Introduction
The boundary layer (BL) is defined as the lowest layer in the atmosphere
directly influenced by the earth's surface. The boundary layer reacts to
surface forcings such as evaporation and transpiration, heat transfer,
frictional drag, and terrain-produced air flows within a timescale of an
hour or less . Other forcings such as pollutant emission, in
particular PM2.5 (particulate matter), can enhance the stability of the
BL and decrease the boundary layer height . Above the
boundary layer is the free troposphere (FT) acting as a cap to the BL.
Convection and turbulence created by surface heating lead to the gradual
growth of the BL starting at sunrise, mixing gaseous compounds and particles
within the convective mixing layer (ML). Above the ML is the stable
entrainment zone (EZ), where the FT is entrained downward into the ML, and ML
thermals overshoot upward into the EZ . The ML
begins to decay as surface heating and turbulence decrease, eventually
creating a near-surface nocturnal stable layer (NSL). Leftover constituents
from the daytime ML form the residual layer (RL) above the NSL
. More complex BL structures can also form in specific
environmental conditions such as multiple stable layers and internal boundary
layers .
The determination of the BL height (BLH) is vital in air pollution studies as
it determines the extent of vertical mixing of pollutants. While this is a
key parameter in air pollution modeling and air quality studies, continuous
monitoring of the BL is rarely available. The most common way of retrieving
the BLH has been with the use of radiosondes. However, radiosondes are
seldom launched more than a few times a day except during extensive and
costly scientific campaigns in which they are only launched for the duration
of the campaign. Apart from a few occasions
e.g.,, NSL measurements are particularly
uncommon since most radiosonde launches are performed during daytime ML
hours. In recent years, remote-sensing techniques such as light detection and
ranging (lidar), radio acoustic sounding systems (RASS), and sonic detection
and ranging (sodar) systems have allowed for the continuous monitoring of the
BL
.
Ceilometers in particular offer a low-maintenance and low-cost solution to
constantly monitoring the ML using aerosol backscatter while also
facilitating the monitoring of the nocturnal stable layer, internal aerosol
layers, and the nighttime residual layer
. The extensive data set from
continuous lidar measurements results in the need for determining the most
reliable and accurate method to be used in automated retrievals.
In order to evaluate the retrieval of BLHs from aerosol lidars, we tested
three distinct methods. Previous studies have evaluated retrieval methods
such as the study done by reviewing various methods
(automated and semi-automated) across three lidars. This study in turn
evaluates a gradient method, a Haar wavelet method, and a cluster analysis
method to retrieve BLHs using aerosol backscatter measured by a Vaisala CL31
ceilometer located in an urban environment. These BLHs are then compared to
radiosonde-derived BLHs for validation in order to arrive at the automated
algorithm with the least manual inspection required. The effect of cloud
signals on the BLH retrieval is also observed in all retrieval methods tested
and discussed in this study.
Data and instrumentation
This study uses Vaisala CL31 ceilometer data and radiosonde profiles measured
at the University of Houston (UH) main campus. UH main campus is located
about 70 km northwest of the Gulf of Mexico and 5 km
southeast of downtown Houston. The UH CL31 was mounted atop a trailer
approximately 3.5 m above ground, and radiosonde launches were
performed next to the CL31 trailer. A total of 85 radiosonde profiles from
the Tropospheric Ozone Pollution Project were analyzed for this study, but
only profiles corresponding to cloud-free aerosol backscatter vertical
profiles were used for the BLH detection comparison. The Tropospheric Ozone
Pollution Project seeks to understand the combination of pre- and
post-frontal conditions ideal for high-ozone events in the Houston area using
ozonesonde and radiosonde profiles. The project is focused in the fall and
spring seasons, when high-ozone events are frequent. This results in the data
set used containing ∼43 % of launches during cloudy pre-frontal
conditions, with a remaining 48 cloud-free launches in post-frontal clear
skies. Launches between January 2011 and March 2015 are used, with the highest
frequency in the months of May, June, September, and October. All launches
occurred between 06:00 and 17:00 CST, with most radiosondes launching during
convective ML hours between 13:00 and 15:00 CST (Fig. 1). The effect of cloud
signals is analyzed separately for each method in Sect. 4.4. In addition,
this data set includes ceilometer and radiosonde data from the NASA
DISCOVER-AQ (Deriving Information on Surface conditions from Column and
Vertically Resolved Observations Relevant to Air Quality) Texas campaign in
September 2013.
Cloud-free radiosonde launches used for the method comparison
specified by the time of launch in CST.
Vaisala CL31
The Vaisala CL31 ceilometer operates at a wavelength of
905 nanometers (nm) using an indium gallium arsenide laser
diode (InGasAs) system with a 1.2 (mJ) pulse for
110 (ns) and mean pulse repetition rate of
8192 (Hz). It uses a single-lens design to both transmit
and receive light signals. This design reduces the optical crosstalk between
transmitter and receiver and in turn increases the signal-to-noise ratio. A
beam splitter gives full overlap of the transmitter and receiver
field of view at an altitude of 70 m .
The backscatter coefficient β(x,λ) or the backscattering
cross section per unit volume is related to the received power with the
following formula:
P(x,λ)=c2x2P0AηO(x)Δt×β(x,λ)τ2(x,λ)+B,
where P is the optical power received by the ceilometer from
distance x, c is the speed of light, Δt
is the pulse duration, P0 is the average laser power during pulse,
A is the area of receiver optics, η is the receiver optics'
efficiency, O(x) is the range-dependent overlap integral
between beam transmitted and received, τ(x,λ) is the
transmittance of the atmosphere between lidar and volume, λ is the
wavelength of the emitted laser pulse, x is the distance between
lidar and scattering volume, and B is the sum of electronic and
optical background noise . The CL31 returns profiles which
are proportional and close to the attenuated backscatter profiles
β(x,λ)τ2(x,λ). For text-shortening
reasons and because at the CL31 wavelength the aerosol backscatter
coefficient dominates over the molecular backscatter coefficient inside the
BL and clouds, these profiles are called aerosol backscatter profiles in this
paper.
Aerosol backscatter profiles with signals from clouds, rain, or fog are
identified as signals higher than 2000×10-9 m-1 sr-1
and were not used for this BLH comparison .
The CL31 can measure aerosol backscatter up to 7500 m. However, the
CL31 does not record these signals but instead only accumulates aerosol
backscatter intensity every 16 s with a maximum height of 4500 and
10 m resolution. The CL31 ran with firmware v1.7 and noise_h2 on.
For more-in-depth information about the instrument see and
.
iMet radiosondes
Radiosondes launched at UH main campus are International Met Systems
Incorporated model iMet-1. iMet-1 radiosondes return GPS (Global Positioning
System) location, GPS altitude, wind speed and direction, pressure,
temperature, and relative humidity with a 1 Hz sampling rate using a
403 MHz transmitter. Radiosondes used here have a resolution of
0.01 hPa, a response time of 1 s, and an accuracy of
0.5 hPa for pressure measurements. Temperature sensing has a
resolution of 0.01 ∘C, accuracy of 0.2 ∘C, and response
time of 2 s. The humidity sensors for the radiosondes have a
resolution of less than 0.1 %, accuracy of 5 %, and response time of
2 s. Average ascent rate for all launches was about
5 ms-1.
Skew-T–log-P method for BLH detection using temperature (black) and
dew point temperature (grey) for (a) stable and
(b) unstable conditions with BLH shown as a grey dashed line.
Soundings from 26 September 2013 at 06:10 CST (a) and 4 May 2014 at
15:40 CST (b).
A total of 85 launches were analyzed for this study, but only launches
corresponding to cloud-free aerosol backscatter vertical profiles are used in
the retrieval method comparison. This results in 48 launches between March
2012 and March 2015, with only four launches before 09:00, six before midday,
and the remaining 38 launches after midday, with the highest number of
launches between 12:00 and 14:00 CST (see Fig. 1).
Boundary layer height retrieval methods
All aerosol-derived BLH methods presented here are based on two assumptions:
(1) the BL contains a somewhat constant concentration of aerosols due to
convective and turbulent mixing, and (2) the clean FT above will create a
negative gradient in aerosol backscatter from higher concentrations within
the BL towards lower concentrations in the FT. The local maximum of this
gradient is identified as the top of the BL . Thermodynamic
radiosonde BLHs are calculated using a skew-T–log-P diagram method and are
compared to aerosol-derived BLHs calculated from aerosol backscatter profiles
closest in time to the radiosonde launch but not exceeding 10 min before or
after the launch.
Skew-T–log-P diagram for radiosonde boundary layer heights
A stable BL is characterized by having an environmental lapse rate greater
than a moist/dry adiabatic lapse rate (Fig. 2a), while an unstable boundary
layer is identified by having a dry adiabatic lapse rate greater than the
environmental lapse rate (Fig. 2b). Stable profiles BLHs are identified as
the top of the shallow stable layer as seen as a strong positive vertical
gradient change in temperature and a strong negative gradient in dew point
temperature profiles (Fig. 2a). BLHs during unstable conditions are
identified as the base of the stable EZ (i.e., temperature inversion) where
the temperature profile intersects dry adiabatics and/or where
relative humidity or dew point temperature profiles sharply decrease as seen
in the skew-T–log-P diagram in Fig. 2b . A
previous study by found a correlation coefficient of 0.96
during unstable conditions and 0.91 during stable conditions when comparing
ceilometer- and radiosonde-derived BLHs (both manually) using the
skew-T–log-P method.
Vaisala Corporation aerosol backscatter gradient
The Vaisala Corp. BL Matlab v3.7 algorithm is used in this study. This
algorithm finds negative gradients with increasing altitude in aerosol
backscatter profiles following the assumptions discussed in Sect. 3. A
10 min and 120 m height averaging is applied to the profile
along with a temperature dependence curve of -10 as recommended by Vaisala
Corporation (C. Münkel, personal communication, September 2013) due to
the tendency of the CL31 having a curvature in aerosol backscatter profiles
with increasing internal temperatures. The temperature correction of -10 is
an algorithm setting that adjusts the shape and curve of temperature-affected
aerosol backscatter profiles with negligible effects on aerosol layer
detection (; ; C. Münkel, personal communication, April
2016).
The change in aerosol backscatter with height
(dβ / dx) is calculated by the algorithm, which then
finds the three largest negative gradients with a minimum aerosol backscatter
change of 200×10-9 m-1 sr-1. This study uses a
minimum gradient height setting of 30 m along with a sensitivity
setting of 15 %, which requires a 15 % change in the relative aerosol
backscatter in the vicinity of the possible BLH. The largest of the negative
gradients is usually defined as the BL ; however,
the largest negative gradient does not always correspond to the BL (see
Sect. 4). Therefore, a manual analysis of the algorithm's three
resulting layers (Fig. 3) is required in order to prevent the incorrect
identification of other aerosol layers. The algorithm gives three maximum
negative gradients every 1 min, of which one is manually chosen as the BLH.
These are then averaged to 10 min for radiosonde comparison. The manual
approach required to select one of the three maximum negative gradients as
the BLH requires a priori knowledge of typical nocturnal and daytime BL
heights. In addition, this manual selection analysis can be time-consuming,
especially when long-term lidar data are evaluated.
Aerosol backscatter time series for 24 October 2013. Three gradient
local minimums are plotted for each 1 min aerosol backscatter profile.
Cluster analysis
This method uses variations in the measured aerosol vertical profiles for BLH
calculations. The BLH is typically identified as the (temporal) variance
local maximum based on the assumption that the EZ contains high aerosol
variability due to clean air masses from the free atmosphere mixing with
masses from the BL. The center of the EZ corresponds to the top of the BL
.
tested nonhierarchical and hierarchical cluster analysis on
lidar-retrieved vertical aerosol distribution and its variance. Both cluster
methods were found to be reliable in calculating BLHs but with a tendency to
overestimate the BLH compared to aerosol backscatter gradient methods. This
overestimation was attributed to the gradient methods identifying the BLH as
a significant decrease in signal, while the cluster method uses a local
maximum in variance corresponding to the middle of the EZ. The maximum
negative gradient does not always correspond to the local maximum in
variance; in these cases the greater the EZ depth, the greater the
overestimation of the BLH . Nevertheless, the cluster method
offers a unique BLH, whereas aerosol gradient methods can give multiple
results.
Averaging heights by height range used on aerosol backscatter
profiles for cluster and wavelet methods.
Altitude range
Averaging height
10–490 m
70 m
500–990 m
330 m
1000–1990 m
590 m
2000–4500 m
690 m
Data processing for cluster analysis and application
Due to low signal-to-noise ratio and noise-generated artifacts, both a
10 min moving time average and moving height average were applied to raw
aerosol backscatter profiles. Height averages were applied as seen in
Table 1. These averaging settings were chosen as they created the most
reliable cluster-calculated BLHs, similar to findings in averaging done for
gradient methods . Because the range correction
needed to invert Eq. (1) increases noise in aerosol backscatter profiles with
height, lower averaging was applied to lower altitudes, while higher averaging
was applied to higher altitudes (Table 1). This study found that these
averaging settings worked best on most aerosol profiles and aerosol
conditions. Typically, lower averaging than that listed in Table 1 caused
artificial variance peaks, while greater averaging smoothed out variance
peaks in the aerosol backscatter profiles. The moving time average also leads
to more profiles containing cloud signals; therefore only 45 comparisons were
found to be valid for this method.
Variance V as a function of height z were then calculated
from cloud-free profiles R using the following formula
:
V(z)=1N-1∑i=1N[R(z,ti)-R¯(z)]2,
where R(z,ti) is the averaged lidar aerosol backscattered signal at
time ti and height z, and R¯ is the averaged profile from
N number of profiles corresponding to 10 min.
K-means clustering can then be applied to identify BLHs. K-means is a
data-partitioning algorithm that assigns standardized 3-D point observations
(height range of profile, aerosol backscatter signal, and variance) to
exactly one of the k clusters defined by centroids (cluster centers), where k
is chosen before the algorithm starts . The
algorithm works as follows:
Step 1. Choose k initial cluster centers (centroid).
Step 2. Compute point-to-cluster-centroid Euclidean distances of all observations.
Step 3. Assign each observation to the cluster with the closest centroid.
Step 4. Compute the average of the observations in each cluster to obtain new
centroid locations.
Step 5. Repeat steps 2 through 4 until cluster assignments do not change,
or the maximum number of iterations is reached, whichever occurs first,
depending on computational resources .
CL31 aerosol backscatter profile (a) and corresponding
calculated variance profile (b) for 25 September 2014 at 14:30 CST.
Dashed line shows the cluster-derived BLH (2360 m) at the height where the
variance cluster assignment changes from cluster 1 to cluster 2.
Previous determination of the number of clusters present or needed in the
data set is required for cluster validation, since the number of clusters is a
parameter to be introduced into the cluster algorithm (Step 1).
By choosing k=2, cluster analysis will typically divide a well-mixed
boundary layer into two clusters, one below a peak in variance corresponding
to the center of the EZ and one above the variance peak (Fig. 4); however,
profiles with increasing noise and/or lofted aerosol layers will cause the
cluster analysis to assign clusters elsewhere (for a detailed description see
Sect. 4). The maximum height of these clusters is limited by the time
of day to prevent the detection of other aerosol layers such as the top of
the residual layer during nocturnal hours when only the NSL is of interest.
Here, the maximum height for nighttime BL detection is 400 m, whereas
it is 2800 m for daytime BL heights.
Daytime aerosol backscatter profile (a) for 13 November
2013 at 13:30 CST and (b–c) its corresponding covariance wavelet
transform coefficients with increasing magnitudes of 30, 100, and 300 m,
respectively. Wavelet-retrieved BLH is shown as the dashed grey line at
750 m.
Haar wavelet method
Aerosol backscatter BLHs are derived with a covariance wavelet transform
utilizing the Haar wavelet compound step function with multiple user-defined
wavelet dilations .
This method identifies the sharp aerosol backscatter gradient corresponding
to the top of the BL by calculating the wavelet transform. The Haar wavelet
function h is defined as follows:
hz-ba=-1:b-a2≤z<b+1:b≤z≤b+a20:elsewhere,
where z is the vertical altitude in this application, a is
the vertical extent or dilation of the Haar function, and b is the
center of the Haar wavelet function. The covariance transform of the Haar
wavelet function, wf, is defined as
wf(a,b)=a-1∫zbztf(z)hz-badz,
where zt and zb are the top and bottom altitudes
in the aerosol backscatter profile, f(z) is the aerosol backscatter
profile as a function of altitude, and a is the normalization factor
or the inverse of the dilation.
Defining the dilation factor a and the range of centers b
of the Haar wavelet function is key in correctly identifying the BLH using
aerosol backscatter profiles. In this study, b ranges from the
lowest ceilometer-recorded aerosol backscatter altitude of 10 m to a
maximum BLH of 2800 m. This limit was set as no previous studies have
found BLHs above 2800 m for the study area
.
As with previous studies , the
dilation factor a affects the number of covariance wavelet transform
coefficient (CWTC) local minimums. Larger values create a few large local
minimums (Fig. 5b and c) at the heights of the biggest aerosol gradients in
the aerosol backscatter profile (Fig. 5a). Lower dilation values also create
numerous CWTC local minimums (Fig. 5d) at heights of smaller aerosol
gradients in the measured profiles. A range of dilation values is applied to
the aerosol backscatter profile. Here we use a maximum dilation of
30 m for nighttime BLHs since the NSL tends to have a smaller aerosol
backscatter gradient than the above RL, creating a need for more than one
local minimum (not shown). In these cases, the CWTC local minimum closest to
the surface is chosen as the BL. A higher limit of 300 m (Fig. 5b)
for the dilation factor a is applied for daytime BLHs and the
strongest CWTC local minimum is used to identify the sharp transition between
ML and FT. This larger dilation value also serves to decrease signals from
smaller aerosol gradients below the BLH. Cloud-free CL31 aerosol backscatter
profiles are averaged first vertically according to Table 1 followed by a
10 min average before applying the Haar wavelet algorithm. The algorithm is
applied to each averaged profile with incremental dilations until the maximum
dilation factor is reached (30 m for nighttime hours and
300 m for daytime hours). The mean of all resulting CWT coefficients
is then calculated, and the local minimum of the mean CWT coefficients is
identified as the BLH.
Results
BLH retrieval methods are evaluated and quantified against radiosonde-derived
BLHs using bias and standard deviation calculated in accordance with
and . Here, the bias is the difference
between the means of aerosol-retrieved BLH and the corresponding radiosonde
BLH, and the standard deviation is the root-mean-square value of the
departures of the individual pair sample differences from the bias. A
two-sided, paired-sample t test is used to define the statistical
significance of the bias:
t=X¯-μSN,
where X¯ is the mean of the aerosol BLH samples, μ is the
radiosonde BLHs mean, S is the standard deviation of samples differences,
and N is the number of pair samples.
The null hypothesis is defined as unbiased aerosol-derived BLHs when compared
to radiosonde BLHs. It was not rejected when the calculated t test value
(t) was within ±1.96 and the p value was greater than 0.05 or 5 %
significance level, in alignment with previous approaches
. Correlation of all methods and radiosonde BLHs is
shown in Fig. 6, and a cross-comparison of the methods is found in Fig. 7. The
uncertainties from the sensor were not calculated for this study as the exact
aerosol backscatter profiles used in the aerosol gradient method are not
given by the Vaisala algorithm and therefore the uncertainties could not be
calculated equally across all BLH retrieval methods. However,
show a promising new statistical method to review sensor-related uncertainties in similar studies.
Comparison of CL31 aerosol backscatter BLHs and radiosonde-derived
BLHs. The three methods tested are compared to radiosonde BLHs calculated
using the skew-T–log-P method. The linear regression lines, regression line
equations, and correlation coefficients r2 are listed for each BLH
retrieval method comparison.
Intercomparison of all methods using cloud-free profiles. One-to-one
line in dashed grey and linear regression lines in solid black.
The algorithms were applied to 24 October 2013, when two radiosondes were
launched in cloud-free conditions. The cluster analysis and wavelet method
were subjected to a 500 m height detection limit during nighttime BLH
detection in order to prevent the detection of RL signals and 2800 m
2 h after sunrise at 09:30 CST (the afternoon decoupling period is not
considered). The 500 m and 2800 m limits are chosen as they
are well above the previously identified BLHs in the study area
. The results are shown in Fig. 8 and discussed
in Sect. 4.1.
Resulting BLH for 24 October 2013 with 10 min averages for all
methods. Radiosonde-estimated BLHs are shown as red squares.
Aerosol backscatter gradient method results
A previous study done by found that ceilometer BLHs derived
from the aerosol backscatter gradient showed excellent correlation with
radiosonde BLHs for both stable and unstable conditions, over a period of 2
years using more than 60 daytime radiosonde profiles. found
the aerosol backscatter gradient capable of continuously identifying the
height of the BL after manually choosing one of the three resulting aerosol
layers, with limited detection following precipitation or during periods of
high wind speeds. Low aerosol content after rain events through wet
deposition of aerosols and dispersion of aerosol due to high winds speeds
limit the formation of aerosol layers, therefore limiting the detection of
the BLH with aerosol gradients. These limitations, however, are less relevant
for air quality studies since typically these situations are also accompanied
by lower pollutant levels (e.g., through air mass change, enhanced vertical
mixing, enhanced dry deposition due to high winds, and wet removal of soluble
gases during the preceding precipitation). Late-afternoon hours also present
a challenge since the discontinuous transition from unstable (ML) to stable
boundary layer (NSL) can create multiple aerosol layers
. This is still an important time period
for primary pollutant concentrations as they would still be critically
determined by the BLH (in particular during evening rush hour); however the
diurnal peak in photochemistry activity for buildup of secondary pollutants
has passed, making this a less crucial time for these pollutants.
This study found similar results using 47 cloud-free radiosondes with a
slight difference in correlation most likely due to the manual analysis used.
does not report a BLH if the height of the BL is not clear,
while this study always reports a gradient found by the algorithm as long as
the algorithm is able to calculate a gradient. The manual analysis used in
this study resulted in a correlation coefficient (r2) of 0.85 (Fig. 6)
when comparing the aerosol backscatter gradient BLHs to daytime radiosonde
BLHs. A bias of -42.5 m, and a standard deviation of 209.5 m
(Table 2) were found (not statistically significant; p>0.05). The bias
indicates aerosol gradient method BLHs are generally lower than radiosonde
BLHs. The overall agreement shows the ability of this method to calculate the
BLH reasonably well once one of the three calculated aerosol backscatter
gradients is chosen as the BL. However, this requires a priori knowledge of
typical BLHs at the measurement site and a manual inspection of aerosol
gradients calculated. In addition, limited detection of the BLH was also seen
in conditions with low aerosol content when the algorithm did not find strong
enough gradients in the aerosol backscatter profile. No combination of
available setting options was found to improve BLH detection in these
conditions. Furthermore, disagreement was found when the largest gradient in
an aerosol profile does not correspond to the thermodynamic BLH found using
radiosonde profiles. This is due to the different assumptions in the
methodologies when using aerosol gradients to detect lidar BLHs or thermal
parameters to detect radiosonde BLHs.
Figure 8 shows a time series of BLHs reported after manual analysis of
radiosonde BLHs and 10 min averaging of the three calculated aerosol layers
(Fig. 3). The gradient method is able to resolve for BLHs under stable and
unstable conditions for this October day but underestimates the BLH by about
300 and 170 m when compared to the first and second radiosonde
launch, respectively. Nocturnal BLHs are similar to those calculated by the wavelet
and cluster analysis method but occasionally measure a lower NSL than the
other two methods, likely due to the difference with the averaging procedure
used for the aerosol gradient method. Daytime BLHs after manual selection of
the three calculated gradients are seen as slightly less variable than those
calculated by the cluster analysis and wavelet methods and are occasionally
lower than those calculated by the wavelet method. Overall, all methods are
able to capture the NSL, the growth of the BL, and the peak BLH reasonably
well, with the cluster method showing the most variability due to the
detection of lofted aerosol layer signals incorrectly identified as the BLH.
The aerosol gradient method and the wavelet method BLHs show very similar
results after the manual selection of the aerosol gradient method BLHs and
are also found to be within the standard deviation of the climatological mean for
the fall season found by for this site. Figure 7 shows the
aerosol gradient method having the best correlation with the wavelet method,
as expected, as both search for the maximum aerosol backscatter gradients in a
profile, but slightly lower agreement with the variance method. Overall, this
method works well under stable and unstable conditions as long as the user is
able to identify the correct BLH from the three gradients reported.
Bias, standard deviation, p value, and number of data points (no.)
for comparison of BLH retrieval methods to radiosonde BLHs.
BLH retrieval method
Bias (m)
Standard deviation (m)
p value
No.
Aerosol gradient
-42.5
209.5
0.17
47
Cluster
-61.0
243.5
0.10
45
Wavelet
51.1
187.0
0.07
48
Cluster method results
CL31 BLHs using the cluster method showed a slightly lower correlation than
the aerosol gradient method with a correlation coefficient of 0.82 (Fig. 6),
a bias of -61.0 m and a standard deviation of 243.5 m (not
statistically significant; see Table 2). Disagreements found between
radiosonde- and cluster-derived BLHs were most commonly due to noise in
aerosol backscatter profiles and lofted aerosol layers. From the 45
comparisons performed, six cases (13.3 %) showed the algorithm finding a
single clear peak in variance not corresponding to the BL but to noise (1
case) or to other aerosol layers (5 cases). Sixteen cases (35.5 %) were
found where noise created multiple variance peaks at higher altitudes;
therefore the cluster analysis divided aerosol backscatter profiles into
clusters of similar variance intensity (Fig. 9) rather than above and below a
single variance peak (as seen in Fig. 4). This division underestimated the
BLH (bias of -61.0) since the cluster was divided into relatively low
variance closer to the surface and high variance at higher altitudes. This is
due to the fact that CL31 displays a significant increase in noise with
increasing altitude. For the five instances where the variance maximum did
not equal radiosonde-derived BLH due to signals from lofted aerosol layers, a
smaller maximum corresponded to the BL. These errors were not due to the
algorithm limitations created by noise (35.5 %) but instead due to the
implicit assumptions in using aerosol backscatter for BLH detection (constant
aerosol backscatter signals within the BL and a negative gradient in aerosol
backscatter corresponds to the top of the BL). When compared to the wavelet
and aerosol gradient method, the cluster analysis agrees well with the
aerosol gradient method (r2=0.82) but slightly less with the wavelet
method (r2=0.76) as seen in Fig. 7.
The errors caused by other aerosol layers can be seen to occur during 24
October 2013 (Fig. 8). Here, the cluster method mistakenly identifies signals
higher than the BL, some of which the aerosol gradient method also identified
(see Fig. 3) but were manually rejected as possible BLH candidates. When
compared to the radiosondes launched in this day, the cluster analysis agrees
well, slightly underestimating the BLH by no more than 100 m in the
first launch and 250 m in the second launch. The cluster analysis
method agrees well during the nocturnal hours, when the algorithm is limited
by height, preventing the detection of the RL, but errors occur when the
nighttime signals are assigned to clusters caused by noise, similar to the
situation shown in Fig. 9b.
Wavelet method results
The Haar wavelet method showed excellent agreement when compared to 48
radiosonde BLHs, with a correlation coefficient of 0.89 (Fig. 6). Statistical
analysis showed a bias of 51.1 m (not statistically significant) and
a standard deviation of 187.0 m (Table 2). Disagreement was found
when aerosol backscatter profiles contained multiple sharp gradients
corresponding to lofted aerosol layers (∼12.5 % of total cases). These
shallow aerosol layers often have stronger gradients than that of the BL. In
these cases, the second-largest gradient is very often the BL (∼67 %).
In addition, another ∼10 % of total cases showed deviations where the
radiosonde-derived BLH did not correspond to the greatest gradient in the
aerosol profile as shown in Fig. 10. This disagreement and positive bias
found can be attributed to the differences in determining BLHs using aerosols
and thermodynamically using radiosondes. Aerosols can penetrate into the
stable layer, transporting aerosols to higher altitudes than the BLH
(inversion height) and causing an overestimation of aerosol-derived BLHs
. Removing the ∼22.5 % of deviations
falling into the cases described above would improve the correlation
drastically (r2=0.98). This provides confidence that all potential
causes of deviations were identified. Overall, the wavelet method showed the
best correlation of all methods when compared to radiosondes. In particular,
this method was superior in the detection of BLHs in profiles with low
aerosol backscatter. Under these conditions it was able to resolve weaker
local maximums, thus reasonably capturing the BLH. This method was also less
affected by noise than the gradient method or the cluster method.
Aerosol backscatter profile (a) on 19 October 2013 at
14:00 CST and corresponding calculated variance profile (b) showing
division of cluster analysis and estimated BLH (1370 m) at the transition
from low to high variance. Radiosonde BLH is shown as a dashed line at
850 m.
Aerosol backscatter profile for 20 October 2014 at 14:00 CST where
radiosonde-derived BLH does not correspond to the height of the largest
negative gradient in the aerosol backscatter profile. Radiosonde BLH at
1290 m is shown as a grey circle, and wavelet-method-derived BLH at 1510 m
is shown as a red circle.
The wavelet method is shown to perform well with the addition of a height
restraint for nocturnal BLH retrievals (Fig. 8) in order to prevent the
detection of RL signals or lofted aerosol layers. Other methods to prevent
the incorrect detection of the BLH include those proposed by ,
, and . However, our study uses the height
restraint as it has been shown to successfully prevent the detection of RL signals
in the example shown in Fig. 8. Both wavelet-estimated BLHs are within
30 m of the radiosonde-derived BLHs. The comparison with the cluster
and gradient methods in Fig. 7 shows that this method generally agrees well
with the aerosol gradient method (r2=0.84) but appears to calculate the
BLH slightly higher, most likely due to differences in the averaging
procedures used. The correlation with the variance method of r2=0.76 is
most likely due to the noise sensitivity of the cluster analysis method and
the calculation of a BLH by using the variance of an aerosol backscatter
profile versus finding a gradient in an aerosol backscatter profile.
BLH retrieval with cloud signals
The identification of the BLH is more difficult in the presence of clouds
when aerosol backscatter algorithms identify the strong signals of the cloud
layer as the BLH. Strong cloud signals (>2000×10-9 m-1 sr-1) can limit the detection of the BLH due to the
extinction of the aerosol backscatter signals above cloud layers. The effect
of these cloud signals is observed for all BLH retrieval methods presented
here (fog or rain events were not analyzed). Although this study observes
daytime cloud signals, continuous ceilometer measurements may find similar
signals during nighttime hours; therefore our findings are not limited to
daytime convective mixed layers.
Aerosol backscatter profiles on 15 September 2013 measured at
09:00 CST (blue), 10:00 CST (black), and 11:00 CST (grey). BLHs retrieved
by each method are shown on all profiles. Cloud layer signals measured at
about 470–870, 1000–1620, and 1000–1520 m for 09:00, 10:00, and
11:00 CST, respectively.
Figure 11 shows hourly aerosol backscatter profiles for 15 September 2013 and
corresponding BLHs retrieved by the aerosol gradient, cluster, and wavelet
methods. Both aerosol gradient and wavelet methods consistently identify the
BLH as the top of the cloud layer due to the large negative gradient created
by strong cloud signals. This is often the height of the thermodynamic BL
identified using relative humidity and dew point temperature methods, which
find the height of the ML as the sharp decrease in moisture at the top of the
cloud layer. Low cloud layers, however, impede the detection of the above
BLH; therefore the aerosol gradient and wavelet method will mistakenly identify
the large gradient of the low cloud layers as the BLH, while the cluster
method will identify the BL as the base of the low cloud layer. The aerosol
gradient method typically found the BLH at the beginning of the large
negative gradient (top of the cloud layer), while the wavelet method
calculated the BLH slightly higher than the aerosol gradient method.
Differences between these two methods were found to not exceed 200 m
and could be attributed to the different averaging settings applied for these
methods.
The cluster method was found to constantly identify the cloud base as the BLH
by assigning aerosol signals into a cluster of cloud signals and a second
cluster of cloud-free signals with the first transition (BLH) of these
clusters located at the base of the cloud layer, for example, at 970 m for
the example shown in Fig. 12. A second transition of clusters is located at
the top of the cloud layer (about 1400 m) corresponding to the BLHs
retrieved by the aerosol gradient and wavelet methods. The cluster method
then essentially calculates the cloud layer depth by assigning a cluster
solely to the cloud layer.
Cluster assignments of aerosol backscatter profile with cloud layer
at about 1000–1520 m on 15 September 2013 measured at 11:00 CST. Automated
BLH was found at 970 m.
The effect of clouds in the overall correlation between aerosol backscatter
methods and radiosonde BLHs in both cloud and cloud-free profiles is seen in
Fig. 13. During a fully developed convective cloud-topped ML, the aerosol
gradient methods agree reasonably well with the radiosonde-derived BLHs.
However, under less developed MLs the agreement decreases due to the aerosol
gradient methods identifying the BLH at the top of a cloud layer, while the
skew-T–log-P method finds the BL at a strong inversion lower than the cloud
layer. This effect can be seen in the radiosonde BLH range of about 800 to
1500 m in Fig. 13. The cluster analysis method showed the highest
decrease in correlation with regard to the cloud-free analysis presented in
Fig. 6 due to the detection of the cloud base.
The presence of clouds creates difficulties in the detection of the BLH for
all methods due to the extinction of aerosol backscatter signals above the
cloud, the presence of low clouds mistakenly identified as the BLH, or the
detection of high cloud signals above the skew-T–log-P-derived BLH. Hence
the removal of profiles with cloud signals is preferred for the automatic
retrieval of the BLH. This affects the cluster and aerosol gradient methods
in particular since the moving time averaging performed before the
application of the algorithms will expand cloud signals to a greater number
of profiles, subsequently eliminating these profiles for BLH detection.
Comparison of CL31 aerosol backscatter BLHs and radiosonde-derived
BLHs including cloud signals. The linear regression lines, regression line
equations, and correlation coefficients r2 are listed for each BLH
retrieval method comparison.
Summary and conclusions
Aerosol-backscatter-derived boundary layer heights from three distinct
methods were tested and compared to radiosonde-retrieved BLHs. An aerosol
gradient method, a cluster analysis method, and a Haar wavelet method were
compared to daytime radiosonde profiles using measured aerosol backscatter
from a Vaisala CL31 ceilometer. This comparison used 47 radiosondes for the
aerosol gradient method, 45 for the cluster analysis method, and 48 for the
Haar wavelet method due to limitations implicit to each algorithm (see
Sect. 4). The first method, the Vaisala Corp. aerosol gradient method,
finds the three largest gradients in an aerosol backscatter profile, one of
which must be chosen as the height of the boundary layer. The second method,
a cluster analysis method, calculates variance in an aerosol backscatter
profile with the BLH correlating to a peak in variance. K-means cluster
analysis then divides a variance profile at the height of the BL (variance
peak). The final method uses a covariance wavelet transform utilizing the
Haar wavelet compound step function to identify a sharp aerosol backscatter
gradient corresponding to the top of the BL by calculating the wavelet
transform at various dilations. The results presented here used daytime
measurements only; however the findings can be applied to similar signals to
those found in the nighttime residual and nocturnal stable layers.
Overall good agreement was found for all methods, with no statistically
significant bias found. Yet all methods found cases where thermodynamic BLHs
from radiosondes did not correlate with a maximum gradient in aerosol
backscatter due to differences in thermodynamic and aerosol BLHs and the
methodology used to derive these heights. The comparison between the aerosol
gradient method and radiosonde-derived BLHs showed difficulties in
determining the BLH in low-aerosol-backscatter conditions. The calculation of
the three largest gradients particular to this method was useful in
situations where the largest gradient does not correlate with the
radiosonde-derived BLH. Yet this requires a priori knowledge of typical boundary layer
heights and evolution in the location of interest. In contrast, the cluster
method showed drawbacks due to sensitivity to noise-generated artifacts or
lofted aerosol layers where the algorithm mistakenly found peaks in variance
and incorrectly identified them as the BLH. Profiles were also mistakenly
divided due to the increasing noise with height rather than a peak in
variance, underestimating the height of the BL. With this automated cluster
analysis method, previous knowledge of the BL aids in identifying such
algorithm errors but is otherwise not necessary. Further work is needed to
improve the cluster method sensitivity to noise and should be kept in mind
when using the cluster method or other variance-based algorithms for BLH
detection. All methods are able to resolve for BLHs under stable and unstable
conditions after manual selection of the calculated aerosol backscatter
gradients reported by the aerosol gradient method and an addition of a
height limit of 500 m for nighttime hours applied to both the wavelet
and cluster methods. The cluster method showed the most variability due to
the incorrect identification of lofted aerosol layer signals as the BLH,
while the aerosol gradient method and the wavelet method BLHs showed very
similar results for the tested time period.
Overall, the wavelet method showed the best agreement of all methods tested
here, with 77.5 % of cases showing excellent agreement with radiosonde BLHs
without previous knowledge of the BL required, as this method is also
automated. The cases where deviations occurred (∼22.5 % of all
observations) were due to multiple sharp gradients corresponding to lofted
aerosol layers and to the thermodynamically derived BLH not corresponding to
the greatest gradient in an aerosol profile (Fig. 10). A bias of
51.1 m was found, indicating that wavelet method BLHs are generally
higher than radiosonde-derived BLHs. This disparity has been previously
attributed to aerosol penetrating into the stable layer above the BLH, leading
to the overestimation of aerosol-derived BLHs .
The wavelet method also showed a higher ability to calculate the BLH under
low-aerosol conditions.
The effect of cloud signals in the determination of the BLH showed a clear
difference between the negative-gradient methods (aerosol backscatter and
wavelet methods) and the cluster analysis method. Both aerosol gradient and
wavelet methods identify the BLH as the top of the cloud layer where a sharp
negative gradient created by strong cloud signals was found, while the
cluster method identified the BLH as the base of the cloud layer. The cluster
method was found to assign a cluster for cloud signal and a cluster for
cloud-free signal along an aerosol backscatter profile (Fig. 12). The
automatic detection of the first transition of clusters identifies the BLH as
the base of the cloud layer with the second transition at the top of the
cloud layer; i.e., it identifies the cloud layer depth. Limited detection of
the BLH in aerosol profiles with cloud signals is seen for all methods
(Fig. 13), with the cluster and aerosol gradient methods being more sensitive
due to the moving time averaging applied, expanding cloud signals to a
greater number of profiles and consequently eliminating these profiles for
BLH detection. Both the wavelet and aerosol gradient methods agree reasonably
well with the radiosonde-derived BLHs in a fully developed convective
cloud-topped ML. Agreement decreases when the aerosol gradient and wavelet
methods identify the BLH at the top of a cloud layer, while the skew-T–log-P
BLHs are calculated at a height lower than the cloud layer under less
developed MLs.
The results presented here demonstrate the ability of the Haar wavelet method
to more accurately detect BLHs than the aerosol gradient and cluster methods
while requiring the least amount of manual inspection. The errors found with
this method were due to lofted aerosol layers, low-level clouds, and
differences in determining BLHs using aerosols and thermodynamically using
radiosondes. In order to use this method on other instruments and locations,
dilation values should be determined carefully and individually. Out of the
three methods tested in this study, it is suggested to employ the wavelet
method in future studies, in particular for long-term seasonal and diurnal
boundary layer studies and spatial analysis of the BL using multiple lidar
aerosol backscatter measurements. A combination of the wavelet method BLH
retrievals during clear skies and the cluster analysis method's ability to
calculate cloud depth is also recommended for more robust BL studies to
retrieve more information about the boundary layer under both conditions, as
both the wavelet and cluster analysis methods were seen to perform well using
various lidar instruments in studies such as ,
, and . Although
not tested in this study, recent work by and
show promising results using an automated method which
reduces incorrect detection of the BLH using graph theory.