Hankuk University of Foreign Studies, Yongin, Korea^{2}School of Earth and Environmental Sciences, Seoul National University, Seoul, Korea^{3}Department of Climate and Environment, Sejong University, Seoul, Korea^{4}Climate Change and Environmental Research Center, Sejong University, Seoul, Korea

^{1}Research Center for Atmospheric Environment, Hankuk University of Foreign Studies, Yongin, Korea^{2}School of Earth and Environmental Sciences, Seoul National University, Seoul, Korea^{3}Department of Climate and Environment, Sejong University, Seoul, Korea^{4}Climate Change and Environmental Research Center, Sejong University, Seoul, Korea

**Correspondence**: Moon-Soo Park (ngeograph2@gmail.com, moonsoo@sejong.ac.kr)

**Correspondence**: Moon-Soo Park (ngeograph2@gmail.com, moonsoo@sejong.ac.kr)

Abstract

Back to toptopAccurate boundary layer structure and height are critical
in the analysis of the features of air pollutants and local circulation.
Although surface-based remote sensing instruments provide a high temporal
resolution of the boundary layer structure, there are numerous uncertainties
in terms of the accurate determination of the atmospheric boundary layer
heights (ABLHs). In this study, an algorithm for an integrated system for
ABLH estimation (ISABLE) was developed and applied to the vertical profile
data obtained using a ceilometer and a microwave radiometer in Seoul city,
Korea. A maximum of 19 ABLHs were estimated via the conventional
time-variance, gradient, wavelet, and clustering methods using the
backscatter coefficient from the ceilometer. Meanwhile, several stable
boundary layer heights were extracted through near-surface inversion and
environmental lapse rate methods using the potential temperature from the
microwave radiometer. The ISABLE algorithm can find an optimal ABLH from
post-processing, such as *k*-means clustering and density-based spatial
clustering of applications with noise (DBSCAN) techniques. It was found that
the ABLH determined using ISABLE exhibited more significant correlation
coefficients and smaller mean bias and root mean square error between the
radiosonde-derived ABLHs than those obtained using the most conventional
methods. Clear skies exhibited higher daytime ABLH than cloudy skies, and
the daily maximum ABLH was recorded in summer because of the more intense
radiation. The ABLHs estimated by ISABLE are expected to contribute to the
parameterization of vertical diffusion in the atmospheric boundary layer.

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Min, J.-S., Park, M.-S., Chae, J.-H., and Kang, M.: Integrated System for Atmospheric Boundary Layer Height Estimation (ISABLE) using a ceilometer and microwave radiometer, Atmos. Meas. Tech., 13, 6965–6987, https://doi.org/10.5194/amt-13-6965-2020, 2020.

1 Introduction

Back to toptopThe atmospheric boundary layer (ABL) is the lowest part of the troposphere, which is directly influenced by the surface of the earth (Garratt, 1994). The ABL is repeated in a daily cycle with a well-mixed layer (ML) or a convective boundary layer (CBL) in the daytime and a stable boundary layer (SBL) at nighttime. The former mixes air vertically via convection which results from surface heating or mechanical turbulence due to vertical wind shear, while the latter appears in the lower ABL, and a residual layer (RL) remains in the upper ABL without any external force. The ML is one of the essential meteorological factors that affect the vertical mixing of air pollutants. In the presence of a well-developed SBL at night, air pollutants near the surface tend to be trapped inside the SBL because of the low vertical diffusivity, and their concentrations could increase sharply (Stull, 1988; Emeis and Schäfer, 2006). In this study, the ABL is confined as a single layer, which is consisted of a ML or a SBL to exclude its complexity.

The ABL height (ABLH) has been primarily utilized as a meteorological factor in estimating the vertical diffusivity near the surface and air pollutant concentration (Stull, 1988; Garratt, 1993). Many previous studies have developed various methodologies for determining ABLH, including only a ML height (MLH) or a SBL height (SBLH). ABLH has traditionally been determined using in situ radiosonde (RS) data. The parcel method using the vertical profile of virtual potential temperature (Holzworth, 1964; Seibert et al., 2000) and the gradient method using the vertical gradient of the virtual potential temperature or mixing ratio have been extensively used (Oke, 1987; Stull, 1988). Alternatively, ABLH can be determined using the bulk Richardson number, which includes the thermal turbulence term generated by surface heating as well as the mechanical turbulence term arising from the vertical wind shear (Vogelezang and Holtslag, 1996; Zilitinkevich and Baklanov, 2002; Zhang et al., 2014). The ABLH estimated using in situ RS sounding has widely been considered as a true reference value in many previous studies (e.g., Eresmaa et al., 2006; Basha and Ratnam, 2009; and Collaud Coen et al., 2014). However, there are still some limitations in terms of clearly distinguishing ABLH from radiosonde observations (Seibert et al., 2000). ABLH tends to be determined as similar values irrespective of the methodologies used under a well-developed convective boundary layer (BL) during daytime and SBL at night, while it gives different values with respect to methodologies under a cloudy sky and in the presence of complex local circulations. Furthermore, the major drawback of RS sounding data their its coarse temporal resolution ranging from 6 to 12 h (Schween et al., 2014).

During the past two decades, several researchers have determined ABLH using
surface-based remote sensing instruments to overcome the coarse resolution
of RS data. An aerosol lidar and a lidar-type ceilometer (hereinafter
referred to as merely ceilometer) measure the intensity of signals which
have been backscattered by atmospheric materials, such as aerosols, clouds,
and mineral dust. The intensity of the backscattered signal at each level
can be converted to the backscattering coefficient at the level with several
assumptions. The measured backscattering coefficient can be used to analyze
the features of the vertical distribution of aerosols, while the ABLH can be
determined through the separation of aerosol layers. In a ML, the vertical
mixing of aerosol particles is active and the backscattering coefficient is
relatively homogeneous, whereas it decreases sharply above the MLH. Based on
the foregoing features, the gradient method designates the altitude with the
maximum vertical gradient of the backscattering coefficient as the ABLH (e.g.,
Flamant et al., 1997; Sicard et al., 2005; Lammert and Bösenberg, 2006;
Münkel et al., 2007; Emeis et al., 2008; Summa et al., 2013; and Schween
et al., 2014). The wavelet method determines ABLH as the altitude at which
the wavelet covariance coefficient is at its maximum (e.g., Gamage and
Hageberg, 1993; Cohn and Angevine, 2000; Brooks, 2003; and Morille et al.,
2007). Menut et al. (1999) analyzed the ABL structure using the inflection
point method (second derivative method) and centroid method (time-variance
method) for the purpose of understanding the chemical and physical processes
involved in pollution events in Paris. The growth and decline of the ABLH are
repetitive due to the heating and cooling of the surface. As a result, the
vertical aerosol distribution in the aerosol layer changes with time, and
the ABLH can therefore be determined using the time variance of the aerosol
temporal distribution. Toledo et al. (2014) and Caicedo et al. (2017) determined ABLH as a classification of the distribution of the backscattering coefficient value
whose vertical profile rapidly decreases or increases using *k*-means
clustering. Moreover, the ABLH was estimated using an extended Kalman filter
(EKF) (Lange et al., 2014, 2015; Saeed et al., 2016). The EKF
technique can be used in low signal-to-noise ratio (SNR) atmospheric
scenarios without long-time averaging and range smoothing except for low SNR
(Dang et al., 2019). Previous studies integrated
multiple methodologies; i.e., Pal et al. (2013) combined the gradient method
based on a first derivative of the Gaussian wavelet covariance analysis and
the spatial/temporal variance method; and Hicks et al. (2015) combined the
error function-ideal profile method and wavelet covariance transform method
to estimate ABLH.

Even though several methods have been developed, no consensus on a specific algorithm has been reached (Schween et al., 2014). Different methodologies provide different ABLHs with respect to weather conditions and phenomena. Under complicated ABL structures (e.g., presence of multiple layers of aerosols), the ABLH could be determined as different values according to the methodology used. Based on the foregoing methodologies, it is difficult to produce a single consistent ABLH with the use of ABLHs using the previous methods. Therefore, this study aims to develop an integrated system for ABLH estimation (ISABLE) to determine a single optimized ABLH with statistically significant results from several ABLH candidates. Furthermore, seasonal and diurnal variation of the ABLH in an urban area in Seoul, Korea, shall be investigated with the use of long-term ABLHs estimated using ISABLE.

Section 2 introduces the observation station and instruments used in this study. Section 3 describes the used data and pre-processing. Section 4 describes the ABLH estimation methods and ISABLE algorithm. In Sect. 5, the ABLH estimated using available methods is compared with the radiosonde-derived ABLH, and the seasonal and diurnal variation features are described. Finally, the summary and discussion on the findings are presented in Sect. 6.

2 Site and instrumentation

Back to toptopWe used a ceilometer, a microwave radiometer (MWR), and a net radiometer
installed at the Jungnang Station (127.08^{∘} E, 37.59^{∘} N, 45 m; Fig. 1), a supersite of UMS-Seoul (urban meteorological
observation system network in the Seoul Metropolitan Area; Park et al.,
2017). The station is located in Seoul city, Korea, and the surrounding
buildings form an environment that can be classified as a dense urban
residential area with homogeneous heights (Park, 2018). The location is
classified as both urban climate zone 2 (UCZ-2; intensely developed high density) according to
the urban climate zone classification (Oke, 2006) and local climate zone 2E (LCZ-2E; compact mid-rise,
bare rock, or paved) according to the local climate zone classification (Stewart and Oke,
2012). Seoul city is affected by local circulation, such as sea–land and
mountain–valley breezes, due to the Yellow Sea and mountainous terrain
(Park and Chae, 2018).

The ceilometer (model CL51, manufacturer Vaisala) produces a real-time vertical profile of backscattering coefficients each minute at intervals of 10 up to 15 400 m above ground level using a laser (InGaAs diode laser) with a wavelength of 910 nm (Vaisala, 2010). It also measures the cloud base heights of three layers up to 13 000 m and the 5 min mean cloud cover at intervals of 1 min.

The MWR (model HATPRO-G4, manufacturer RPG) observes atmospheric attenuation and brightness temperature from electromagnetic radiation emitted from the atmosphere using 14 channels (22 to 31 GHz, 7 water vapor channels; 51 to 58 GHz, 7 temperature channels) (RPG, 2015). The measured atmospheric attenuation and brightness temperature were converted to a vertical profile of atmospheric temperature, relative humidity, and liquid water path using a neural network model. The MWR produces two types of temperature profiles, i.e., zenith measurements for the entire troposphere (0 to 10 km) and elevation scanning that provides an enhanced vertical resolution within the boundary layer (0 to 2 km). The temperature profiles of the two types are merged into a single profile. The vertical resolution is denser in the lower layer; however, it decreases with regard to height (30 m up to 1.2 km, 200 m up to 5 km, and 400 m up to 10 km), and a profile is produced every 1 min.

The net radiation obtained via the net radiometer (model CNR 4, manufacturer Kipp & Zonen) was used to classify ABLH as daytime and nighttime values (Kipp and Zonen, 2014).

3 Data and pre-processing

Back to toptopVertical profiles observed using RS sounding are widely used in verifying surface-based remote sensing instruments because it directly observes the temperature, relative humidity (or mixing ratio), wind direction and speed, and pressure with height. The vertical profile of the potential temperature and virtual potential temperature can be calculated using the observed meteorological variables.

In order to analyze the structure of the atmospheric boundary layer in urban areas, 171 RS sounding data were acquired during the four intensive observation campaigns at Jungnang Station. Because of 23 precipitation cases, 148 RS soundings were used to estimate the ABLH (Table 1). Weather conditions were divided into two categories, i.e., clear sky (cloud cover (CC) ≤30 %) and cloudy sky (CC ≥80 %) for the purpose of investigating the features of the ABLH with respect to weather.

The backscattering coefficients observed using the ceilometer contain noise, especially near-range artifacts in the lower atmosphere proximate to the lens of the instrument, as well as atmospheric scattering due to intense daytime solar radiation, clouds, and precipitation. The noise can be reduced through the temporal and spatial moving averages of the backscattering coefficients, and they can maintain the vertical and temporal characteristics of backscattering coefficients. Moving average for 10 range gates (100 m) and 10 time steps (10 min) was conducted.

The SNR is introduced to prevent noise from causing the estimation of the ABLH at unreliable heights (de Haij et al., 2006; Heese et al., 2010; Kotthaus et
al., 2016). Generally, backscattering coefficients at a higher level than
the SNR stop level (*h*_{SNR}), the first altitude at which the SNR is less
than one, are not used. The SNR at height *z* is calculated using the
formulas introduced by de Haij et al. (2007), as follows:

$$\begin{array}{}\text{(1)}& {\displaystyle}\mathrm{BN}={\displaystyle \frac{\mathrm{1}}{N}}{\sum}_{z=\mathrm{12}\phantom{\rule{0.125em}{0ex}}\text{km}}^{\mathrm{15}\phantom{\rule{0.125em}{0ex}}\text{km}}\mathit{\beta}\left(z\right),\text{(2)}& {\displaystyle}{\mathit{\sigma}}_{{\mathit{\beta}}_{\mathrm{SNR}}}=\sqrt{{\displaystyle \frac{\mathrm{1}}{N}}{\sum}_{z=\mathrm{12}\phantom{\rule{0.125em}{0ex}}\text{km}}^{\mathrm{15}\phantom{\rule{0.125em}{0ex}}\text{km}}{\left(\mathit{\beta}\left(z\right)-\mathrm{BN}\right)}^{\mathrm{2}}},\text{(3)}& {\displaystyle}\mathrm{SNR}\left(z\right)={\displaystyle \frac{\mathit{\beta}\left(z\right)}{\mathrm{BN}+{\mathit{\sigma}}_{{\mathit{\beta}}_{\mathrm{SNR}}}}},\end{array}$$

where *z* is the height; *β*(*z*) pertains to the backscattering
coefficient at *z*; BN refers to background noise, which is calculated as
the mean of *β*(*z*) from 12 to 15 km; and *N* denotes the number of levels
between 12 and 15 km (*N*=300). ${\mathit{\sigma}}_{{\mathit{\beta}}_{\mathrm{SNR}}}$ is the standard
deviation of *β*(*z*) at altitudes between 12 and 15 km. If the upper
layer contains much noise, the SNR of the lower layer becomes smaller, and
if the lower air is clean, *h*_{SNR} can be distributed in the lowest layer.
When the SNR is being calculated, heights above 120 m are used to eliminate
the discontinuity due to the instrumental limitation in the lower
atmosphere.

Figure 2 shows the comparison of the backscattering coefficients, *h*_{SNR},
before and after pre-processing. Strong noises with random backscattering
coefficients were found at heights above 2500 m throughout the day (Fig. 2a). When the shortwave radiation was intense during the daytime, the noise
was mainly due to sunlit scattering and low SNR values. Especially in the
presence of daytime clouds (14:00 to 16:00 LST), the SNR decreased and
the *h*_{SNR} became lower. Furthermore, the backscattering coefficient is
often found to decrease rapidly around 120 and 400 to 500 m high during
the daytime with intense solar radiation. It was considered an error in the
mechanical instruments or artifacts resulting from the surrounding
environment. After pre-processing, noise signals at higher altitude have
decreased and maintained their main features (Fig. 2b). But
vertical broadening at heights with intense signals was shown as a result of
the moving average. And the mean *h*_{SNR} became 331 m higher than before.
The pre-processing made the values much more stable, although under poor
circumstances with strong solar radiation and daytime clouds. Also,
artifacts at high altitudes were mitigated.

The temperature of the MWR and the humidity depend on the generalized
atmospheric conditions because they are estimated using an artificial neural
network (Collaud Coen et al., 2014). In order to retrieve temperature and
humidity with an artificial neural network, a training data set is required.
The variables were retrieved using software embedded in the MWR. Given that
the neural network cannot guarantee the accuracy of the retrieved data
beyond the range of the training data set, the retrieved data include
uncertainties. Nevertheless, the SBL formed via surface cooling during
nighttime is determined only by the thermal parameter. Cimini et al. (2006)
found that most methods had the best performances near the surface and that
the bias and standard deviation increased with height. It was also
determined that the bias in temperature retrieval is acceptable (*<*0.5 K) in most methods. The potential temperature calculated by the MWR was
used to determine the nocturnal SBLH.

The potential temperature was computed using the vertical profiles of
temperature, humidity, and pressure, which were calculated using the ideal
gas equation with the assumption of the hydrostatic equation (Holton and
Hakim, 2012). The vertical pressure *p*_{2} at *z*_{2} is calculated as
follows:

$$\begin{array}{}\text{(4)}& {p}_{\mathrm{2}}={p}_{\mathrm{1}}\mathrm{exp}\left(-g{\displaystyle \frac{{z}_{\mathrm{2}}-{z}_{\mathrm{1}}}{R{\stackrel{\mathrm{\u203e}}{T}}_{z}}}\right),\end{array}$$

where *p*_{1} is the air pressure *z*_{1} below the *z*_{2}, ${\stackrel{\mathrm{\u203e}}{T}}_{z}$ pertains to the mean temperature between *z*_{1} and *z*_{2}, *R*
refers to the gas constant for air (287 J kg^{−1} K^{−1}), and *g*
denotes the gravitational acceleration. The potential temperature is
calculated using the following equation:

$$\begin{array}{}\text{(5)}& {\mathit{\theta}}_{z}={T}_{z}{\left({\displaystyle \frac{{p}_{\mathrm{0}}}{{p}_{z}}}\right)}^{{\scriptscriptstyle \frac{R}{{c}_{\mathrm{p}}}}},\end{array}$$

where *θ*_{z} is the potential temperature at height *z*, and *p*_{0}
and *p*_{z} are the air pressures at the 1000 hPa level and height *z*,
respectively. Moreover, *c*_{p} pertains to the specific heat of dry air at
constant pressure (1004 J kg^{−1} K^{−1}).

4 Methodology

Back to toptopA parcel method, a gradient method, and a bulk Richardson number method can
be considered to estimate the ABLH using the sounding data obtained via
radiosonde. Among them, the bulk Richardson number method was used to
determine the reference ABLH. The bulk Richardson number (*R**i*_{b}) is
defined as the ratio of buoyancy forcing vis-à-vis mechanical forcing by
vertical wind shear:

$$\begin{array}{}\text{(6)}& R{i}_{\mathrm{b}}={\displaystyle \frac{\left(g/\phantom{g{\mathit{\theta}}_{\mathrm{0}}}{\mathit{\theta}}_{\mathrm{0}}\right)({\mathit{\theta}}_{z}-{\mathit{\theta}}_{\mathrm{0}})}{{{u}_{z}}^{\mathrm{2}}+{{v}_{z}}^{\mathrm{2}}}}z,\end{array}$$

where *z* is the height, *u*_{z} and *v*_{z} are the west–east and
south–north wind speeds at *z*, respectively, *θ*_{0} pertains to the
surface potential temperature, and *θ*_{z} refers to the potential
temperature at *z*. According to Stull (1988), laboratory research suggested
that turbulence occurs when *R**i* is smaller than the critical *R**i*,
*R**i*_{c}. Many previous studies have reported *R**i*_{c} values between 0.1
and 1.0 (e.g., Holtslag and Boville, 1993; Jeričević and Grisogono,
2006; and Esau and Zilitinkevich, 2010). The values of 0.25 and 0.5 were the
most utilized *R**i*_{c} (Zhang et al., 2014). In this study, we used a
value of 0.5 for the *R**i*_{c}.

In order to determine the ABLH in the case of stable stratification, Collaud
Coen et al. (2014) determined the nocturnal SBLH using the temperature and
potential temperature profiles from the radiosonde and MWR. SBLH is
determined as a surface-based temperature inversion (SBI) height at which
the temperature decreases with height (Δ*T*∕Δ*z**<*0) for the first
time (Stull, 1988; Seidel et al., 2010). Actually, it is not easy to detect
a SBLH using RS sounding. This is because the vertical variations of the
temperature and the wind in the RL can be more substantial compared to those
in the SBL. Thus, the SBLH has been generally estimated using the
methodologies with temperature inversion. In this study, the ABLHs were
estimated with *R**i*_{b} in both daytime and nighttime, and if a SBL was
formed at nighttime, the SBLHs were determined via the SBI method.
Nonetheless, the top of the RL is still determined as a SBLH due to the large
variation of temperature and turbulence (Collaud Coen et al., 2014).

The time-variance method (VAR) computes for the standard deviation (${\mathit{\sigma}}_{{\mathit{\beta}}_{(z,t)}}$) of the backscattering coefficient profile measured by the ceilometer for 10 min using Eq. (7).

$$\begin{array}{}\text{(7)}& {\displaystyle}{\mathit{\sigma}}_{{\mathit{\beta}}_{\mathrm{VAR}}}=\sqrt{{\displaystyle \frac{\mathrm{1}}{N}}{\sum}_{t=\mathrm{1}}^{N}{\left(\mathit{\beta}(z,t)-\stackrel{\mathrm{\u203e}}{\mathit{\beta}(z,t)}\right)}^{\mathrm{2}}},\text{(8)}& {\displaystyle}{h}_{\mathrm{VAR}}=\mathrm{max}\left({\mathit{\sigma}}_{{\mathit{\beta}}_{\mathrm{VAR}}}\right),z\mathit{<}{h}_{\mathrm{SNR}},\end{array}$$

where *β*(*z*,*t*) is the backscattering coefficient profile at time *t*,
$\stackrel{\mathrm{\u203e}}{\mathit{\beta}(z,t)}$ pertains to the 10 min mean backscattering
coefficient, and *N* refers to the number of profiles (in this study,
*N*=10). ${\mathit{\sigma}}_{{\mathit{\beta}}_{\mathrm{VAR}}}$ represents the peak at high
temporal variability, and thus the ABLH estimated by VAR (*h*_{VAR}) is
determined as the height at which ${\mathit{\sigma}}_{{\mathit{\beta}}_{\mathrm{VAR}}}$ shows a maximum
value, which is less than *h*_{SNR} (1480 m). The ${\mathit{\sigma}}_{{\mathit{\beta}}_{\mathrm{VAR}}}$
profile was smoothed using a local quadratic polynomial regression
(Cleveland and Loader, 1996) to eliminate spurious variance peaks at
small-scale fluctuations. Nevertheless, *σ*_{β(z,t)} contains a
spurious peak above *h*_{SNR} and gradually increases with height. For the
foregoing reasons, *h*_{VAR} was calculated only below *h*_{SNR}.

Figure 3a shows the profiles of the ${\mathit{\sigma}}_{{\mathit{\beta}}_{\mathrm{VAR}}}$ (red line),
$\stackrel{\mathrm{\u203e}}{\mathit{\beta}(z,t)}$ (black line), and *β*(*z*,*t*) at intervals of 1 min (dashed gray line) for 10:50 to 11:00 LST on 23 September 2016, and the
ABLH was determined by VAR (*h*_{VAR}=670 m).

The gradient method is one of the most commonly used methodologies for estimating ABLH. The maximum negative peak of the first derivative with respect to the height of the backscattering coefficient from the ceilometer was determined as the ABLH. Generally, the first derivative (GM: gradient method), second derivative (IPM: inflection point method), and logarithmic derivative (LGM: logarithmic gradient method) are used, and the equations are shown below:

$$\begin{array}{}\text{(9)}& {\displaystyle}{h}_{\mathrm{GM}}=\mathrm{min}\left({\displaystyle \frac{\partial \mathit{\beta}\left(z\right)}{\partial z}}\right),\text{(10)}& {\displaystyle}{h}_{\mathrm{IPM}}=\mathrm{min}\left({\displaystyle \frac{{\partial}^{\mathrm{2}}\mathit{\beta}\left(z\right)}{\partial {z}^{\mathrm{2}}}}\right),\text{(11)}& {\displaystyle}{h}_{\mathrm{LGM}}=\mathrm{min}\left({\displaystyle \frac{\partial \mathrm{ln}\mathit{\beta}\left(z\right)}{\partial z}}\right).\end{array}$$

Figure 3b shows the results of the gradient methods corresponding to 11:00 LST on 23 September 2016. The bold solid line is a smoothed *β*(*z*)
profile, while the GM, IPM, and LGM results are represented by the solid,
dotted, and dash-dotted lines, respectively. *h*_{GM}, *h*_{IPM}, and
*h*_{LGM} indicate ABLH with a maximum negative gradient for each method.
The value of *h*_{GM} (790 m) is slightly higher than that of *h*_{IPM} (690 m) and lower than that of *h*_{LGM} (1580 m). The fact that *h*_{GM} is
slightly higher than *h*_{IPM} and lower than *h*_{LGM} is consistent with
the findings of previous studies (e.g., Emeis et al., 2008). The
second-largest negative (800 m) in the LGM was similar to *h*_{GM}, and the
second-largest negative in GM (1570 m) was also similar to the *h*_{LGM}
height. The *h*_{IPM} is similar to *h*_{VAR} (670 m), and both are located
at an altitude where *β*(*z*) begins to decrease sharply. Notwithstanding
that the altitude at which the maximum negative gradient for each method can
be different, they can be similar to the altitude corresponding to the
second peaks for other methods.

The wavelet covariance transform method (WAV) is also one of the most commonly used methods. The WAV uses the Haar step function, which is defined as follows:

$$\begin{array}{}\text{(12)}& h\left({\displaystyle \frac{z-b}{a}}\right)=\left\{\begin{array}{l}+\mathrm{1}:b-\frac{a}{\mathrm{2}}\le z\le b\\ -\mathrm{1}:b\le z\le b+\frac{a}{\mathrm{2}}\\ \mathrm{0}:\phantom{\rule{0.25em}{0ex}}\mathrm{elsewhere}\end{array}\right.,\end{array}$$

where *b* is the translation of the function (the location at which the function is centered), and *a* pertains to the dilation of the function (the spatial extent). The
covariance transform of the Haar function, *W*_{β}, is defined as
follows:

$$\begin{array}{}\text{(13)}& {\displaystyle}{W}_{\mathit{\beta}}(a,b)={\displaystyle \frac{\mathrm{1}}{a}}{\int}_{{z}_{\mathrm{b}}}^{{z}_{\mathrm{t}}}\mathit{\beta}\left(z\right)h\left({\displaystyle \frac{z-b}{a}}\right)\mathrm{d}z,\text{(14)}& {\displaystyle}{h}_{\mathrm{WAV}}=\mathrm{max}\left({W}_{\mathit{\beta}}\right(a,b\left)\right),\end{array}$$

where *z*_{b} and *z*_{t} are the bottom and top heights of the profile,
respectively. The altitude with the maximum value of *W*_{β}(*a*,*b*) is
determined using ABLH (*h*_{WAV}). In this study, *a* is set to 24 dilations at
intervals of 15 m from 15 to 360 m, while *b* is set to 10 m step size from
60 to 3000 m (de Haij et al., 2006, 2007).

Davis et al. (2000) illustrated the importance of determining the dilation
through experiments that used the airborne lidar backscattering profile.
Smaller dilations are sensitive to small-scale fluctuations of *β*(z) and are inclined to include noise, while larger dilations tend to
ignore small-scale structures and detect changes in scale, such as the
entrainment zone. Especially in the real atmosphere, small-scale fluctuation
of *β*(z) due to sudden turbulence appears, and it plays
an important role in mechanical mixing in ML. In order to consider
small-scale features, *W*_{β}(*a*,*b*) profiles were processed by averaging
over *a**<*100 m (WAV1), *a**>*300 m (WAV2), and the total *a*
(WAV3) (de Haij et al., 2007). The height with the maximum values of
*W*_{β}(*a*,*b*) by WAV1, WAV2, and WAV3 can be determined as the ABLH
(*h*_{WAV1}, *h*_{WAV2}, *h*_{WAV3}), respectively.

Figure 3c shows the results of the wavelet method. The bold solid line is a
smoothed *β*(z), while the solid, dashed, and dash-dotted
lines indicate the results of WAV1, WAV2, and WAV3, respectively. As
described in Sect. 4.2.2, *β*(z) decreases rapidly at
altitudes of approximately 700 and 1500 m, while *W*_{β}(*a*,*b*) peaks at
very close altitudes. In WAV1, the first peak (*h*_{WAV1}) appeared at 680 m, which is very close to *h*_{VAR} (670 m) and *h*_{IMP} (690 m). WAV2
(WAV3) showed two peaks at 750 m (730 m) and 1550 m (1550 m). The first
peaks (*h*_{WAV2}, *h*_{WAV3}) were similar to *h*_{GM} (790 m), and the second peaks were similar to *h*_{LGM} (1580 m; second peak of *h*_{GM}).

The *k*-means clustering analysis (CLST) is a nonhierarchical clustering
method that can determine the ABLH by dividing the height where the
backscattering coefficient profile from the ceilometer sharply decreases or
increases. The cluster center is applied to the backscattering coefficient to
minimize the sum of the squared errors (Toledo et al., 2014). The number of
cluster seeds was determined using the Dunn index (Dunn, 1974; Toledo et
al., 2014).

Figure 3d shows the ABLH estimation results using the *k*-means clustering
analysis method at 11:00 LST on 23 September 2016. As a result of the cluster
validation, the optimal number calculated by the Dunn index was three, and
the clusters were distinguished at 800 m (*h*_{CLST1}) and 1430 m
(*h*_{CLST2}). The altitude at which a cluster changes to another cluster
can be determined as the ABLH. The values of *h*_{CLST1} were similar to those
of *h*_{GM} (790 m) and *h*_{WAV1} (770 m). *h*_{CLST2} was slightly lower
than *h*_{LGM} (1580 m) and *h*_{WAV2} (1530 m).

It is possible to estimate the nocturnal SBLH by determining the thermal
stability and instability from the microwave-radiometer-derived vertical
profiles of thermal parameters, such as temperature and potential
temperature (Collaud Coen et al., 2014; Saeed et al., 2016). Given the
vertical profile of the atmospheric temperature, it is possible to determine
the altitude of d$T/\mathrm{d}z=\mathrm{0}$ according to the SBI method for the
purpose of establishing the thermal stability. However, in real atmospheric
conditions, the air parcel follows the environmental lapse rate (ELR), which
differs depending on the time and place rather than the theoretical lapse
rate (TLR), and the criterion of the potential temperature gradient is also
dominant in the ELR. In this study, it is assumed that there is a high
possibility that SBL (d*θ*∕d*z*) exists near the surface to be larger
than the ELR. After that, we set the threshold (${\stackrel{\mathrm{\u203e}}{\mathrm{\Gamma}}}_{f}$) of
the ELR, taking into consideration the vertical variability of d*θ*∕d*z*
to distinguish the distinct layers.

Figure 4a and b show the vertical profiles of the potential temperature and
the vertical gradient of the potential temperature obtained by a MWR at
Jungnang Station at 15:00 LST (solid line) and 21:00 LST (dashed line) on 23 September 2016, as well as
00:00 LST (dotted line) on 24 September 2016. The potential temperature
decreases with height at a constant rate above 2000 m (Fig. 4a), and it can
be considered a slope of the ELR. The TLR and ELR are shown in Fig. 4b as
solid and dashed gray lines, respectively. It was thermally unstable at 15:00 LST on 23 September 2016 when the value near the surface was smaller than
the TLR (Fig. 4b). As the near-surface temperature decreased due to surface
cooling after sunset and a stable layer with a positive value of d*θ*∕d*z* appeared, the slope of d*θ*∕d*z* increased and a more stable layer
was formed at 00:00 LST on 24 September 2016. At this time, the daily mean
potential temperature gradient in the free atmosphere over 2000 m was 5.5 K km^{−1}, and this value is used as the threshold (${\stackrel{\mathrm{\u203e}}{\mathrm{\Gamma}}}_{f}$) for the ELR.

Thus, it can be concluded that the layer is considered as a stably affecting
layer if d*θ*∕d*z* is greater than ${\stackrel{\mathrm{\u203e}}{\mathrm{\Gamma}}}_{f}$ and an
unstably affecting layer if d*θ*∕d*z* is smaller than ${\stackrel{\mathrm{\u203e}}{\mathrm{\Gamma}}}_{f}$. The d*θ*∕d*z* in the lower atmosphere at 21:00 LST on 23 September 2016 is greater than 0 K km^{−1}, which is the stable condition
in the TLR criterion; however, it was smaller than 5.5 K km^{−1}.
Therefore, it is difficult to determine it as stable in the ELR. Figure 4c
shows the vertical variance of d*θ*∕d*z*. The vertical variance was
calculated for 150 m at each altitude. At 15:00 LST on 23 September 2016,
which was well mixed vertically, the variance of d*θ*∕d*z* in the lower
atmosphere was close to 0 K km^{−1}, whereas there was a significant
variance of d*θ*∕d*z* at 21:00 LST on 23 and 00:00 LST on 24 September 2016. It is possible to determine the altitude at which the vertical
variance decreases rapidly (500 m; gray line in Fig. 4b) at 00:00 LST on 24 September 2016, satisfying the ELR condition, and d*θ*∕d*z* at an
altitude of 3.6 K km^{−1}.

Since both ${\stackrel{\mathrm{\u203e}}{\mathrm{\Gamma}}}_{f}$ and d*θ*∕d*z* depend on time, we
determined the altitude at which the vertical variance of the daily data
decreases sharply every 10 min while satisfying the stable ELR condition
($\mathit{>}{\stackrel{\mathrm{\u203e}}{\mathrm{\Gamma}}}_{f}$) for threshold setting. With regard to
the distinct layer classification, the altitude of the maximum vertical
variance during a day and the potential temperature gradient of that day as
the critical lapse rate of that day (CLR Γ_{cr}) were determined.

$$\begin{array}{}\text{(15)}& {\displaystyle}\mathrm{Var}{\left({\displaystyle \frac{\partial \mathit{\theta}}{\partial z}}\right)}_{z}={\displaystyle \frac{\mathrm{1}}{H}}{\sum}_{z=\mathrm{1}}^{H}{\left[{\left({\displaystyle \frac{\partial \mathit{\theta}}{\partial z}}\right)}_{z}-{\left(\overline{{\displaystyle \frac{\partial \mathit{\theta}}{\partial z}}}\right)}_{z}\right]}^{\mathrm{2}},\text{(16)}& {\displaystyle}{\mathrm{\Gamma}}_{\mathrm{cr}}={\scriptscriptstyle \begin{array}{c}max\\ t=\mathrm{1}\phantom{\rule{0.125em}{0ex}}\mathrm{d}\end{array}}\left\{max{\left(\mathrm{Var}\left({\displaystyle \frac{\partial \mathit{\theta}}{\partial z}}\right)\right)}_{t}\right\},\end{array}$$

where $\mathrm{Var}{\left(\frac{\partial \mathit{\theta}}{\partial z}\right)}_{z}$ is the
vertical variance of the potential temperature gradient at *z* height,
${\left(\frac{\partial \mathit{\theta}}{\partial z}\right)}_{z}$ pertains to the
potential temperature gradient at *z* height, ${\left(\frac{\overline{\partial \mathit{\theta}}}{\partial z}\right)}_{z}$ represents the mean potential temperature
gradient over ±150 m at *z* height, and *H* denotes the number of
vertical intervals (*H*=6; 300 m).

As a result, on 23 September 2016, Γ_{cr} was 7.0 K km^{−1}, and
the altitude at which the d*θ*∕d*z* profile crosses CLR was determined
as SBLH. In order to improve the quality of the MWR data, surface heating
via shortwave radiation (net radiation *>*0 W m^{−2}) and
precipitation were removed.

During the radiosonde intensive observation period, only four SBL cases were
detected using the SBI methodology from the radiosonde. The SBLH via the SBI
method was compared with that obtained using the CLR method. Figure 5 shows
the vertical profile of the potential temperature gradient, threshold of
lapse rate (Γ_{cr}), and SBLH estimated using each methodology,
i.e., SBI using the radiosonde (RS_SBI), SBI using the MWR
(MWR_SBI), and CLR using the MWR (MWR_CLR).
SBLHs were estimated at the same time using the radiosonde and MWR (Fig. 5a to c). In case of Fig. 5d, the MWR
showed SBL an hour later (01:00 LST). The MWR_SBI was
estimated to be lower than MWR_CLR and only when the
atmosphere condition was markedly stable (Fig. 5b, c). In this study, the
CLR method was applied to estimate SBLH using the MWR, which estimates SBLH
more accurately and stably.

In a real atmosphere, there is not only one ABL but a complicated structure with several layers that are dependent on time, place, and atmospheric phenomena. Therefore, ABLH shows differences among methodologies and is an arbitrary decision by the researcher. In this study, an integrated system for ABLH estimation (ISABLE) was developed to determine the optimal ABLH. ISABLE applies the four methodologies described above using the backscattering coefficient from the ceilometer as well as the CLR method that uses the potential temperature profiles from the MWR.

Figure 6 shows the schematic flow of the ABLH candidate group selection process. INPUT is the ABLH estimated by applying the four methods using a backscattering coefficient from the ceilometer, and in the present study, it was estimated to be up to 19 layers. The VAR selects a maximum of three peaks as ABLH candidates. In the GM, a maximum of five peaks are found to minimize redundancy at the chosen level. In the WAV method, up to three altitudes are selected as ABLH candidates for WAV3 considering the full dilation, and WAV1 and WAV2 select two altitudes to minimize the redundancy to WAV3. The CLST selected a maximum of four altitudes to remove the possible noise structure. The minimum distance between the nearest two ABLH candidates was set to 150 m. The reason is that the typical thickness of a well-defined entrainment zone was reported to be between 100 and 300 m (Angevine et al., 1994). If there were multiple peaks chosen using each methodology within a 150 m interval, the remaining peaks except for the most significant one were removed from the ABLH candidates for the method.

The ABLH candidate groups were selected via the *k*-means clustering analysis
method for the maximum of 19 ABLHs. Through the first clustering, groups
with three or more members and RMSE less than or equal to 50 m are
classified into the ABLH candidate groups. If the number of members is less
than three and the RMSE is higher than 50 m, the member is excluded from the
ABLH candidate groups. If the number of members is greater than or equal to
three but the RMSE exceeds 50 m, a second clustering analysis is performed.

The second clustering analysis on members of the undetermined candidate group is performed such that if the number of members is greater than or equal to two and the RMSE is less than 50 m, the group is classified into the ABLH candidate groups. If the number of members is less than two, the members are removed; if the number of members is greater than or equal to two and the RMSE exceeds 50 m, the member with the farthest distance from the mean of the group is removed. The foregoing procedure is repeated until the number of members is greater than or equal to two and the RMSE does not exceed 50 m. Thereafter, the last group is classified as an ABLH candidate group.

The final OUTPUT, the ABLH candidate groups, is ranked in descending order of the number of members, and if the number of members is the same, the RMSE is ranked in ascending order. Up to five groups were selected, and the average of each group was determined as the final ABLHs estimated by the ceilometer backscattering coefficient. If the SBLH is observed by the MWR, it is added to the final ABLHs.

Various ABLH estimation methodologies have been merged with ISABLE. However,
there are still limitations in terms of estimating the ABLH, such as
observational errors and small-scale fluctuations in a real atmosphere, and
the appropriate post-processing, which is required as per Kotthaus and
Grimmond (2018). Unreasonable ABLHs, such as the ABLH above *h*_{SNR}, and near-range artifacts caused by instrument-related and isolated ABLH-related
small-scale structures are removed through the three-step post-process.

Figure 7a shows the ABLHs determined by ceilometer observations without
post-processing (CM_ABLH) from 18:00 LST on 22 September 2016 to 12:00 LST on
25 September 2016. There are not only ABLHs higher than *h*_{SNR} within
the range of 10:00 to 12:00 LST on 25 September 2016, but also near-range ABLHs in
the daytime (12:00 to 16:00 LST) when the convective is well developed, and
isolated ABLHs that seem independent without time–space continuity are
formed. First, the ABLHs that are higher than *h*_{SNR} are removed. As a
result, the ABLHs that appeared at approximately 2500 m within 10:00 to 12:00 LST on 25 September 2016 were removed (Fig. 7b). As mentioned in Sect. 3.2, the altitude higher than *h*_{SNR} contained less meaningful
information because the backscatter signal, as compared with the background
noise, is weak. Second, the ABLHs in the lower atmosphere during the
daytime, represented by the near-range artifacts, were removed (Fig. 7c).
The ABLH grows slowly after sunrise, while it overgrows approximately 1 to 2 h before noon. The maximum ABLH appears approximately 2 to 3 h after noon
(14:00 to 16:00 LST). During this period, vertical mixing through convection
is active due to surface heating, and thus the ABLH grows to the maximum.
Therefore, the ABLH that appears in the lower layer at the time might be
inappropriate due to instrumental noise or near-range artifacts. Using the
radiation observation at Jungnang Station, the convective mixing period was
set from 1 h before the time of maximum net radiation to 1 h after sunset
(the net radiation is 0 W m^{−2}). It was found that backscattering
signals were weakened at about 120 m and 400 to 500 m high, respectively,
during the daytime with intense solar radiation (Fig. 2a). Due to the
weakened signal, the 400 to 500 m could be often
estimated as an ABLH. So, ABLHs below 500 m at the time were assumed to be
unreasonable and were neglected (Fig. 7b). Third, in order to find the
discontinuous ABLH caused by small-scale fluctuations and a separated
small-scale aerosol layer, the ABLH is assumed to be discontinuous if no
other ABLHs are present within ±10 time steps (100 min) and ±12 range gates (120 m). Additionally, the density-based spatial clustering
of applications with noise (DBSCAN; Ester et al., 1996) can eliminate isolated
ABLHs. DBSCAN is an algorithm that extracts the noise contained in a
cluster. Each point (core point) of a cluster and neighborhoods (border
points) within a given radius (*ε*) must contain a minimum number
of points (MinPts) within *ε*. In order to apply the same
*ε* to the time–height axes, DBSCAN is performed on a
normalized ABLH with values between 0 and 1. Figure 7d shows the result of
the discontinuity check using DBSCAN with *ε*=0.0125 (*t*=72 min; *z*=56 m) and MinPts = 3. The discontinuous
and sole ABLHs were removed, and the boundary layer distinction became more
pronounced.

Figure 7e shows the backscattering coefficient and CM_ABLH from those after post-processing. In addition, the nocturnal SBLH estimated using a microwave radiometer (MWR_ABLH) was merged with the CM_ABLH. Finally, the ABLHs determined via ISABLE (ISABLE_ABLH) were determined as the lowest of the remaining CM_ABLHs and MWR_ABLH.

5 Results

Back to toptopABLHs were calculated using the 148 radiosonde observations launched at the Jungnang Station in Seoul from 2015 to 2018. Figure 8 shows the diurnal variation of the ABLH. The ABLH estimated using radiosonde exhibited a maximum at 15:00 LST (mean = 1019 m, median = 925 m) and a minimum at 06:00 LST (mean = 418 m, median = 250 m). At night, the mean ABLHs were determined as around 500 m, and outliers appeared above 1 km, which were identified as the RL or clouds (Fig. 8). The interquartile range (IQR; Q3–Q1) showed the minimum value (268 m) at 09:00 LST and the maximum (740 m) at 18:00 LST. Overall, ABLHs were concentrated in the lower layer at night, and the IQR values increased as the ML developed after sunrise.

The SBL over rural areas such as a grass field or crop field is well developed due to active radiative cooling at night, especially under clear skies. In contrast, the radiative cooling over urban areas was not always active because of heat storage by urban materials and anthropogenic heat by energy use (Hong et al., 2013; Park et al., 2014). As a result, formation and evolution of SBL were not active over dense urban areas such as Jungnang Station.

Figure 9 shows the ABLHs obtained by radiosonde observation (RS), the
ISABLE algorithm, and the results of each methodology obtained using a ceilometer and
a MWR from 18:00 LST on 22 September 2016 to 12:00 LST on 25 September 2016.
The period corresponds to the longest observation period with an interval of
3 h and without any missing data among available RS data. The same diurnal
variation was observed in the RS and ISABLE results. The correlation
coefficient (*R*) between the two exhibited a high correlation of 0.98, with a
mean bias (MB) of −101 m and a root mean square error (RMSE) of 135 m. The
ABLHs from ISABLE as well as ceilometer-based methods (GM, WAV2, WAV3, and
CLST) were similar to those by RS during the daytime; however, the ABLHs
from the former appeared at higher levels than those from the latter during
the nighttime. This might be mainly due to the more significant signal in
the RL. ISABLE tried to complement the shortcomings by integrating the four
methodologies through considering the SBL using a vertical temperature from
MWR at night. The maximum ABLHs during daytime appeared at 16:00 LST on 23 September 2016, and
the RS and the ISABLE algorithm estimated ABLHs of 1620 and 2009 m, respectively. At
this time, a cumulus cloud was formed over the top of the ABL due to strong
convection, and the cloud base height observed by the ceilometer was 1910 m. The ABLH estimation results showed that RS was below the cloud, while
ISABLE and individual methodologies (GM: 2080 m, WAV2: 2060 m, WAV3: 2050 m) detected ABLHs as the cloud. In the presence of clouds, the *R**i*_{b}
method tends to detect the base of the cloud layer, where the temperature
profile changes rapidly. The GM and WAV2 methods using the ceilometer
determine the ABLHs as the top of the layer because of the strong negative gradient
of the backscattering coefficient, whereas the CLST can detect both the base and
top of the cloud layer. In ISABLE, the effect of clouds is compensated for
by averaging multiple heights determined by individual methodologies. However,
the ISABLE algorithm still has limitations in the presence of thick clouds.

Table 2 shows the performance of the ABLHs estimated by ISABLE and the four
methodologies with respect to the ABLH determined using the *R**i*_{b}
calculated via RS. Moreover, Fig. 10 shows the scatter plots of ABLHs
estimated via RS and ceilometer/MWR (WAV1 and 3 are not included). The total
RSs (number of data sets: 148) were classified into four time zones: i.e.,
near sunrise (*N*=47; 06:00 to 11:00 LST), daytime (*N*=31; 12:00 to 17:00 LST), near sunset (*N*=34; 18:00 to 22:00 LST), and nighttime (*N*=36;
23:00 to 05:00 LST). The correlation coefficient between the ABLHs of RS and
ISABLE for the entire period was 0.72, MB was −34 m, and RMSE was 322 m.
With regard to the individual methodologies, VAR exhibited the best
performance (*R*=0.60; MB = 219 m; RMSE = 372 m), and CLST exhibited
the second best performance (*R*=0.45; MB = 125 m; RMSE = 474 m).
These two methodologies showed the best performances during the daytime. The
scatter distribution of GM, WAV2, and CLST at sunrise, sunset, and nighttime
could be fitted to two groups with different linear functions. In cases
where symbols were plotted below the trend line (dashed line), RLs during
nighttime or cloud layers in daytime existed at the layer. ISABLE (Fig. 10e)
showed significant improvement near sunrise and sunset time but showed a
lower correlation with the individual methodologies in nighttime because
the ABLH was often underestimated, as compared with RS. There were only four
SBLH estimations via RS, while 24 SBLHs were observed via MWR, which
resulted in significantly lower ISABLE performance at nighttime, as compared
with those of the four methodologies. Overestimation of RS_ABLHs could lead to an underestimation of ABLHs. Anthropogenic heat release
from urban materials could be one reason for detecting a lower number of SBLHs
at night (Hong et al., 2013; Park et al., 2014). Further analysis is
required in considering the accuracy and uncertainty of the two instruments
as well as the effects of urban heat islands. The performances of WAV1 and
WAV3 were significantly poorer than those of other individual methodologies.
The shorter dilation (*a**<*100 m) used in WAV1 seems to be unsuitable
for estimating the ABLH, and it might affect the ABLH of WAV3.

Table 3 and Fig. 11 show the performances of the ABLHs via ceilometer/MWR
and the scatter plots between two ABLHs for two categories of clear (*N*=36; CC ≤ 30 %) and cloudy (*N*=26; CC ≥ 80 %) skies. The
foregoing analysis is made with the use of data from 2016 to 2018 due to the
availability of cloud cover data. GM and WAV2 were found to show lower
verification scores in clear-sky cases in previous studies. This is mainly
because the GM and WAV2 methods tend to determine the altitude of clouds or
RL. As a result, even in Fig. 11, scatter plots could be fitted to two
groups with different linear lines, and the resulting performance scores
decreased. Most deviations were related to the RL at nighttime. In order to
reduce the deviation in GM and WAV2, ISABLE statistically integrates up to
five candidates of the ABLHs estimated from four methodologies and is set
to determine the lowest candidate as the final ABLH so that it could detect
the height below the RL or cloud base.

The MB and RMSE for nocturnal SBLH were as good as 6.7 and 72 m, respectively, although the number of available data were not sufficient.

For the period from August 2016 to October 2018, the ISABLE ABLH was determined using the vertical profiles of the backscattering coefficient from the ceilometer and potential temperature from the MWR at Jungnang Station in Seoul. Unfortunately, cloud cover from 2015 to July 2016 was not observed, and the period was excluded from the analysis. Figure 12 shows the diurnal variations over the observation period of clear (Fig. 12a) and cloudy (Fig. 12b) skies. The period mean hourly ABLHs were high in the clear skies during the daytime and in the cloudy skies during the nighttime. The ABLHs for clear skies were significantly higher than those for cloudy skies during the daytime; however, the difference was not as significant during the nighttime. The period mean hourly maximum ABLH was 1220 m at 16:00 LST on clear skies, while it was 1090 m at 15:00 LST on cloudy skies. The diurnal pattern and mean of the ABLH on clear skies seemed to be similar to those on cloudy skies. But the median of the ABLH was 1170 m at 16:00 LST on clear skies, which is 210 m higher than that (960 m) at 15:00 LST on cloudy skies. Variances of the ABLH on cloudy skies were also larger than those on clear skies. Generally, IQR values of the ABLH were large during the daytime and small at nighttime. IQR values were significantly large during the transition period, especially during the developing ML period (11:00 to 12:00 LST), and during the declining ML and developing SBL periods (18:00 to 19:00 LST).

Figure 13 shows the diurnal variations of the ABLH for clear skies by season. The period mean maximum hourly ABLH was 1401 m at 15:00 LST in JJA (June, July, August; Fig. 13c) and the second-highest was 1257 m at 16:00 LST in SON (September, October, November; Fig. 13d). In DJF (December, January, February; Fig. 13a), the period mean maximum hourly ABLH was as low as 1093 m at 16:00 LST. This is consistent with the net radiation in an urban residential area in Seoul (Park et al., 2014). The minimum hourly ABLH showed the lowest value of 333 m at 02:00 LST in DJF and occurred at a relatively higher level of 470 m at 03:00 LST in JJA. The ABL during the nighttime in JJA is less thermodynamically stable than that in DJF, mainly due to anthropogenic heat release in urban areas.

The hourly IQR is small before sunrise, increases with the evolution of ML, and decreases again after sunset in all seasons. Notably, it was the most considerable transition time near sunrise and sunset. The difference in IQR between the daytime and nighttime by season was evident in DJF, MAM, and SON but not in JJA. The ratio of IQR during nighttime to daytime in DJF was as low as 0.29 (02:00 LST, 92 m; 1600 LST, 311 m), while it was as high as 0.52 in JJA (02:00 LST, 295 m; 16:00 LST, 567 m). This implies that the estimated ABLHs are relatively dispersed both in daytime and nighttime in JJA.

ML and SBL growth and decline are directly affected by the sunrise and sunset periods. In the transition period, the uncertainty of the ABLH and the IQR increases. The IQR peaks occurred at 12:00 and 18:00 LST in DJF and at 11:00 and 19:00 LST in MAM. It can be seen that the evolution of ML occurred quickly, but the decline of ML or SBL evolution occurred slowly. The large IQR at 10:00 and 20:00 LST in JJA implied that the ML developed at the earliest time and declined at the latest time in summer. The large IQR at 12:00 and 18:00 LST in SON was due to the delayed sunrise and earlier sunset (Fig. 13d).

Figure 14 shows the seasonal distribution of the ABLH during the daytime (14:00 to 16:00 LST) and nighttime (03:00 to 05:00 LST). The mean ABLH during daytime was 1377, 1222, and 1184 m in JJA, SON, and MAM, respectively (Fig. 14a). The IQR in JJA (528 m) was larger than those in MAM (389 m) and SON (464 m). In DJF, the mean ABLH was the lowest (1049 m), and the IQR was the smallest (302 m). The mean ABLH at nighttime was the highest (474 m), and IQR was the largest (240 m) in JJA (Fig. 14b). The mean ABLH (IQR) was 413 m (151 m), 368 m (133 m), and 359 m (113 m) in MAM, SON, and DJF, respectively.

Figure 15 shows diurnal variations of hourly mean net radiation and its 90th and 10th percentiles, as well as hourly mean ABLH estimated by ISABLE during the clear skies. Theoretically, the surface is heated from the time when net radiation becomes positive, and a ML evolves to balance the energy provided from the surface during the positive net radiation with the energy consumed to heat the overlying air volume. In reality, the ABL started to evolve from 3 h after the positive net radiation. The peak of net radiation occurred at 12:00 LST, while the peak of the ABLH occurred at about 16:00 LST. The ABLH declined rapidly at 1 to 2 h before the negative net radiation. The net radiation in MAM was similar to that in JJA and larger than that in SON, while the ABLH in MAM was similar to that in SON. The difference between the 10th and 90th percentiles of net radiation around 07:00 to 08:00 LST was more significant in MAM than in the other seasons. The differences around 12:00 to 13:00 LST in DJF are lower than in the other seasons. It implies that net radiation, as well as other minor factors, could fully explain the diurnal variation of the ABLH. The difference of net radiation at the same time in the same season could be mainly due to cloud and partly due to moisture and air pollutants.

6 Summary and discussion

Back to toptopThe ISABLE algorithm developed in this study integrated the conventional ABLH
estimation methodologies to produce optimal ABLH and applied statistical
post-processing techniques to improve accuracy. A maximum of five ABLHs were
estimated every 10 min using the ceilometer backscattering coefficient for
each methodology (i.e., time-variance method, gradient method, wavelet
covariance transform method, and clustering analysis method). The determined
ABLHs were divided into five maximum clusters via the *k*-means cluster
analysis method, and the ABLH was finally determined as the average of the
members of the clusters satisfying the statistical conditions. The nocturnal
SBLH was estimated using a potential temperature profile from a microwave
radiometer. The SBLH was determined using the CLR method proposed in this
study, which uses the threshold of the environmental lapse rate of potential
temperature over the day. The ABLHs estimated by the ceilometer were
post-processed in three steps (i.e., SNR threshold, instrument-related
near-range artifact, and isolated ABLHs) to remove unreasonable values. The
lowest altitude among the ABLH and the nocturnal SBLH was finally determined
as an optimized ISABLE ABLH.

From 2015 to 2018, ABLH levels were determined using the ISABLE algorithm
(ISABLE_ABLH) at 10 min intervals and were compared with and
verified against the ABLH estimated by radiosonde observations
(RS_ABLH) at Jungnang Station in Seoul city, Korea. The
*R**i*_{b} was calculated using the vertical profile of the potential
temperature and wind obtained by RS to estimate the ABLH during the entire
sounding. The nocturnal SBLH was determined by the vertical temperature
profile with the use of the SBI method at nighttime. The performance of
ISABLE was verified by comparing the ISABLE_ABLH and ABLH
estimated from each methodology with RS_ABLH. It was
determined that the correlation coefficient between ISABLE_ABLH and RS_ABLH was the highest (*R*=0.72), as compared to
other methodologies. The MB and RMSE showed the smallest values (−34 and
322 m), implying the best performance. Furthermore, the ISABLE algorithm was verified
through the separation of the data into four time zones: i.e., daytime (12:00
to 17:00 LST), nighttime (23:00 to 05:00 LST), sunrise transition time (06:00 to
11:00 LST), and sunset transition time (18:00 to 22:00 LST). As a result, the
correlation coefficient, MB, and RMSE between ISABLE_ABLH and
RS_ABLH exhibited the best performance at 0.86, −3, and
236 m during daytime, respectively. Generally, the performance of ISABLE was
found to be superior to the other four conventional methods, with some
exceptions, especially in sunrise/sunset periods.

On the other hand, the ISABLE performance at nighttime was not as good as that in the other four conventional methods. It seems to be the difference in SBLH estimation between the RS and MWR, and further analyses on the difference are required. The presence of a RL and cloud layer caused large deviations by instruments and methodologies, thereby resulting in somewhat lower performance. The performances for all methodologies on clear skies were better than those on cloudy skies.

The diurnal variation of ISABLE_ABLH was also analyzed for the period from August 2016 to October 2018. ABLH began to grow from 09:00 to 11:00 LST after sunrise, reached a maximum at 15:00 to 16:00 LST, and declined at 18:00 to 20:00 LST. If the SBL was detected from the vertical profile of temperature at nighttime, the SBLH was estimated using the CLR method. Sometimes the top of the RL or cloud layer was determined as the ABLH; thus, the IQR of the ABLH increased.

The IQR of the ABLH was large during the daytime and small during the nighttime, and the deviations of the ABLH in both daytime and nighttime were more significant on clear days. Maximum hourly ABLH occurred in spring and summer, while minimum hourly ABLH occurred in winter. The IQR differences between the daytime and nighttime showed a large value in winter, spring, and autumn and a small value in summer. The differences showed two maxima at 10:00 and 18:00 LST in winter and at 09:00 and 20:00 LST in summer. The diurnal variation of net radiation was closely related to that of the ABLH, and further analyses on the peak time and energy balance are needed.

Most conventional methodologies have been verified for daytime clear skies over several days, while this study tried to attempt to include cloudy as well as complex conditions using the available data set during the 4 years. Poor performance was mainly due to multiple factors, such as strong backscattering signals in the RL, presence of clouds, and weak backscattering signals. Overall, the performance of ISABLE_ABLH was found to be better than that of the conventional methods. There were 28 cases with a difference between the RS-ABLH and the ABLH for each methodology exceeding 1000 m. Among them, 20 cases showed strong backscattering coefficients in RL at nighttime; thus, the ABLH was estimated as the corresponding altitude, especially using the GM and WAV2 methods. The remaining eight cases occurred during the daytime, six cases occurred in the presence of clouds, and two cases occurred in apparently clear skies with very weak backscattering signals. The foregoing cases often appear in a real atmosphere; however, it is difficult to estimate the consistent ABLHs under the aforementioned atmospheric conditions. In this study, as the ABLH was estimated using as much data as possible, regardless of time or atmospheric conditions, their performances seemed to be somewhat lower. When convection is robust during the daytime, the atmospheric structure is relatively homogeneous below the ABLH, and the results of ABLH determinations via different methodologies are similar. On the other hand, if the atmospheric structure is complicated, such as the presence of nocturnal SBL, RL, and daytime clouds, the ABLH may be different from those of the methodologies, and the criteria for determining true ABLH remain with researchers. In addition, in the estimation of the SBLH by the CLR method using the MWR, further studies are needed due to the lack of verification cases.

Although the ISABLE-estimated ABLH exhibited better performance than those estimated by the earlier conventional methodologies, there are still many limitations. In particular, ABLHs estimated from the ceilometer in the lower layer are not reliable due to near-range artifacts, especially under intense solar radiation. ABLHs at higher levels at nighttime could be supplemented by the temperature profile obtained by the MWR. ABLHs are challenging in terms of estimating under cloudy sky or precipitation, severe fog, and smog events. Since the ISABLE algorithm is in the early stage of development, it did not address all the known issues yet, such as precipitation, lofted aerosol layer, and too clean (little aerosol) a condition. These limitations and drawbacks should be overcome by combining enough observation data, instrumental advances, and the corresponding improvements of ISABLE.

Data availability

Back to toptopData availability.

Data used in this study can be provided on request. For further inquiries contact either Jae-Sik Min (min_jaesik@snu.ac.kr) or Moon-Soo Park (moonsoo@sejong.ac.kr).

Author contributions

Back to toptopAuthor contributions.

JSM performed the data processing, design, and development of the ISABLE algorithm and wrote the manuscript. MSP prepared and wrote the manuscript. JHC and MK performed the data acquisition, pre-processing, and field experiment. All authors have read and agreed to the published version of the paper.

Competing interests

Back to toptopCompeting interests.

The authors declare that they have no conflict of interest.

Acknowledgements

Back to toptopAcknowledgements.

This work was funded by the Korea Meteorological Administration Research and Development Program under grant no. KMI2018-05310. Most of the data used in this study were supported by the Korea Meteorological Administration's National Institute of Meteorological Sciences Development of Advanced Research on Biometeorology and Industrial Meteorology (136500304) and the Hankuk University of Foreign Studies.

Financial support

Back to toptopFinancial support.

This research has been supported by the Korea Meteorological Administration (grant no. KMI2018-05310).

Review statement

Back to toptopReview statement.

This paper was edited by Laura Bianco and reviewed by three anonymous referees.

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Short summary

An algorithm for an integrated system for ABLH estimation (ISABLE) was developed and applied to the vertical profile data obtained by a ceilometer and a microwave radiometer in Seoul city, Korea. The ISABLE algorithm finds an optimal ABLH through the post-processing including *k*-means clustering and density-based spatial clustering of applications with noise (DBSCAN) techniques. The ISABLE ABLH exhibited better performance than those obtained by most conventional methods.

An algorithm for an integrated system for ABLH estimation (ISABLE) was developed and applied to...

Atmospheric Measurement Techniques

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