To better measure the planetary boundary layer inversion strength (IS), a novel profile-based method of estimated inversion strength (EISp) is developed using the ERA5 daily reanalysis data. The EISp is designed to estimate the IS based on the thinnest possible reanalysis layer above the lifting condensation level encompassing the inversion layer.
At a ground-based site in North America, the EISp correlates better
with the radiosonde-detected IS (R=0.74) than the lower-tropospheric
stability (LTS, R=0.53) and the estimated inversion strength (EIS,
R=0.45). The daily variance in low cloud cover (LCC) explained by the
EISp is twice that explained by the LTS and EIS. Higher correlations
between the EISp and the radiosonde-detected IS are also found at other radiosonde stations of the subtropics and midlatitudes.
Analysis of LCC observed by geostationary satellites and the Moderate Resolution Imaging Spectroradiometer shows that the EISp explains
78 % of the annual mean LCC spatial variance over global oceans and land, which is larger than that explained by the LTS and EIS (48 % and 13 %). Over tropical and subtropical low-cloud-prevailing eastern oceans, the LCC range is more resolved by the EISp (48 %) than by the LTS and EIS (37 % and 36 %). Furthermore, the
EISp explains a larger fraction (32 %) in the daily LCC variance as compared to that explained by the LTS and EIS (14 % and 16 %). The seasonal LCC variance explained by the EISp is 89 %, which is larger than that explained by the LTS and EIS (80 % and 70 %). The LCC–EISp relationship is more uniform across various timescales than the LCC–LTS and LCC–EIS relationships. It is suggested that the EISp is a better cloud-controlling factor for LCC and is likely a useful external environmental constraint for process-level studies in which there is a need to control for large-scale meteorology in order to isolate the cloud responses to aerosols on short timescales.
National Natural Science Foundation of China41875004National Key Research and Development Program of China2016YFC0202000Introduction
The inversion strength (IS) of the planetary boundary layer (PBL) is an
important factor that affects PBL moisture trapping and low-cloud formation. Strong IS inhibits the dry air above the inversion from being incorporated into the PBL and traps moisture below the inversion to favor greater cloud cover (Wood and Bretherton, 2006; Mauger and Norris, 2010). In contrast, weak IS promotes the drying effect of entrained air from the free
troposphere and reduces the PBL moisture to decrease cloud cover (Bretherton and Wyant, 1997; Myers and Norris, 2013). Currently, two approximate measures of the IS based on reanalysis data are widely used as meteorological constraints on low cloud cover (LCC): the lower-tropospheric stability (LTS; Klein and Hartmann, 1993) and the estimated inversion strength (EIS; Wood and Bretherton, 2006). They are both defined as a two-level potential temperature (θ) difference between the 700 hPa level and the surface, but for the EIS the moist adiabatic θ increase above the lifting condensation level (LCL) is additionally removed. The EIS can be combined with the moisture difference between the 700 hPa and surface to form a new stability index, the estimated cloud-top entrainment index (ECTEI). The ECTEI and the EIS have similar correlations with LCC on the seasonal timescales (Kawai
et al., 2017).
The LTS and EIS are the best known and most widely used cloud-controlling
factors for the explanation of LCC variations. Enhanced LTS can moisten PBLs and has
been shown to precede LCC changes by about 24–36 h
(Mauger and Norris, 2010; Klein, 1997). Similarly,
Myers and Norris (2013) found that the EIS is the main cause of
LCC variations, and enhanced subsidence actually decreases LCC for the same
value of the EIS. These LCC–LTS and LCC–EIS relationships are vital for not only
separating observational aerosol effects on clouds from meteorological
influences (L'ecuyer et al., 2009; Rosenfeld et al., 2019; Murray-Watson
and Gryspeerdt, 2022; Coopman et al., 2016) but also estimating low cloud
climate feedbacks (Klein et al., 2017; Sherwood et al., 2020). In terms
of aerosol–cloud interactions, the LTS and EIS can be used to constrain
meteorological influences and thus largely reduce the confounding influence
of meteorology to separate aerosol effects on low clouds (Mauger
and Norris, 2007; Coopman et al., 2016), since LCC variations are most
explained by the LTS and EIS among all the LCC-controlling meteorological factors
(Stevens and Brenguier, 2009). Without strong cloud-controlling factors,
the confounding influence of meteorology is poorly constrained, and over half
of the relationship between aerosol optical depth and LCC results from
meteorological covariations (Gryspeerdt et al., 2016). Besides, in
climate projections, Webb et al. (2012) found that most climate
models cannot reproduce the observational LCC–LTS and LCC–EIS relationship, and thus
low cloud feedbacks have the largest spread among climate models. To help
constrain future climate projections, the LTS- and EIS-induced low cloud feedback
can be more accurately estimated by multiplying the observational
LCC–LTS and LCC–EIS sensitivity by the LTS and EIS changes of climate model projections
(Webb et al., 2012; Qu et al., 2014; Myers and Norris, 2016; Klein et
al., 2017; Mccoy et al., 2017; Myers et al., 2021; Seethala et al., 2015;
Kawai et al., 2017).
Although the LTS and EIS are best correlated with LCC among all meteorological
factors, the LTS and EIS only explain a small portion of LCC variance on short
timescales. A total of 12 % of daily LCC variance are explained by the LTS, but when
the monthly means are subtracted from the data, only 4.8 % of the daily LCC
variance are explained by the LTS at the subtropical ocean weather station
(OWS) N (Klein, 1997). Similarly, when the monthly means are
removed, only 4 % of daily LCC variance are explained by the EIS over the
typical subtropical eastern oceans (Szoeke et al., 2016). LCC
on daily time scales is not as well explained by the LTS/EIS as the LCC on
longer time scales. But the LCC sensitivity to LTS/EIS is assumed to be
time-scale invariant to estimate the LTS/EIS-induced low cloud feedback and
thus leads to some uncertainty (Klein et al., 2017). The
explanation for the variant relationship between LCC and LTS/EIS across
different time scales is not clear. And it is also not known whether the LTS
and EIS can approximate the IS with the same accuracy across different time
scales.
Grounded on the well-mixed condition, the PBL's thermal structure is
relatively simple, and both the LTS and EIS are likely to be good measures of IS.
However, the actual PBL thermal stratification may not always be well mixed.
In deep decoupled PBLs, a strong stratification with a large θ
increase between cloud layers and surface-mixed layers would exist
(Jones et al., 2011; Nicholls, 1984). In this case, both
the LTS and EIS likely count the stable layer of the decoupling into the IS
estimates and thus overestimate the real IS atop the PBL. Previous studies
also showed that the free-tropospheric lapse rate has small biases and large
spreads, although on average it is close to the moist adiabat on daily timescales (Wood and Bretherton, 2006). Thus, further refinements of
the algorithm for IS estimations are possible if we can reduce the biases and
errors resulting from the deviations from the well-mixed conditions. Given
the importance of the LTS and EIS for studies of cloud–aerosol interactions and
climate predictions, a better measure of the IS can lead to more accurate
quantification and increasing confidence in these fields. Based on the
previous EIS framework, this study further establishes a profile-based EIS
(EISp) algorithm to take advantages of the reanalysis and thus to estimate more
accurately the IS.
This paper is laid out as follows: Sect. 2 briefly describes the
observation and reanalysis data and introduces methodologies used in our
analysis; Sect. 3 illustrates the development and validation of the new
EISp; Sect. 4 evaluates the relationship between LCC and EISp at
the global scale, with conclusions in Sect. 5.
Data and methods
Data used in this study include the following: (1) high-vertical-resolution radiosondes
and cloud radar and lidar observations from the ground site of the Atmospheric
Radiation Measurement (ARM) Program; (2) radiosondes of several subtropical
and midlatitude stations from the Integrated Global Radiosonde Archive
(IGRA) of the National Oceanic and Atmospheric Administration (NOAA); (3)
global satellite observations of LCC; (4) the fifth-generation atmospheric
reanalysis from the European Centre for Medium-Range Weather Forecasts
(ECMWF). Methodologies of data processing are also introduced.
Radiosonde and cloud observations at the ground-based sites
Long-term ground-based observations are from two sites of the ARM Program at
the southern Great Plains (SGP) and the eastern North Atlantic (ENA)
(Ackerman and Stokes, 2003). ARM was established by the US Department of
Energy's Office of Biological and Environmental Research to provide an
observational basis for studying the Earth's climate. At the SGP observatory
(97.5∘ W, 36.6∘ N and 318 m above sea level) and the ENA observatory (28.1∘ W,
39.5∘ N and 30 m a.s.l.), high-quality
radiosondes and cloud radar and lidar observations are provided to validate
the new algorithm of EISp and to investigate the relationship of IS and IS
estimates (i.e., LTS, EIS and EISp) with LCC. However, the ENA is
located on Graciosa Island in the midlatitude ocean, where low clouds
frequently occur but with no inversion (Norris, 1998) so that
it is not an ideal site to investigate the relationship of LCC with IS.
Thus, the observations at the ENA are only used to validate the accuracy of
EISp by comparing with the radiosonde-measured IS.
The atmospheric temperature, relative humidity (RH) and pressure profiles
measured by the SGP balloon-borne sounding system (SONDE) from 2002 to 2011
are used. The sondes at the SGP are launched four times a day at 05:30,
11:30, 17:30 and 23:30 UTC. To avoid the
diurnal-cycle influence on our analysis, only the sondes launched at 17:30 UTC (11:00 LT) are used. At this time, the PBL is relatively more
well mixed by turbulence with more uniform vertical distribution of θ than at the other times of the day (Liu and Liang, 2010). The data at
different times are also tested, and they come to similar results. The
precision of the sonde-measured temperature, RH and pressure is 0.1 K, 1 %
and 0.1 hPa (Ken, 2001), respectively. Their accuracy is 0.2 K,
2 % and 0.5 hPa, respectively (Ken, 2001). Its vertical
resolution is normally about 10 m from the ground level up to 30 km. The
sonde temporal resolution is less than 2.5 s with 6m s-1 ascent rate at the
1000 hPa level. The θ profile is computed from the sonde temperature
and pressure profiles as follows:
θ=T1000pRacpa,
where Ra is the specific gas constant of dry air, and cpa is the
specific heat capacity for dry air at constant pressures. T and p are the
sonde temperature and pressure. The θ vertical-gradient (dθ/dz) profile is derived from the θ difference between two adjacent
levels:
(dθdz)zi+1+zi2=θi+1-θizi+1-zi,
where z is the height above the ground level (AGL). The subscript “i”
indicates the ith level detected by the sonde.
Cloud profiles are observed every 10 s by the 35 GHz millimeter-wavelength
cloud radar and the micro-pulse lidar from 2002 to 2011 at the SGP. The ARM
best-estimate cloud radiation measurement (ARMBECLDRAD) product is used
(Chen and Xie, 1996), which provides radar and lidar cloud
profiles derived from the Active Remote Sensing of Clouds (ARSCL). Its
vertical resolution is 45 m. To match the sonde launched at 17:30 UTC,
the hourly segment of cloud measurements during 17:00–18:00 UTC is used. The
cloud base and top heights of an hourly segment are recognized as the
lowest and highest levels of cloud layers (non-zero cloud fraction) detected in
that hourly segment. In a cloud profile, distinct cloud layers are separated
by a minimum distance threshold of 250 m (Li et al., 2011). Low
clouds are defined as having a cloud base height of less than 3 km and a top height of
less than 4 km. These low clouds are dominated by stratus, stratocumulus and
shallow cumulus clouds (Dong et al., 2005). Segments of
solely other types of clouds but no low cloud are excluded in our analysis.
Segments that have low clouds but with other clouds aloft are kept. The LCC
of an hourly segment is defined as the ratio of the number of cloudy
profiles to the total number of profiles in that segment.
These hourly segments are further sorted into three categories: clear sky,
coupled cloudy and decoupled cloudy segments. Clear sky segments are those
in which no cloud is present within that segment. The coupled and decoupled
cloudy segments are segments containing low clouds in coupled and decoupled
PBLs, respectively. A straightforward indicator to distinguish coupled and
decoupled PBLs is the height difference between the cloud base and the LCL
(Δzb) (Jones et al., 2011). When the PBL is well
mixed, Δzb is close to zero, but in the decoupled PBLs the
cloud and subcloud layers would be separated by a stable layer, and the LCL
may diverge from the cloud base by hundreds of meters with large Δzb (Nicholls, 1984; Jones et al., 2011). The threshold
value of Δzb is empirical; for different instrument
capability, vertical resolution and locations, the threshold may be a little
different. In reference to the linear least-squares fit between Δzb and Δθ in Jones et al. (2011), where 150 m of Δzb correspond to 0.5 K of the θ
difference in the subcloud layer, a similar linear relationship is found, but
the slope is a little different in that 180 m of Δzb
corresponds to 0.5 K of the θ difference at the SGP site. Thus, at the
SGP site, a threshold value of 180 m for Δzb is used to
distinguish coupled and decoupled PBLs.
At the ENA, data of radiosondes and LCC from 2014 to 2020 are used. The data
product and processing method of the ENA site are the same as those of the
SGP. The ENA site is characterized by marine stratocumulus clouds but at
midlatitudes, where the correlation between LCC and IS is much weaker as
compared to that at the SGP. This will be verified and discussed later.
Radiosonde stations of subtropics and midlatitudes
The IGRA of NOAA collects radiosondes from globally distributed stations
(Durre et al., 2018; Durre et al., 2006). The radiosonde temperature, RH,
pressure and geopotential height profiles in the IGRA are used. The θ and θ gradient profiles are computed from Eqs. (1) and (2). These
atmospheric parameters of radiosondes are available at the standard pressure
levels (1000, 925, 850, 700 and 500 hPa) or variable levels. It provides
reliable instantaneous observations for the PBL IS (see definitions in
Sect. 2.5). However, most low-cloud-dominated regions are over the ocean
with no available radiosondes in the IGRA. Thus, five radiosonde stations
with relatively higher occurrence frequencies of low clouds are selected:
the OWS N in the subsidence and steady trade wind circulation of the
northeast Pacific (Klein, 1997; Klein et al., 1995), the
OWS C in the frequently decoupled PBLs of the North Atlantic
(Norris, 1998), the tropical East Pacific coast with the
classic stratocumulus condition (Albrecht et al., 1995), the
southeast Pacific coast with the stratocumulus-capped PBLs
(Bretherton et al., 2004) and the southeast Chinese coast of
subtropical low-cloud domains (Klein and Hartmann, 1993).
Locations, observational period and time of data for each station are listed
in Table 1.
The location, observational period and time of the IGRA radiosonde
stations.
Global LCC observations of the geostationary satellites (GEOs) and the
Moderate Resolution Imaging Spectroradiometer (MODIS) on board the Aqua and
Terra satellites are provided by the Clouds and the Earth's Radiant Energy
System (CERES) project (Doelling et al., 2013, 2016;
Trepte et al., 2019). Global hourly LCC between 60∘ S and 60∘ N during
2006–2011 is used. It is available in the Synoptic 1 ∘ (SYN1deg)
edition 4.1 product of the CERES project (Doelling et al., 2013, 2016; Trepte et al., 2019). The GEO-MODIS LCC here refers to the
cloud area fraction of the identified cloudy pixels with cloud top pressure
above 700 hPa divided by the total number of pixels in the 1∘×1∘ grids. The MODIS pixel-level cloud identification is based on the
CERES MODIS cloud algorithm (Minnis et al., 2008, 2011).
The sampling frequency of clouds derived from the MODIS narrowband radiance
is four times a day (two from each of the Aqua Terra). GEOs with radiances
calibrated against the MODIS provide hourly cloud retrievals between MODIS
observations (Doelling et al., 2013). The GEO cloudy pixel
identification is also based on the CERES-MODIS-like cloud algorithm to
achieve more uniform MODIS and GEO clouds. An advantage of this product over
cloud retrievals of the first-generation GEO is that the CERES project uses
the latest generation of the GEO imager capability with more additional
channels to enhance the accuracy of cloud retrievals (Doelling
et al., 2016). Hourly LCC is used to match the IGRA radiosondes. Daily LCC
used in Sect. 4 is the mean of the full-day hourly GEO-MODIS LCC from the
CERES SYN1deg edition 4.1 product (Doelling et al., 2016).
The fifth-generation ECMWF atmospheric reanalysis (ERA5)
Reanalysis data from the ECMWF are to provide the atmospheric profile
information. The ERA5 combines observations with model outputs by the 4D-Var
assimilation to achieve the 1 h resolution (Hersbach et al., 2020).
The hourly atmospheric temperature, RH, geopotential profiles in the ERA5
dataset are used to match the SGP, IGRA and GEO-MODIS observations. The
θ and θ gradient profiles are computed based on Eqs. (1) and
(2). Atmospheric profiles at the 16 pressure levels between 500 and
1000 hPa are available. At the SGP site, the ERA5 atmospheric profiles
between the years 2002 and 2011 at the grid point (97.5∘ W,
36.625∘ N) nearest to the SGP site (within about 2.8 km) are
used. For the IGRA radiosonde stations, the ERA5 hourly data of the
0.125∘ grid point nearest to them during the same observational period
are used. At the global scale, the ERA5 atmospheric profiles are averaged to
1∘ resolution data, centered at 0.5∘, 1.5∘,… during the years between 2006 and 2011. This resolution is
consistent with the global LCC data. Those three metrics, LTS, EIS and
EISp, are then computed based on the 3 h 1∘ ERA5 atmospheric
profiles. All metrics at longer (i.e., from daily to seasonal) timescales
are computed from the 3 h metrics.
LTS, EIS and radiosonde-measured IS
The LTS and EIS over the ocean are defined as follows:
3LTS=θ700hPa-θ0,4EIS=LTS-Γm(z700hPa-zLCL),
where θ and z are, respectively, the potential temperature and the
height. The subscripts “700 hPa”, “0” and “LCL” indicate the levels of
700 hPa, 1000 hPa and the LCL, respectively. zLCL is calculated using
temperature and RH at 1000 hPa based on the exact expression in Romps (2017), indicating the height at which an air parcel would saturate if
lifted adiabatically. Γm is the moist adiabatic θ
gradient at 850 hPa calculated using the mean temperature of the 1000 and
700 hPa levels. Γm can be calculated as follows:
ΓmT,p=1000pRacpa⋅gcpa1-1+LvqsT,p/RaT1+Lv2qsT,p/cpaRvT2.qs is the saturated mass fraction of water vapor. Lv is the latent
heat of vaporization. Rv is the specific gas constant for water vapor.
Over land, the LTS and EIS are computed following Eqs. (3)–(5) but based on
the heights of 0.15 and 3 km a.g.l. The height of the initial air parcel, set
as 0.15 km a.g.l., is to avoid noisy and contaminated readings of the RH near the
surface from the radiosondes and the influence of surface layers (Liu and
Liang, 2010). The temperature, RH and pressure at 0.15 and 3 km a.g.l. over land can be directly derived from the radiosondes or linearly interpolated
from the ERA5 profiles. zLCL over land is calculated using the
temperature and RH at 0.15 km a.g.l. Γm over land is computed
using the mean temperature and pressure of the two heights.
To derive the IS from the radiosonde profiles, the layer of the greatest
θ gradient (dθ/dz) between the LCL and 5 km a.g.l. is firstly
identified, similarly to Mohrmann et al. (2019) but with an LCL
constraint to guarantee that it is above the cloud layer. For the SGP
high-resolution (10 m) radiosondes, the inversion top and base are defined
as the nearest levels above and below the layer of maximum dθ/dz, where
dθ/dz is equal to three-fourths of maximum dθ/dz. The IS is defined as
the θ jump across the inversion layer after removing the θ
increase due to the moist adiabat in this layer:
IS=θIST-θISB-ΓmISBzIST-zISB.
The subscripts “IST” and “ISB” indicate the identified top and base
heights of the corresponding layers, respectively. ΓmISB is the
moist adiabatic dθ/dz computed from Eq. (5) using the temperature and
pressure at the identified inversion base. The method that determines the IS
in low-resolution soundings of IGRA is exactly the same as the new
profile-based method of EIS and will be introduced in detail in Sect. 3.1.
t test and multiple timescale analysis
In our study, the Pearson's correlation coefficient (R) and the slope of the
least-squares linear fit are used. R square is used with a minus or plus sign
for a negative or positive correlation. The existence of a correlation and
confidence interval for the true mean value (μ) is estimated based on
the t test. The number of independent samples is determined by dividing the
total length of samples by the distance between independent samples
(Bretherton et al., 1999). All correlations listed in this study
are at the 95 % significance level if there is no mention of their
significance. The confidence bound of R is computed based on the Fisher z
transformation. The confidence interval of the slope is computed from the
residual error of the least-squares linear fit. Besides, for isolating the
correlation and the regression slope on different timescales, window
anomalies are defined as being consistent with those in Szoeke et al. (2016):
xΔi=[x]Δi-[x]Δi+1.
The brackets represent the mean of x over the window of length Δ. The
superscripts Δi and Δi+1 are the ith window length
and the next longer window length.
The profile-based method of EIS (EISp)
In this section, the new EISp algorithm is established based on
ground-based observations at the SGP and validated at other radiosonde
stations of the subtropics and midlatitudes. In Sect. 3.1, the new EISp
algorithm is described. In Sect. 3.2, at the SGP site with long-term
10 m resolution radiosondes, two questions are discussed: (1) why and how is
EISp a better estimate for the IS than LTS and EIS? (2) How well does
EISp control LCC as compared to LTS and EIS when it is a better
estimate for the IS? In Sect. 3.3, the EISp is further validated at
radiosonde stations of the subtropics and midlatitudes.
An illustration of finding the location of three possible layers
encompassing the inversion between the LCL and 5 km a.g.l. in ERA5 or coarse
sounding profiles. The red block is one single layer of (dθ/dz)max that includes the inversion. The blue and green blocks are a
combination of two adjacent layers if the inversion is distributed into the
two layers but not just in the layer of (dθ/dz)max.
EISp 1–3 are computed accordingly, and the largest value among them is
regarded as the true EISp.
The algorithm of the new EISp
The EISp is designed to capture the IS information from the thinnest
layer encompassing the inversion in low-resolution (hundreds of meters)
atmospheric profiles. For these coarse-resolution profiles (e.g., ERA5), it
is difficult to accurately locate the exact place of the inversion because,
usually, the thickness of the inversion is much smaller than the distance
between two adjacent vertical levels. Thus, only one or two adjacent layers
that could encompass the inversion are located. The latter is for the
consideration that an inversion layer may be across two adjacent layers of
the ERA5. Specifically, the EISp is computed as follows:
Locating the layer of the maximumθvertical gradient(dθ/dz)max.
For each hourly ERA5 profile, the layer of (dθ/dz)max is
firstly located between the LCL and 5 km a.g.l. (the red zone in Fig. 1), since
the inversion only features strong gradients in thermodynamical properties.
Finding the layers encompassing the full inversion.
The layer of (dθ/dz)max may not encompass the full inversion if
the inversion crosses two adjacent layers of the ERA5. Thus, the layer of
(dθ/dz)max is combined with an adjacent layer just above and
below it, respectively, to constitute another two candidate layers that could
encompass the full inversion (the blue and green zones in Fig. 1).
Calculating the EISp.
The EISp is calculated for the three possible layers identified in the
second stage, respectively:EISp=θtop-θbase-Γmztop-zbase,where subscripts “top” and “base” represent the top and base levels of a
candidate layer. Γm is computed using Eq. (5) at the base level.
The θ increase of the moist adiabat is removed to extract the
strength of the inversion between the top and base levels, which is
consistent with the EIS framework in Wood and Bretherton (2006).
The final EISp is determined by which layer in Fig. 1 encompasses the
stronger inversion computed from Eq. (8) and thus refers to the largest
value among the three candidates EISp 1–3.
The EIS (Wood and Bretherton, 2006) assumes that the PBL is well
mixed (dry adiabat below the LCL and moist adiabat above the LCL) for
estimating the IS. If that is the case, EISp would give the same
results as EIS. However, it will be shown in the following sections that the
actual PBL often deviates from the well-mixed conditions, where the
EISp provides a physically more reasonable estimate for the IS than the
EIS and thus a stronger cloud-controlling factor.
When high-resolution radiosondes are available, the exact IS can be obtained
fairly straightforwardly (Sect. 2.5, Eq. 6). The computation of EISp is
in fact adapted from the algorithm for obtaining the IS from high-resolution
radiosondes but is adjusted to suit coarse-resolution atmospheric profiles
in reanalysis. Because high-resolution soundings are rare, an applicable
metric derived from reanalysis would be much more beneficial. Because the
IGRA soundings have similar vertical resolutions as ERA5 in the lower
troposphere, the IS of these soundings (used in Sect. 3.3) is derived in
exactly the same way as the EISp.
Illustrations of PBL θ profiles (a), with the LCL heights
indicated by dashed horizontal lines and the moist adiabat represented by
light dashed lines. PDFs of the θ difference between the LCL and 150 m a.g.l. (b), the θ difference with the moist adiabat removed between the
LCL and the inversion base (c), and the θ difference with the moist
adiabat removed for the free troposphere between the inversion top and 3 km a.g.l. (d). The red, blue and black lines are for coupled cloudy, decoupled
cloudy and clear-sky segments, respectively. In (c), the θ
differences of decoupled cloudy segments are further separated into those
between the LCL and the cloud base (dashed blue line) and those between the
cloud base and the inversion base (solid blue line).
PBL stratification and the establishment of the EISp at the SGP
The characteristics of PBL thermal structures are examined by using the SGP
high-resolution radiosondes as shown in Fig. 2. Figure 2a illustrates an
idealized θ profile of the well-mixed condition consistent with
Wood and Bretherton (2006) and an idealized θ profile of
the decoupled PBLs based on the observations in Jones et al. (2011). The primary difference in the θ profiles between the coupled
and decoupled PBLs is whether a stable layer exists to decouple the cloud
and subcloud layers (Nicholls, 1984). Hence, under the decoupled
conditions, the LTS and EIS would include the sum of the PBL IS and the
θ increase from the ground to the LCL (the blue line in Fig. 2a).
The LTS and EIS can be separated into different terms:
9aLTS=θLCL-θ0+Δθ+IS,9bEIS=θLCL-θ0+(Δθ-ΓmΔz)+IS,9cΔθ=θ3km-θLCL-IS,9dΔz=z3km-zLCL.
The subscripts of “3 km”, “0” and “LCL” indicate the levels of 3 km,
150 m a.g.l. and LCL. If over oceans, the levels of 3 km and 150 m can be replaced with 700 and 1000 hPa. In Eq. (9a), the LTS can be regarded as the sum of the θ difference between the LCL and 150 m a.g.l.
(θLCL-θ0), the θ increase (Δθ) due to the actual θ gradient above the LCL, and the PBL IS. Similarly, in Eq. (9b), the EIS is similar to the LTS, except for the fact that the θ increase due to the moist adiabat (ΓmΔz) above the LCL is removed. It can be seen that the first two terms on the right-hand side of Eq. (9a) and (9b) contribute to the LTS and EIS even though they are not a part of the IS. In the well-mixed PBLs, the two terms θLCL-θ0 and Δθ-ΓmΔz are both equal to zero. Thus, the EIS defined by Eq. (9b) is exactly the IS, and the LTS defined by Eq. (9a) is equal to IS+ΓmΔz under perfectly well-mixed conditions.
At the SGP site, 29 %, 32 % and 39 % observational samples are
classified into the coupled cloudy, decoupled cloudy and clear-sky segments,
respectively. Note that the Δzb method cannot distinguish
whether the PBL is coupled or decoupled when a segment has no low cloud.
Thus, the clear-sky segments might contain both coupled and decoupled PBLs. The following is noted about
Fig. 2b: (1) the probability distribution functions (PDFs) of θLCL-θ0 for the coupled cloudy segments peak at zero and have relatively positive skewness. The exact reason for the positive skewness
is not clear. Because the height of the LCL being close to the simultaneously
observed cloud base height is only a necessary condition of a PBL being
coupled, a decoupled surface layer and overlaying cloud layer coincidently
having the height of an LCL close to the cloud base is not a surprise. Either the advection of clouds from other places or the development of a new surface stable layer while clouds that were formed earlier are still left above might result in
positive θLCL-θ0. (2) Strong stratification below the LCL
(large positive θLCL-θ0) frequently occurs in the
decoupled cloudy and clear-sky segments, with mean values of 6.3 and 11.5 K,
respectively. Thus, the non-zero term of θLCL-θ0 will
cause LTS and EIS to largely deviate from the real value of IS in the
decoupled cloudy and clear-sky segments.
Besides, a premise of using LTS and EIS to measure the IS is that the
lower-tropospheric θ gradient can be predicted by the moist adiabat
above the LCL. This moist adiabatic assumption is supported in previous
studies but still with some uncertainties on the daily timescales
(Stone, 1972; Wood and Bretherton, 2006; Schneider and O'Gorman, 2008).
According to PDFs of the θ difference between the LCL and inversion
base or between the inversion top and 3 km a.g.l. with the moist adiabat removed
(Δθ-ΓmΔz), θ likely follows the moist
adiabat above the LCL (Fig. 2c and d), with a peak at zero, but all PDFs of
Δθ-ΓmΔz have broad distributions. The standard
deviation of Δθ-ΓmΔz above the LCL is about 4 K.
Note that, here, the Γm is computed using Eq. (5) but is based on
the temperature and pressure at the base level of each layer.
Typically, the real IS is less than 10 K. Thus, the term θLCL-θ0 in Eq. (9a) and (9b) will cause a strong overestimation of the IS by
the LTS and EIS. Furthermore, the variation of the LTS and EIS is attributed not
only to variations of IS but also to variations of the systematical deviations of
temperature profiles from the dry adiabat below the LCL. As a result, at the
SGP site, the decoupled cloudy and clear-sky segments (with weak IS but
large θLCL-θ0) are mixed with the coupled cloudy
segments with strong IS when using the LTS and EIS to sort data. Large
values of LTS and EIS correspond not only to strong IS but also to weak IS with
strong stratification below the LCL. On short timescales (like the daily
scale), the spread of Δθ-ΓmΔz (Fig. 2c and d)
resulting from the θ gradient deviating from the moist adiabat above
the LCL could add additional uncertainty into the LTS and EIS. Hence, weak and
even unphysical relationships of clouds and moisture with the LTS and EIS might
exist.
(a–c) LCC composites of the coupled cloudy (red line) and
decoupled cloudy segments (blue line) and the occurrence frequency of the
clear-sky segments (black line). (d–f) Composited RH profiles.
Composites are based on the SGP radiosonde-measured LTS (a and d), EIS (b, and e) and IS (c and f), respectively. Error bars in (a–c) show
the 95 % confidence interval of the mean based on the t test. The solid
and dashed black lines in (d–f) indicate the average height of the
inversion center and the LCL, respectively. All composites are based on
daily data of all seasons for the full period at the SGP.
Figure 3a–c shows that the composited LCCs of cloudy segments are all
positively proportional to the radiosonde-measured LTS, EIS and IS. However,
the composites of LCC are slightly (significantly) more sensitive to the
changes of IS than the changes of LTS (EIS). The occurrence frequency of the clear-sky
segments (the number of clear-sky segments divided by the number of total
segments) is investigated separately. Figure 3c shows that clear-sky segments
are rarely observed when the IS is very strong (∼0 % at
10 K) and more frequently exist with weaker IS (60 % at 0 K). This is
consistent with the fact that stronger IS inhibits the entrainment of dry air from
the free troposphere and thus favors the formation and maintenance of low
clouds and corresponds to less occurrence of the clear sky. On the contrary,
such a physically reasonable expectation is not seen (even qualitatively) in
the composites of the clear-sky segments based on the LTS and EIS. Figure 3a–b shows that the occurrence frequency of clear-sky segments changes little
(even increases) with increasing LTS (EIS). This is also expected based on
Fig. 2b showing the existence of a large positive skewness in the term
θLCL-θ0 in the clear-sky segments. This strong static
stability below the LCL results in large LTS and EIS, even when the real IS
is weak.
Composited moisture distribution shows information that is consistent with the LCC
composites. Figure 3f shows that the composited RH has an increasing trend
towards stronger IS, and high values of RH (RH>80 %) are
restricted below 1 km a.g.l. at the large IS value bins. However, the composited
RH distribution is completely reversed when sorted by the EIS, with high (low)
RH being related to weak (strong) EIS (Fig. 3d). The RH distribution sorted by the
LTS has a similar dependence on the magnitude of the LTS (Fig. 3c) as the IS does,
but with weaker variations and smaller PBL RH as compared to the composites
based on the IS (Fig. 3e). Thus, respectively, the LTS and EIS poorly and incorrectly represent
the IS at the SGP site; hence, the dependence of the PBL moisture
conditions and LCC on the IS are weakly and erroneously reproduced by the
LTS and EIS.
Joint PDFs of the θ difference (Δθ) between
the levels of 3 km and the LCL (with the IS excluded) and θLCL-θ0(a), and PDFs of LCC and θLCL-θ0(b). Joint PDFs of the absolute value of the θ difference with the
moist adiabat removed (Δθ-ΓmΔz) and the height
difference (Δz) from the LCL to the inversion base (c) and from the
inversion top to 3 km in the free troposphere (d). Correlation coefficients
(R) are listed in the upper-right corner of each panel. The dashed black lines
indicate the least-squares fit.
An interesting phenomenon is that the LTS overall performs better than the
EIS with respect to constraining LCC at the SGP site. To understand why this
happens, the LTS and EIS in Eq. (9) both have been separated into three
terms to discuss. For the LTS, the two terms θLCL-θ0 and
Δθ of Eq. (9a) usually offset each other, with a negative
correlation of -0.56 and a slope of the least-squares fit of -0.5 K K-1 (Fig. 4a).
In contrast, the slope of the least-squares fit between Δθ-ΓmΔz and θLCL-θ0 is only
-0.05 K K-1 (not shown). Furthermore, the LTS and EIS equation can be
transformed into the following:
10aLTS=1+ΔθθLCL-θ0θLCL-θ0+IS,10bEIS=1+Δθ-ΓmΔzθLCL-θ0θLCL-θ0+IS.
On average, the coefficient before θLCL-θ0 for the LTS
in Eq. (10a) is 0.5, while that for EIS in Eq. (10b) is 0.95. The variations
of LTS and EIS result from both the changes of IS (positively correlated
with LCC, as shown in Fig. 3c) and the changes of θLCL-θ0 (negatively correlated with LCC, as
shown in Fig. 4b). According to Eq. (10a) and (10b), the LTS actually only
involves half of the bias caused by θLCL-θ0 and is thus not as strongly influenced by θLCL-θ0 as the EIS. As a result, removing only
the moist adiabat (ΓmΔz) does not make the EIS a better
estimate for the IS at the SGP but instead makes the EIS more influenced by θLCL-θ0. This explains why the LTS is better
correlated with LCC and RH (Fig. 3a and d) than the EIS (Fig. 3b and e)
at the SGP. However, the physical reason why the PBL stratification
changes in this way is unclear to us, and it is beyond the scope of this
study.
As shown in Fig. 2c and d, the θ difference between the
actual environmental θ gradient and the moist adiabatic θ
gradient (Δθ-ΓmΔz) is another source of
uncertainty in the EIS based on Eq. (9b), especially on short timescales.
However, Fig. 4c and d suggest that the spread of |Δθ-ΓmΔz| increases with the layer thickness, either
between the LCL and the inversion base or between the inversion top and 3 km a.g.l. (with a correlation of 0.59 or 0.58, respectively). Thus, the thicker
the layer encompassing inversion involved in the EIS calculation is, the
larger the uncertainty is. Including more layers around the inversion layer
in estimating the IS likely results in more uncertainty. This suggests a
possible way of better estimating the IS if we can reduce the layer
thickness (Δz) associated with the second term on the right-hand side of Eq. (9b), which also makes the IS estimate less dependent on the moist adiabatic assumption.
The above results suggest that there are two major bias and error sources when
estimating the IS using the LTS and EIS metrics. One is caused by systematic
deviations from the dry adiabat below the LCL, and the other is the errors
resulting from the spread of the actual θ gradient around the moist
adiabat above the LCL. To exclude the former source, we can locate the LCL
and only consider the inversion above the LCL to drop the first term on the
right-hand side of Eq. (9b). The impact of the latter one can be indirectly reduced by
finding the thinnest layer encompassing the inversion that is involved in
the computation of the second term on the right-hand side of Eq. (9b). Thus, the new
EISp (as described in Sect. 3.1) is proposed accordingly to achieve a
better estimate of the IS.
Joint PDFs of the SGP radiosonde-measured IS and the ERA5-derived
LTS (a), EIS (b) and EISp(c), respectively. In (a–c), the solid black line is the least-squares fit, and the dashed line is the reference line
of y=x. The composites of the radiosonde RH profiles based on the
ERA5-derived LTS (d), EIS (e) and EISp(f). The solid black and dashed
lines in (d–f) are the heights of the IS and the LCL, respectively. The LCCs
composited based on the LTS, EIS and EISp are shown in (g–i), respectively. The cycles in (g–i) correspond to the 5 %
and 95 % quantiles of LTS, EIS and EISp and the composited value of
LCC in the bins of the smallest and largest 10 % of LTS, EIS and EISp
values. Error bars in (g–i) show the 95 % confidence interval of the mean
based on the t test.
The LTS, EIS and EISp derived from the hourly ERA5 reanalysis are
directly compared against the SGP radiosonde-measured IS. In Fig. 5c, the
R square between the EISp estimated from the ERA5 and the IS measured
by radiosondes is 0.55, which is much larger than those of the LTS (0.28,
Fig. 5a) and EIS (0.20, Fig. 5b). The slope of the least-squares fit of the
IS to the EISp is 0.86 K K-1. This indicates that the value of the EISp is
much closer to the IS as compared to the LTS (0.26 K K-1) and EIS (0.19 K K-1).
The composites of LCC and RH based on the EISp (Fig. 5f) show similar
results to that based on the IS (Fig. 3f). Stronger EISp corresponds to
larger RH trapped below about 1 km, and with the EISp weakening and the
inversion layer lifting, RH decreases but distributes to higher levels.
However, the LCC and RH composites based on the LTS and EIS (Fig. 5d, e,
g and h) show weak or erroneous relationships similar to the results based
on the radiosonde-measured LTS and EIS (Fig. 3a, b, d and e). Thus, the
EISp offers a better fit to the real IS and better constrains the PBL
moisture distribution and LCC. The slope of the composited LCC to the
EISp is 6 % per kelvin, in contrast to that of the LTS (1.9 % per kelvin) and the EIS
(0.4 % per kelvin). Since the ranges of the LTS and EIS are larger than that of the
EISp, larger slopes of the LCC to the EISp than those to the LTS
and EIS are expected. To measure the sensitivity of LCC to changes of LTS,
EIS and EISp, we consider the effective range of LCC resolved by
changes in a metric. The sensitivity of LCC to a metric here is defined as
the difference between the composited LCC values associated with the largest
and smallest 10 % of that metric:
LCC Sensitivity to x=LCC(x≥x90%)‾-LCC(x≤x10%)‾.
The bar over the LCC head represents the mean value of LCC sorted by x
quantile. x90% and x10% are the 90 % and 10 % quantiles of x.
The LCC sensitivity of all segments to the EISp is 50 %, which is
larger than that to the LTS (39 %) and EIS (12 %). These weaker and erroneous
dependences of LCC on the LTS and EIS, respectively, are expected, since large errors (Fig. 2b–d) are carried in the LTS and EIS. Although the vertical resolution of the
ERA5 profiles may not always suffice to resolve the inversion layer, the IS
estimated from the ERA5 profile-based algorithm (EISp) is highly
consistent with the IS directly derived from the SGP 10 m resolution
radiosondes, and they present similar relationships with the PBL RH and LCC.
R square (a) and slope of the least-squares fit (b) of the SGP
radiosonde-derived IS to the ERA5 reanalysis-based LTS (blue cycle), EIS
(green square) and EISp (red cross) on daily, 7, 15, 30 and
90 d timescales, respectively. R square (c) and slope (d) of LCC to the
LTS, EIS, EISp and IS (dashed black line) on daily to seasonal timescales, respectively. Error bars and shadows show the 95 % confidence
interval of the mean based on the t test.
The ERA5-based LTS, EIS and EISp are further examined on the different
timescales with respect to their relationships with radiosonde-measured IS
and LCC (Fig. 6). Overall, the R square and the slope of the EISp with
the IS are the largest throughout all timescales as compared to those of the
LTS and EIS. Particularly on the daily, 7 and 15 d timescales, the
lower bounds of the 95 % confidence interval of the EISp–IS R square
are much higher than the upper bounds for the LTS and EIS. On the seasonal
timescale, three metrics have similar correlations with the IS, but as
shown in Fig. 6b, the slope of the IS to the EISp (nearly 1) is still
much larger than those to the LTS (0.28 K K-1) and EIS (0.23 K K-1). The limited
accuracy restricts the LTS and EIS in reproducing the relationship between the
true IS and LCC. In Fig. 6c, on daily timescales, the LTS explains 3.1 %
of variance in LCC, which is comparable to the 4.8 % variance explained by
the LTS at OWS N (a typical low-cloud-dominated site over the ocean) in
Klein (1997)). For the EISp, it explains 9.1 % of the daily
LCC variance, which is remarkably close to that explained by the IS. Similar
conclusions can be drawn from weekly timescales. On longer timescales, the
EISp and the LTS both explain comparable variance in LCC but much
larger variance than that explained by the EIS. In Fig. 6d, the slope of LCC
composited based on the IS is nearly reproduced by the EISp
consistently. The slopes of LCC composited based on the LTS and EIS are much
smaller than those based on the EISp and IS.
Blue asterisk marks the SGP and ENA sites. Red cycles mark the
locations of radiosonde stations from the IGRA. Eight 10∘×10∘ boxes are the most typical low-cloud-dominated regions defined in Klein and Hartmann (1993).
The characteristics of the PBL thermal structures and evaluation of the
LTS, EIS and EISp in terms of estimating the IS and the IS–LCC relationships of
the six radiosonde stations. Coupled and decoupled PBLs of all stations are
distinguished by αθ. Italics indicate not-significant
correlations. Bold indicates the largest correlation. The daily IS–LCC
correlation is based on the data after subtracting 7 d means.
ARM SGPARM ENAOWS NOWS CTropical East Pacific coastSoutheast Pacific coastChinese coastθLCL-θ0 in coupled PBLs (standarddeviation)0.33 K (0.36 K)0.26 K (0.39 K)1.33 K (0.74 K)0.85 K (0.86 K)0.70 K (1.34 K)0.17 K (0.28 K)0.16 K (0.93 K)θLCL-θ0 indecoupled PBLs(standard deviation)8.69 K (5.82 K)2.55 K (2.37 K)3.53 K (2.23 K)2.73 K (2.30 K)10.46 K (6.71 K)1.41 K (2.05 K)3.34 K (3.50 K)Δθ-ΓmΔz above the LCL (standarddeviation)1.22 K (3.98 K)0.07 K (1.64 K)-0.39 K (2.26 K)1.65 K (2.74 K)-1.06 K (2.36 K)0.48 K (2.34 K)-1.16 K (2.93 K)IS-LTS correlation0.530.510.350.290.430.620.62IS–EIS correlation0.450.580.410.36-0.060.530.76IS–EISp correlation0.740.760.600.480.750.740.79IS–LCC dailycorrelation (slope ± confidence intervals)0.34 (2.82±0.42 %/K)0.16 (3.05±0.97 %/K)NANNAN0.26 (2.61±0.43 %/K)0.30 (2.71±0.39 %/K)0.16(3.07±0.85 %/K)IS–LCC monthlycorrelation (slope ± confidence intervals)0.65 (3.65±0.78 %/K)0.43 (6.44±3.34 %/K)NANNAN0.38 (6.95±4.02 %/K)0.71 (4.52±1.06 %/K)0.76 (6.57±1.38 %/K)Validation of the EISp at radiosonde stations of the subtropics and
midlatitudes
As shown in Sect. 3.2, at the ARM SGP site, the EISp estimates
the PBL IS better than both the LTS and EIS when the PBL thermal structure is
largely deviated from the idealized structure of well-mixed PBLs. Next, we
want to see if such a deviation exists at other radiosonde stations of the
subtropics and midlatitudes. The ARM ENA site and another five ground-based
radiosonde stations are selected to examine their characteristics of PBL
thermal structures. Their locations are shown in Fig. 7. Because the cloud
base height information is not available at the radiosonde stations of IGRA,
the method used at the SGP to distinguish the coupled cloudy,
decoupled cloudy and clear-sky segments is not accessible. Thus, an
alternative indicator, the decoupling degree (αθ), is used
to distinguish coupled and decoupled PBL according to the PBL thermal
structures. The definition of αθ is introduced in
Wood and Bretherton (2004) by using the liquid potential
temperature (θL) as the conserved variable during the moist
adiabat. Here, θ is used to construct the moist adiabatic conserved
variable by removing the moist adiabatic θ increase above the LCL to
express the αθ parameter:
αθ=θISB-θ0-Γm(zISB-zLCL)θIST-θ0-Γm(zIST-zLCL).
The subscripts “ISB”, “IST”, “0”, “700 hPa” and “LCL” indicate the
base and top of the inversion layers, the levels of 1000 and 700 hPa, and the
LCL, respectively. To understand its meaning, Eq. (12) can be transformed
as follows:
αθ=θLCL-θ0+θISB-θLCL-ΓmzISB-zLCLIS+θLCL-θ0+θISB-θLCL-ΓmzISB-zLCL≈EIS-ISEIS.
The numerator of αθ can be understood as the strength of
the PBL thermal structures deviating from the coupled conditions. The
denominator of αθ can be understood as the sum of the
deviation strength of the PBL thermal structure from the coupled conditions
and the IS (or EIS). By Eq. (13), the EIS can also be expressed as
IS/(1-αθ). Thus, whether the EIS is the real IS is actually
determined by the decoupling parameter αθ. In perfectly
coupled conditions, αθ is zero and the EIS is exactly equal to the
IS. In decoupled PBLs, when αθ is larger, the EIS actually
accounts more for the deviation of the PBL thermal structure from the
coupled condition. A small value of αθ would suggest a
state very close to the coupled condition, and here, a threshold value of 0.2
is used to distinguish the coupled and decoupled PBLs based on Eq. (12). αθ has been tested for the high-resolution soundings, and it comes
to similar results. In fact, results listed in Table 2 at the SGP based on
αθ show consistent results with that based on Δzb.
As shown in Table 2, it is found that the two terms θLCL-θ0 and Δθ-ΓmΔz in Eq. (9) are non-negligible,
even over the subtropical oceans. Both the mean and standard deviation of
θLCL-θ0 are very small in the coupled PBLs. The mean of
θLCL-θ0 at the other sites in the decoupled PBLs is
usually smaller (about 1–4 K) as compared to that at the SGP (8.69 K), except
at the tropical East Pacific coast, where it is larger (10.46 K) than that at
the SGP. Theoretically, a constant shift on the θ difference between
the LCL and the ground level will not change the correlation coefficient and
regression slope between the LTS and EIS and the IS and LCC. However, the term
θLCL-θ0 is systematically different between the coupled
and decoupled PBLs. Thus, using the LTS and EIS to sort the PBL structures
will unequally mix the coupled and decoupled conditions in their different
composite bins. Moreover, this bias is distinct for different places, and
thus, the regional difference would make the LTS and EIS not uniform in terms of
their accuracies when estimating the IS. In contrast, this will not happen in
the EISp, since this bias caused by the term θLCL-θ0
in the LTS and EIS is completely excluded from the EISp.
The standard deviation of the term Δθ-ΓmΔz, as
shown in Table 2, suggests that the errors in estimating the IS based on Eq. (9) due to the moist adiabatic assumption above the LCL of the ENA and the other
five radiosonde sites range from 57 %–74 % of that of the SGP site
(3.98 K). Thus, the term Δθ-ΓmΔz at these six
sites will likely also be reduced when measuring the IS by the EISp.
Thus, it is not surprising that the ERA5 EISp is best correlated with
the IS directly derived from the radiosondes over all stations (Table 2).
Regional differences of the correlations with the IS still exist for all
metrics to measure the IS but are relatively small for the EISp.
On the relationship of global LCC with LTS, EIS and EISp
In this section, the relationship of global LCC with LTS, EIS and EISp
is discussed through daily to seasonal timescales. Since ground-based
observations of radiosondes from ARM and IGRA are all assimilated in the
ERA5 reanalysis (Hersbach et al., 2020), it is not surprising that the
assimilated output can capture well the PBL thermal structures to estimate
the IS for these locations where ground-based observations are available.
However, for most areas of the oceans, only limited radiosondes are available
over scattered islands or during short-term campaigns of field experiments to
be used in ERA5 assimilation, and thus, whether the IS can be rightly captured
from the ERA5 profiles needs further examination. In this section, whether
the EISp derived from the ERA5 profiles at the global scale (especially
for oceans with few radiosondes assimilated into the ERA5) can better
constrain LCC than LTS and EIS is explored.
Spatial distribution of the ERA5 reanalysis-based LTS (a), EIS
(b), EISp(c) and the GEO-MODIS LCC (d) between 60∘ S
and 60∘ N. The black contours enclose regions with LCC
larger than 60 %. The specific R square and LCC sensitivity to the LTS
(blue cycle), EIS (green square) and EISp (red cross) over the ocean,
land and all is shown in (e) and (f), respectively. The error bars show the
95 % confidence interval of the mean based on the t test.
Figure 8 shows the 6-year mean map of the ERA5-based LTS, EIS and EISp.
The GEO-MODIS LCC global pattern is also used to examine its spatial
correlation with the above three metrics. For the LTS, EIS and EISp,
the plateau regions with surface pressures smaller than 700 hPa are not
investigated here, where no GEO-MODIS LCC is observed. Overall, the annual
mean values of LTS and EIS are obviously larger than the EISp value,
except in the inner tropical convective zone, where the EIS value is largely
negative. In addition, there are three differences between the spatial
distributions of LTS, EIS and EISp.
Over the subtropical eastern oceans, the center locations of LTS, EIS and EISp are different. For LTS and
EIS, their center locations are more eastward and adjacent to the coast as
compared with the center locations of EISp and LCC. For EISp, its
center locations are relatively far away from the coast and more consistent with
the center locations of LCC.
Over midlatitude oceans, the contrast of the values between the midlatitudes and the tropics is
different for LTS, EIS and EISp. The midlatitude LTS reduces to the
minimum but still corresponds to about 40 % of LCC. The midlatitude EIS is
as strong as the EIS over the subtropical eastern oceans but corresponds to
a much smaller LCC than the subtropical LCC. Only the variation of
EISp from the tropics to midlatitudes is more reasonably consistent with the
spatial variation of LCC.
Over land, the LTS and EISp explain over half of the LCC spatial variance
according to their linear fit, but the EIS only explains 2 % of the LCC
spatial variance. This implies that the IS is still a controlling factor for LCC
distribution over land. The EIS barely correlates to continental LCC,
possibly because the EIS poorly estimates IS due to the strong influence of
the term θLCL-θ0, as discussed in Sect. 3.
On the whole, the performance of EISp is better and less dependent on
surface types. Over all global oceans and land, the EISp explains
78 % of the spatial variance in LCC, which is significantly higher than that
explained by the LTS (48 %) and the EIS (13 %). The spatial variations
of LCC are also more sensitive to the EISp (Fig. 8f).
R square between the GEO-MODIS LCC and the ERA5 reanalysis-based
LTS (left column), EIS (middle column) and EISp (right column) at the
all timescales (a–c), daily timescale (d–f), 7 d timescale (g–i) and monthly time scale (j–l). The black contours
enclose regions with LCC larger than 60 %. Only R squares at the 95 %
significance level are shown. The minus (plus) sign of R square indicates
negative (positive) correlations.
In Fig. 9, the dependence of LCC on the LTS, EIS and EISp is further
examined globally for the full daily time series (i.e., all timescales) and
for the daily, 7 d window-averaged anomalies and monthly means (i.e.,
daily, 7 d and monthly timescales). It is noted that the dependence of
LCC on the three ERA5-based metrics varies across different regions.
LCC is best correlated with three metrics over the subtropical eastern
oceans and some land regions that are most dominated by low clouds. Over
midlatitude oceans and the inner Tropical Convergence Zone, the LCC is weakly or
negatively correlated with three metrics. Thus, it is discussed separately
for the most LCC-dominated regions over subtropical oceans, midlatitude
oceans and land.
Over the subtropical eastern oceans with more than 60 % of LCC, on all timescales (Fig. 9a–c), the EISp explains 36 % of the
variance in LCC on average, which is larger than that explained by the LTS (21 %)
and the EIS (20 %). The fact that EIS does not provide a stronger
correlation with LCC than LTS was also recognized by Park and Shin (2019) and by Cutler et al. (2022). In contrast, the explained variance
of the linear fitting between LCC and EISp is 1.8 times that with
LTS and EIS. Besides, the mean LCC sensitivity (defined in Eq. 11 and not
shown in the figure) to the EISp on all timescales is 48 % over
these regions, which is significantly higher than that to the LTS (37 %) and the
EIS (36 %). Although radiosondes are rare and the ERA5 profiles are mostly
from the model output over these regions, the EISp still provides a
much stronger constraint on LCC than LTS and EIS. As shown in Fig. 9d–i
through daily to monthly timescales, the EISp robustly explains larger
LCC variance, more so than the LTS and EIS, especially on short timescales.
Over midlatitude oceans, weak and not-significant correlations between LCC and the three metrics
exist through all of the timescales in Fig. 9. This poor relationship is also
found at the ENA site (Table 2), even when using the radiosonde to derive the IS,
and thus, it is not caused by using the ERA5 to estimate the IS. This
suggests that the IS–LCC relationship is indeed not uniform but varies with
regions. Klein et al. (2017) also indicated that the LCC
relationship with cloud-controlling factors (e.g., the IS and sea surface
temperature) is systematically different between the subtropical
stratocumulus region and other regions (e.g., trade cumulus and midlatitude
regions). Thus, when the IS is used to constrain the environmental influence
on LCC variations, it should be noted that LCC is not all uniformly
constrained by the IS for different regions. For some regions such as
midlatitude oceans, the IS might not be a good constraint on LCC. But by
more accurately estimating the IS, the EISp is more correlated with LCC
than the LTS and EIS over midlatitude oceans such as the North Pacific and North
Atlantic on all timescales in Fig. 9a–c.
Over land regions of relatively more LCC (about 15 %–25 % in South America, China and Europe), the correlation between EISp and LCC is comparable to the
subtropical oceanic regions through all of the timescales in Fig. 9. This
suggests that the EISp is also an important controlling factor for
continental LCC over these regions. Besides, the EISp is more
correlated with LCC than the LTS and EIS over most land regions, except over
China, where the LTS explains larger LCC variance than the EIS and EISp.
The higher correlation of LTS with LCC over China might not be attributed only to the IS (LTS is not a direct measure of inversion but static
stability). But more comprehensive and in-depth investigations on the
LTS–LCC dependence are needed to understand the exact reason for this
phenomenon.
R square (left panel), slope (middle panel) and relative
sensitivity (right panel) of the GEO-MODIS LCC to the ERA5-based
10∘×10∘ regional mean LTS (blue
cycle), EIS (green square) and EISp (red cross) through daily to
seasonal timescales over the five typical eastern oceans defined in
Klein and Hartmann (1993). The error bars show the 95 %
confidence interval based on the t test. The dashed black lines in the left
panel are the fraction of the LCC variance on different timescales divided
by the total variance.
In Klein and Hartmann (1993), several key low-cloud regions
are defined. Those regions are of a particular interest in climate
projections due to their strong low cloud albedo effects. As shown in Fig. 7, we pick eight key low-cloud regions according to Klein and Hartmann (1993), and the linear relationships between LCC and the three metrics are
investigated. These regions lack radiosondes for long-term observations of
IS. They are separated into a group of five typical tropical and subtropical
low-cloud-prevailing eastern oceans (Fig. 10) and a group of midlatitude
oceans and subtropical land (Fig. 11).
As shown in Fig. 10 (the dashed line in the left panel), over the five key
tropical and subtropical eastern oceans, the daily and seasonal
window-averaged LCC anomalies account for a larger portion of the total LCC
variance, indicating that the LCC variation mainly happens at the daily and
seasonal timescales. Over the Peruvian, Namibian and Canarian regions, over
50 % of LCC variances are from the seasonal variations, and much smaller LCC
variances are from other four shorter timescales. But over the Californian
and Australian regions, 40 % and 51 % of the LCC variances are from the
daily timescale, which are larger than those on other timescales. Although the LCC
variances on the 7 d, 15 d and monthly timescales are relatively
smaller, the sum of them still accounts for about 20 % ∼ 30 %
of the total LCC variance.
In Fig. 10, the LCC variance explained by the LTS, EIS and EISp and the
LCC slopes of the linear regression to them are examined through daily to
seasonal timescales. In addition, the relative LCC sensitivity to those
three metrics refers to the LCC sensitivity as defined in Eq. (11) divided
by the LCC range. Here, the LCC range is the difference between the mean
values of the largest and the smallest 10 % of LCC. The LCC variance is
explained most by the EISp among the three metrics (left panel of Fig. 10), and LCC is most sensitive to the EISp (right panel of Fig. 10)
through all of these timescales, except in the cases of the monthly timescale over the
Peruvian region and the seasonal timescale over the Namibian region. On the daily
timescale, 32 % of LCC variances are explained by the EISp on average
over the five eastern oceans, which is more than 2 times the variance
explained by the LTS (14 %) and EIS (16 %). On the longer timescales
(30–90 d), overall, the EISp explains 89 % of the LCC seasonal
variance on average over the five eastern oceans, in contrast to 80 % for
the LTS and 70 % for the EIS. Only the EISp can robustly explain the
seasonal variance of LCC exceeding 80 % for all locations. However, the
EIS cannot explain well the seasonal variation of LCC over the Californian
and Canarian regions, and the LTS cannot explain well the seasonal variation
of LCC over the Australian region.
It is also noted that the slopes of LCC associated with each metric are not
uniform across these key low-cloud regions or on different timescales. A
similar regional and temporal difference is also found in the LCC–IS
relationships (Table 2). Klein et al. (2017) and
Szoeke et al. (2016) also found the LCC slopes to the LTS and EIS
are variant on different timescales, and this timescale dependence would
lead to uncertainties in the final estimates of low cloud feedbacks. Thus,
the error estimates of the LCC slopes to the LTS, EIS and EISp are
needed for the final uncertainty estimates of low cloud feedbacks. To
quantify the relative variation (or the uniformness) of the LCC slope to
LTS, EIS and EISp, we compute the ratio between the standard deviation
and the mean of grouped slopes. For the temporal relative variation, slopes on different timescales of each region are grouped together, while for
the regional relative variation, on each timescale, slopes over different
regions are grouped together. The temporal relative variation of the LCC
slope to the LTS and EIS is 32 % and 29 % on average over the five
eastern oceans. In contrast, the temporal relative variation of the LCC
slope to the EISp is 21 %. Besides, the regional relative variation
of the LCC slope to the LTS, EIS and EISp is 24 %, 21 % and 18 %
between the five eastern oceans, respectively. This suggests that the
regional and temporal dependence of the LCC slope in the estimate of low cloud
feedbacks is also non-negligible and needs to be considered in the final
error estimates or to estimate low cloud feedbacks by separating regions.
Similar to Fig. 10 but for the other three regions defined in
Klein and Hartmann (1993), including two midlatitude oceans
and one subtropical land. The minus (plus) sign of R square indicates
negative (positive) correlations.
Figure 11a and d (the dashed line) show that, over the North Pacific and North
Atlantic regions, 67 % of the LCC variance is from the daily timescale,
while over the China region in Fig. 11g, variance is mostly from the seasonal
timescale (57 %). Over the North Pacific and North Atlantic regions, LCC
is not necessarily correlated with the IS. Norris (1998) has
found that fogs and bad-weather stratus clouds frequently occur over the
midlatitude ocean but with less inversion and poor IS–LCC relationships.
Similarly, poor correlations (Fig. 11a and d) and sensitivity (Fig. 11c
and f) between LCC and LTS, EIS and EISp are found over the North Pacific
and North Atlantic. However, the EISp is closest to the radiosonde-detected
IS as compared with the LTS and EIS at the ENA and OWS C, as shown in Table 2. This suggests that the EISp is still a reliable estimation for the
IS to represent the true IS–LCC relationship. But the LTS–LCC and EIS–LCC
relationships are not necessarily due to the IS influence on LCC. Figure 11a,
d, c and f also show that the LTS–LCC and EIS–LCC correlations and sensitivities
are very different from those between LCC and EISp on the daily and
seasonal timescales. Unfortunately, the
midlatitude LCC–IS relationship has not been well explored. The poor EISp–LCC relationship is
representative of the fact that the IS cannot be a cloud-controlling factor that is as important as
that over subtropical oceans. Over the Chinese region, the EIS and EISp
are both better correlated with the IS, as shown in Table 2. Figure 11g and
i show that LCC is slightly more correlated with and sensitive to the
LTS through all timescales. These higher correlations and sensitivities are
not related to the IS, since the LTS correlates the least with the IS. Since
the LTS not only includes the IS but actually represents the total static
stability from 1000 to 700 hPa to influence the amount and liquid water
path of low clouds (Klein and Hartmann, 1993; Kawai and Teixeira, 2010),
it may imply that there are other thermal factors in addition to the IS in
LTS that contribute to these higher correlations and sensitivities. Overall, it
should be noted that the IS may not be a strong cloud-controlling factor
over the midlatitude oceans and subtropical land, but EISp is still the
best estimation for the IS. The IS is not the only LCC-controlling factor,
and other factors (e.g., sea surface temperature, cold advection,
free-tropospheric humidity and vertical velocity) are also important for
influencing LCC (Myers and Norris, 2013; Klein et al., 2017).
All the above analyses (Figs. 8–11) are based on the daily averaged LTS, EIS and
EISp data, which are computed based on the 3 h 1∘ ERA5
atmospheric profiles. Based on the monthly mean atmospheric profiles, over
the region of LCC larger than 60 %, the LTS and EIS explain 50 % and
48 % of LCC variance, which is similar to the value of 53 % based on the
3 h ERA5 atmospheric profiles. However, the EISp based on the
monthly mean ERA5 profiles explains 49 % of the LCC variance, which is
significantly lower than the 65 % based on the 3 h profiles. Thus, for
accurately computing the EISp on either short or long timescales, a high
temporal resolution of reanalysis data is necessary.
Conclusions
In this paper, a novel profile-based estimated IS (EISp) is developed
based on the thinnest possible layer that contains the inversion layer in
the ERA5 profiles. By this method, the effects of the static stability below
the LCL are completely removed. The errors due to the spread of the
environmental θ gradient around the moist adiabat above the LCL are
reduced.
At the ARM SGP site, the EISp more accurately estimates the IS, with a
correlation of 0.74, than the LTS (0.53) and EIS (0.45). Thus, the EISp
reasonably replicates the constraints of IS on the PBL moisture distribution
and LCC, while the LTS and EIS respectively have a weak and erroneous relationship with the PBL
moisture and LCC. The LCC sensitivity to LTS, EIS and EISp is
39 %, 12 % and 50 %, respectively. On the daily timescale (7 d mean
excluded), the variance in LCC explained by the EISp (9.1 %) is more
than twice that explained by both the LTS (3.1 %) and EIS (-0.4 %). At
the ARM ENA site, the EISp has similar advantages when estimating the IS.
At other available oceanic and coastal observation stations, the EISp
is still a better estimation for the IS than the LTS and EIS are.
At the global scale, according to the GEO-MODIS LCC observations, the
EISp explains the spatial and temporal variations of LCC better than
the LTS and EIS do. Over oceans, the EISp distribution is more consistent
with the LCC pattern compared with those of the LTS and EIS. The locations of the
strongest EISp are consistent with the centers of the largest LCC
relatively far away from the coast, while the centers of the strongest LTS and
EIS are over the coast. Over the subtropical LCC domains, the LCC
sensitivity to the EISp is 48 %, which is larger than that to the LTS (37 %)
and EIS (36 %) on all timescales. Furthermore, the increased LCC sensitivity to
EISp primarily comes from timescales shorter than a month. Over the
typical low-cloud-prevailing eastern oceans, as defined in Klein and Hartmann (1993), the LCC daily variance explained
by the EISp is 32 % and twice that explained by the LTS and EIS. Furthermore, the
LCC seasonal variance explained by the EISp increases to 89 % as
compared with that explained by the LTS (80 %) and EIS (70 %).
No uniform relationship between the LCC and any of the IS, LTS, EIS and
EISp is found across timescales or different regions. As compared to
the LTS and EIS, the temporal relative variation of the LCC slopes to the
EISp is reduced from 32 % and 29 % to 21 %. The regional relative
variation of the LCC slope to the EISp is slightly smaller than that
of the LTS and EIS. This non-uniform LCC sensitivity to cloud-controlling
factors across different regions and timescales suggests that using a
single observational multi-linear regression between LCC and
cloud-controlling factors to estimate the global low cloud feedbacks is not
recommended.
Overall, the EISp is an improved measure of the IS and better
constrains LCC, especially on timescales shorter than a month. On short
timescales, the enhanced dependence of LCC on the EISp makes the
EISp more suitable to resolving process-oriented studies associated with
LCC variations. Therefore, the EISp is likely a better constraint to
reduce the meteorological covariations to separate the aerosol effects in
aerosol–cloud interactions.
Code availability
The code for determining the EISp of an atmospheric profile can be obtained by request to the authors.
Data availability
All data used in this study are available online. The ARM SGP and ENA radiosonde and cloud observations were obtained from the ARM Research Facility and are available at 10.5439/1595321 (Ken, 2001) and 10.5439/1333228 (Chen and Xie, 1996). The IGRA radiosondes (Durre et al., 2006, 2018) are available from the NOAA National Centers for Environmental Information at https://www.ncei.noaa.gov/products/weather-balloon/integrated-global-radiosonde-archive (NOAA, 2021). The GEO-MODIS LCC product (Doelling et al., 2013; Doelling et al., 2016; Trepte et al., 2019) is provided by the NASA Langley Research Center at 10.5067/TERRA+AQUA/CERES/SYN1DEG-1HOUR_L3.004A (NASA et al., 2021). The ERA5 reanalysis (Hersbach et al., 2020) used in this study is from the ECMWF and available at 10.24381/cds.bd0915c6 (Copernicus Climate Change Service, 2021).
Author contributions
JY and RW designed the experiments, and ZW carried them out. JY and ZW
prepared the first version of the paper with contributions from all
co-authors. YC prepared the ERA5 data, and TT inspected some individual
profiles and cloud images. All authors verified the final version of the
paper.
Competing interests
The contact author has declared that none of the authors has any competing interests.
Disclaimer
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
This research has been supported by the NSFC-41875004, the National Key R&D Program of China-2016YFC0202000 and the Jiangsu Collaborative Innovation Center for Climate Change. The first author thanks the “Double First-class” initiative program for providing an opportunity for him to visit the University of Washington. We thank two anonymous referees for their helpful comments.
Financial support
This research has been supported by the National Natural Science Foundation of China (grant no. 41875004) and the National Key Research and Development Program of China (grant no. 2016YFC0202000).
Review statement
This paper was edited by Johannes Quaas and reviewed by two anonymous referees.
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