ABL, KIAB, LHR, LTM

Currently at: 2 Council on Energy, Environment and Water, 4, ISID Campus,
Vasant Kunj, New Delhi 110070 India K R Sreenivas, Engineering Mechanics Unit,
Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur PO, Bengaluru
560064, India<EMAIL_ADDRESS>1 Engineering Mechanics Unit, Jawaharlal Nehru
Centre for Advanced Scientific Research, Jakkur PO, Bengaluru 560064, India a.
Technical Research Centre, Jawaharlal Nehru Centre for Advanced Scientific
Research (JNCASR), Bengaluru 560 064, India,
b. Bengaluru International Airport Limited, Bengaluru 560 300, India AND
c. National Supercomputing Mission, JNCASR, Bengaluru 560 064, India Research
Article

# Investigation of the Thermal Structure in the Atmospheric Boundary Layer
During Evening Transition and the Impact of Aerosols on Radiative Cooling

Suryadev Pratap Singh  Engineering Mechanics Unit, Jawaharlal Nehru Centre for
Advanced Scientific Research, Jakkur, Bengaluru 560064, India  Mohammad
Rafiuddin  Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced
Scientific Research, Jakkur, Bengaluru 560064, India  Subham Banerjee
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific
Research, Jakkur, Bengaluru 560064, India  Sreenivas K R  Engineering
Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research,
Jakkur, Bengaluru 560064, India

###### Abstract

The evening transition is crucial in various phenomena including boundary
layer stability, temperature inversion, radiation fog, vertical mixing, and
pollution dispersion. We have explored this transition using data from eighty
days of observations across two fog seasons at the Kempegowda International
Airport, Bengaluru (KIAB). Through field experiments and simulations
integrating aerosol interaction in a radiation-conduction model, we elucidate
the impact of aerosols on longwave cooling of the Atmospheric Boundary Layer
(ABL).

Field observations indicate that under calm and clear-sky conditions, the
evening transition typically results in a distinct vertical thermal structure
called the Lifted Temperature Minimum (LTM). We observe that the prevailing
profile near the surface post-sunset is the LTM-profile. Additionally, the
occurrence of LTM is observed to increase with decreases in downward and
upward longwave flux, soil sensible heat flux, wind speed, and turbulent
kinetic energy measured at two meters above ground level (AGL). In such
scenarios, the intensity of LTM-profiles is primarily governed by aerosol-
induced longwave heating rate (LHR) within the surface layer. Furthermore, the
presence of clouds leads to increased downward flux, causing the disappearance
of LTM, whereas shallow fog can enhance LTM intensity, as observed in both
field observations and simulations.

Usually, prevailing radiation models underestimate aerosol-induced longwave
heating rate (LHR) by an order, compared to actual field observations. We
attribute this difference to aerosol-induced radiation divergence. We show
that impact of aerosol-induced LHR extends hundreds of meters into the
inversion layer, affecting temperature profiles and potentially influencing
processes such as fog formation. As the fog layer develops, LHR strengthens at
its upper boundary, however, we highlight the difficulty in detecting this
cooling using remote instruments such as microwave radiometer.

Keywords — Aerosols, radiation divergence, fog, longwave cooling, lifted
temperature minimum

##  1 Introduction

The evening transition in the Atmospheric Boundary Layer (ABL) holds practical
significance, as highlighted in various studies [27, 18, 2]. Post-sunset, this
transition leads to the formation of the stable Nocturnal Boundary Layer
(NBL), influencing several meteorological phenomena including inversion layer
growth, fog occurrence, and the impact of stable layers on vertical mixing and
pollution dispersion. The cooling rate and moisture accumulation within a few
meters above ground level in the NBL are crucial for determining the onset,
progression, and dissipation of radiation fog [28]. Additionally, cooling
rates affect the occurrence and strength of temperature inversions,
complicating pollution dispersal [33]. Surface-heat flux, a key factor in dew
formation at night, is regulated by near-surface temperature and relative
humidity [45]. Therefore, comprehending and analyzing the evening transition
and its detailed characteristics through vertical temperature and radiative
cooling rate profiles holds practical importance.

Atmospheric turbulence subsides around sunset and a stable inversion layer
forms. According to conventional explanations found in textbooks [70], the
process starts with radiative cooling of the ground and subsequent cooling of
the air layers above it, with lowest temperature occurring on the ground.
However, an intriguing observation by Ramdas and Atmanathan [60] under calm
and clear sky conditions is that the ground does not attain the lowest
temperature locally. Instead, a local minimum temperature, known as the Lifted
Temperature Minimum (LTM), appears a few decimeters above the ground surface.
The height at which this minimum occurs is referred to as LTM height, and the
difference between the surface temperature and the LTM is termed LTM
intensity.

Despite the robust observations of the LTM in numerous field experiments
worldwide, it took considerable time to provide an explanation for its
occurrence. Ramdas and Atmanathan [60] and Ramanathan and Ramdas [59]
initially hypothesized the role of radiation in LTM formation, but this was
met with skepticism due to several reasons: (a) it contradicted the prevailing
belief that the ground cools faster than the surrounding air layers after
sunset, (b) the challenge of maintaining LTM against convective instability
for extended periods, and (c) alternative explanations such as drainage flow
or measurement errors [24]. However, over time, Lake [39], Ramdas and
Atmanathan [61], Oke [53], Mukund et al. [46, 47], Blay-Carreras et al. [3],
Jensen et al. [35] conducted meticulous field experiments on various types of
soils in different regions of the world. These experiments confirmed the
robust and widespread occurrence of LTM across diverse terrains, including
snow, bare soil, grassland [39, 53, 3], concrete surfaces [46, 47], and
mountainous terrain [35], with varying LTM intensities. Moreover, they refuted
the role of drainage flow in LTM development through precise measurements of
local winds. By manipulating surface properties in field experiments, Mukund
et al. [47] demonstrated that LTM intensity is strongly influenced by surface
emissivity and thermal properties. Additionally, their controlled laboratory
experiments, which avoided drainage flow, conclusively showed that LTM
intensity decreases with lower aerosol concentrations. They observed
significant radiative cooling in the air layer adjacent to the ground,
highlighting the importance of aerosol-induced radiation divergence in LTM
development. This phenomenon underscores the complexity of nocturnal
temperature profiles and emphasizes the significance of radiative cooling in
modeling the nocturnal atmospheric boundary layer.

Apart from the field experiments, there have been efforts to develop
mathematical and numerical models to understand the origin and parametric
dependence of the LTM on other factors. For instance, Varghese et al. [72]
modified the radiation model by Chou et al. [8], incorporating energy transfer
from radiation, conduction, and forced convection into a mathematical model.
However, Edwards [15], Ponnulakshmi et al. [54, 55] identified erroneous
assumptions in Varghese et al. [72]’s treatment of ground reflection,
particularly regarding the downward longwave (LW) flux, leading to spurious
cooling. Subsequent corrections, as proposed by Ponnulakshmi et al. [54, 55],
failed to replicate an LTM profile. Mukund et al. [46] suggested the inclusion
of aerosol-radiation interaction to explain the LTM phenomenon, a proposition
supported by conclusive experimental evidence from Mukund et al. [47].
Building on the findings of Mukund et al. [47], we incorporated aerosol-
radiation interaction into the corrected model of Edwards [15], Ponnulakshmi
et al. [54, 55] to simulate the thermal structure in the nocturnal boundary
layer. Further details of the models are provided in Section 3.

Despite the significant role of radiation divergence in the Nocturnal Boundary
Layer (NBL) under low-wind conditions [26, 42, 23, 14] and its importance in
numerical weather prediction (NWP) [66, 65, 29], current radiation
parameterizations in NWP models fail to accurately simulate the evolution of
radiative fluxes [67, 68]. Additionally, radiative cooling rates reported in
many field experiments lack robustness due to measurement uncertainties and
are comparable to reported longwave (LW) cooling rates [21, 40, 20, 52, 50,
76, 51, 70]. However, a set of observations by [31, 32, 14, 68] have conducted
careful measurements and reported significant radiative cooling within a few
tens of meters near the ground during the night.

In addition to measurements, numerous researchers have endeavored to simulate
radiative cooling using various methods [22, 78, 23, 17, 66, 68]. However,
these modeling approaches have encountered challenges such as limited vertical
resolution, and unrealistic assumptions, or adjustments to parameterizations
to capture observed radiative cooling [58, 65]. HA and Mahrt [29] noted
discrepancies between estimated radiative and turbulent flux divergence and
observed cooling in the Stable Boundary Layer (SBL). While Steeneveld et al.
[66] found reasonable agreement between modeled radiative cooling rates and
CASES-99 observations, however, parameterization coefficients for modeling
needed to be adjusted for getting agreement. Through meticulous observations,
Steeneveld et al. [68] and Sun et al. [71] reported high radiative cooling
rates, particularly during evening transitions and under clear sky conditions.
They also highlighted that commonly used longwave radiation models
underestimate observed cooling during the evening transition by an order of
magnitude, whereas a physical model [11] showed better agreement without
aerosols. However, this physical model’s applicability is limited due to
assumptions like logarithmic temperature and humidity profiles, stationarity,
and other parameterizations based on Monin-Obukhov theory [11, 43], rendering
it less suitable for the use in NWP models [68].

The observed deficiencies in radiative parameterization have been highlighted
in both observational and numerical investigations [74, 62, 65]. While
Zdunkowski et al. [79], Coantic and Seguin [11], André and Mahrt [1], Mukund
et al. [46] have speculated on the potential significance of aerosols in
longwave radiative modeling, laboratory experiments by Mukund et al. [47]
demonstrated the necessity of considering aerosols to explain temperature
profiles near the ground. Despite the dominance of LW radiation divergence
over turbulent flux divergence in low-wind conditions, as observed in our
study [26, 42, 23, 14], aerosols have not been incorporated into LW radiation
modeling to elucidate observed radiative cooling in the nocturnal boundary
layer.

In summary, the preceding discussion underscores the necessity of conducting
field experiments alongside numerical simulations, incorporating aerosol-
radiation interaction, to elucidate the influence of aerosols on radiative
processes in the nocturnal boundary layer. Additionally, it aims to determine
the height within the atmosphere, where aerosols impact thermal structure. In
this pursuit, we present field observations of evening transitions and nights
spanning an extensive eighty-day period across two fog seasons. We integrate
aerosol-radiation interaction into the corrected band model [55]. Through
simulations and field observations, we explore the impact of aerosol-induced
cooling on evening transition and LTM in calm and clear sky conditions.

This paper is organized in the following way: Field experiments,
instrumentation details, and observational data are presented in Section 2.
The longwave (LW) radiation model and integration of the aerosols model into
it are elaborated in Section 3. LTM observations and analysis, LHR during
evening transitions, and the influence of fog/cloud on LTM are presented in
Section 4. Limitations of current radiation models and observations regarding
LTM and LHR have been discussed in Section 5, and last, we conclude this work
in Section 6.

##  2 Field campaign and observational data

Figure 1: Observation site and mounted instruments. (a) Field experiments have
been conducted in the airfield of KIAB (Red star) (obtained by
$\mathrm{Google-Earth^{TM}}$). (b) Aerial view of KIAB, observation site
(dropped pin), and (c) Instruments installed on the concrete base.

The field campaign has been conducted in the airfield of Kempegowda
International Airport, Bengaluru (KIAB), located at 13.20∘N, 77.70∘E and
$\sim$900 m above mean sea level (Figure 1a). The observation site is
$\sim$175 m north of the north-runway (09L/27R; pin dropped in Figure 1b). All
instruments (except soil temperature profiler and sensible heat flux sensors)
are mounted on a concrete base (9 m $\times$ 3 m) to maintain their alignment
and orientation during the campaign, whereas soil sensors are installed into
the soil, 0.5 m away from the concrete base. Although sensors are installed
either directly on the concrete base or in close proximity to it, measurements
may still differ from those taken on soil. Nevertheless, the thermophysical
and radiative properties of soil are comparable to those of concrete, and we
anticipate that the results will not vary significantly [47]. For safety
purposes, the observation site is enclosed by a thin metal wire fence
extending up to approximately $0.5$ m above ground level around its perimeter.
The flat grassland surrounding the observation site, with grass approximately
$\sim 10$ cm in height maintained by the airport authority, offers an
unobstructed view for remote-sensing instruments to scan with minimal
disruptions. The description of geographical details such as terrain, soil
properties, vegetation, and climate around KIAB, which influence its
thermodynamic and dynamic parameters (e.g., wind speed and direction,
temperature and moisture in atmosphere and soil, etc.) can be found in a
recent article by Kutty et al. [38].

As the observation site is located in the tropical region, convective systems
of local to large scale are commonly observed throughout the year. In the KIAB
region, it is difficult to get enough days that are completely free from
clouds. Hence, for analysis, we have selected days when reported cloud cover
in the Meteorological Aerodrome Report (METAR) at KIAB is $<2$ octas during
the analysis period (10:00 UTC [03:30 IST] and 18:30 UTC [23:59 IST]) which we
call clear-sky days. Since the field campaign at the site is an ongoing
project; we report data and analysis for a total of 80 clear-sky days from
2021-22 and 2022-23, which consists of two winter seasons (December and
January) as well as two spring season (February and March). During these days,
calm and clear sky conditions prevailed. In the winter season, the ABL is
found to be stable with frequent occurrence of dense fog in the morning hours.
Because of the prevailing easterly wind in both the seasons, meteorological
conditions at the observation site get modulated by large-scale systems
developed in the Bay of Bengal (BoB), which are observed most days of the
year.

Several instruments have been deployed at the observation site to measure
different parameters in the atmosphere and the soil (see Table
LABEL:tab:_instruments). The probe locations range from 0.5 m inside the soil
to 10 km into the atmosphere (See Figure 1c). The category of instruments,
measured quantities, range, resolution, and sampling interval have been
presented in Table LABEL:tab:_instruments. Windcube, an active lidar-based
remote sensing device, provides wind profiling in the hemispherical volume of
a radius of 3 km using three different modes of scan: Doppler Beam Swinging
(DBS), Range Height Indicator (RHI), and Plan Position Indicator (PPI). Wind
data quality is ensured based on the carrier-to-noise ratio (CNR), which
depends on the concentration and size distribution of aerosols, dust
particles, clouds, and fog droplets in the atmosphere. Since emitted radiation
from the windcube can not penetrate through the thick cloud/fog layer, CNR
drops significantly above that layer, which leads to noisy wind data, but it
detects the presence of fog/cloud above KIAB.

Temperature and humidity profiles play a key role in modulating the radiation
budget in the atmosphere. Humidity and Temperature profiling (HATPRO)
radiometer, a passive remote sensing device, continuously retrieves
temperature and moisture profiles up to a height of 10 km using 14 channels of
microwave (MW) radiation. However, moisture profiling is coarse in vertical
resolution [4]. An Infrared (IR) sensor integrated with HATPRO retrieves the
cloud/fog base, its thickness, and liquid water mixing ratio with poor
accuracy. In case of heavy rain, the optical window (Radome sheet cover) of
HATPRO wets and introduces noise in observed vertical profiles, but a high-
temperature blower integrated with HATPRO dries the optical cover just after
rain, and the data quality gets restored. LN2 calibration of HATPRO was
performed periodically to ensure quality data of the temperature and humidity
profiles.

An automatic weather station (AWS) integrated with HATPRO gives temperature,
pressure, relative humidity (RH), rain rate, wind speed, and direction at 2 m
above ground level (AGL). Observations from AWS and vertical profiles from the
HATPRO are used to retrieve many thermodynamic parameters such as water vapor
mixing ratio, total precipitable water, liquid water mixing ratio, liquid
water path, dew point temperature profile, different stability indices such as
convective available potential energy (CAPE) and convective inhibition energy
(CINE). Although HATPRO misses and misplaces the liquid water mixing ratio in
the vertical direction and gives poor profiling of the liquid water mixing
ratio, the windcube detects the cloud and fog base height based on the sudden
change in CNR. The occurrence of cloud/fog is also well detected through a
sharp change in the incoming longwave radiation from the 4-component radiation
sensor (Discussed in Section 4).

Two humidity sensors and two radiation sensors, integrated with two internal
Pt100 temperature sensors, are installed at 1.14 m and 1.93 m heights on a 2 m
vertical mast. Note that the height of the mast is limited to 2 m due to
operational constraints at the airport. A 1.5 W heater, integrated with each
radiation sensor, is kept on to avoid condensation on the optical window of
sensors. However, radiation sensors are not integrated with ventilated units,
which can introduce errors up to $\pm$ 15 W m-2 whenever natural ventilation
is not sufficient. Additionally, twenty temperature sensors are mounted on the
same mast, enabling high vertical resolution measurements from 4.5 cm to 2 m
above ground level (AGL). These sensors are calibrated in an isothermal bath,
and the maximum relative errors among the sensors are $<0.1$ K. The high
vertical resolution close to the surface is intended to capture the Lifted
Temperature Minimum (LTM) height and its intensity. To obtain a temperature
profile in the soil and measure sensible heat flux (SHF) at the soil surface,
a soil temperature profiler and two heat flux sensors are installed near the
concrete base. All sensors, including those on the mast and within the soil,
are connected to a data logger (Keysight DAQ970A) to record the measurements
continuously. Windcube, HATPRO, and the data logger are connected through
three mini-computers with uninterrupted internet connections, facilitating
continuous remote monitoring. To ensure a continuous and stable power supply,
all computers and other accessories are installed in two IP65 electrical
enclosures (each measuring 0.5 m × 1.0 m × 1.0 m) located near the concrete
base and connected to the reliable airport’s electricity supply.

Table 1: Details of instruments deployed at the observation site (KIAB) and
description of different meteorological variables Details of Instruments
Deployed
---
Categories |  Instruments |  Measured quantities |  Range (RA), Sampling interval (SA) and resolution (RE)
Soil sensors |  Soil temperature profiler (STP01, Hukseflux) |  Soil Temperature at 0.02, 0.05, 0.1, 0.2 and 0.5 m depth of soil |  RA: -30 to 70∘C, Absolute uncertainty: $\pm$0.7 K, relative uncertainty: $\pm$0.05 K, SA: 5 sec
Soil Heat flux (HFP01, Hukseflux) |  Heat flux at 0.05 m depth of soil |  RA: -2000 to 2000 W, uncertainty: $\pm$3 $\%$, SA: 5 sec
Surface layer within 2 meters AGL |  20 thermistors (Te connectivity sensor NTC Discrete MBD 10 kilo-ohm) |  Temperature |  RA: -40 to 125∘C, uncertainty: $\pm$0.2∘ between 0–70∘C, SA: 5 sec
2 humidity sensors (HIH-5030/5031 series, Honeywell) |  RH |  RA: 0 to 100$\%$, uncertainty: $\pm 3\%$ from 11–89$\%$, otherwise $\pm 7\%$, SA: 5 sec
Weather sensors at 2 m AGL |  Multi-component weather sensors (Vaisala, WXT530 Series) |  Air temperature |  RA: -52∘C–60∘C, uncertainty: $\pm$0.3∘C, SA: 1 sec
RH |  RA: 0–100 $\%$, uncertainty: $\pm 3\%$ at 0–90$\%$ & $\pm 5\%>90\%$, RE: 0.1$\%$, SA: 1 sec
Barometric pressure |  RA: 600 to 1100 hPa, uncertainty: $\pm$0.5 hPa, RE: 0.1 hPa, SA: 1 sec
Precipitation |  RA: 0 to 200 mm/h, uncertainty: $\pm 5\%$, SA: 10 sec
Wind speed |  RA: 0 to 60 m/s, Accuracy: $\pm 3\%$ at 10 m/s, RE: 0.1 m/s, SA: 1 sec
Wind direction |  RA: 0 to 360∘, accuracy: $\pm$3∘ at 10 m/s, RE: $1^{\circ}$, SA: 1 sec
Radiative fluxes |  4-component net radiometer (NR01, Hukseflux) |  Radiative flux (upward LW and SW, downward LW and SW) |  Calibration uncertainty solar: $<1.8\%$, calibration uncertainty longwave: $<7\%$, SA: 5 sec
Atmospheric profiles |  Wind lidar (Windcube 100S, Leosphere) |  Wind speed and direction in the hemisphere of 3 km radius |  RA: -30–30 m/s in the radial direction, accuracy: $\pm 0.5\%$, RE: 0.1∘ resolution, range resolution: 50 m, SA: 20 sec to 3 minutes (based on mode of scan)
Humidity and temperature profiler (HATPRO, Radiometer Physics, A Rohde & Schwarz Company) |  Profile of temperature, RH, water and liquid water mixing ratio, ABL height, cloud base height, and stability profiles |  Total 93 vertical levels from 10 m AGL to 10 km, having a resolution of 25 m to 300 m, RMS accuracy of water vapor mixing ratio: $\pm 0.3$ g m-3, Temperature accuracy: $\pm$0.25 K with 500 m, boundary layer ($<2$ km) mixing ratio accuracy: $\pm$ 0.03 g m-3, SA: 60 sec

To study the effect of fog on LTM and radiation divergence, fog data is taken
from the METAR, an airport weather monitoring report used for aviation
purposes [44]. Since the METAR station is located $\sim$1 km east from our
observation site and METAR reporting is half-hourly, there exists a chance of
temporal offset in the reporting of fog by METAR and the corresponding
response of sensors at our observation site. In this paper, 5-minute averaging
has been performed on all data except METAR to avoid spurious observations.
Unless stated otherwise, all heights are reported relative to the local ground
level.

##  3 Radiation model with aerosols

The radiation model used in this study is the modified version of the band
model used by Varghese et al. [72], which itself is adopted from the band
model developed and improved by Chou et al. [8], Chou and Suarez [7], Chou et
al. [9]. Later, Edwards [15], Ponnulakshmi et al. [54, 55] pointed out the
erroneous assumption of the Planckian nature of downward longwave (LW)
radiation in the reflected radiation term used in the model by Varghese et al.
[72] (which results in a spurious source of cooling near the surface, having a
nonphysical length scale). We take the model with the corrections suggested by
Ponnulakshmi et al. [54, 55]. In the modified version of the model, downward
and upward radiative flux divergence at height $z$ is given by

$\frac{dF^{\downarrow}_{ji}}{dz}=-A^{i}_{j}[c_{i}^{j}\pi
B_{j}(T)-F_{ji}^{\downarrow}]$ (1)

$\frac{dF^{\uparrow}_{ji}}{dz}=A^{i}_{j}[c_{i}^{j}\pi
B_{j}(T)-F_{ji}^{\uparrow}]$ (2)

The top boundary condition comes from the fact that there is no incoming
longwave radiative flux at the top of the atmosphere, and fluxes for the
bottom boundary are given by reflected and emitted components of longwave
radiation from the ground.

$F_{ji}^{\downarrow}(\infty)=0$ (3)

$F{ji}^{\uparrow}(0)=c_{i}^{j}[\epsilon_{s}\pi
B_{j}(T_{s})]+(1-\epsilon_{s})F_{ji}^{\downarrow}(0)$ (4)

where $F_{ji}$ is the radiative fluxes for sub-band $i$ of band $j$.
$A_{j}^{i}$ is given by

$A_{j}^{i}=dk_{j}^{i}\bigg{(}\frac{P}{P_{r}}\bigg{)}^{m}f_{j}(T,Tr)\rho_{w}$
(5)

The value of $c_{i}^{j}$, $d$, $k_{j}^{i}$, $P_{r}$, m, and $T_{r}$ as well as
pressure and temperature scaling have been taken from Chou and Suarez [7],
Chou et al. [9]. $B$ is the Planck function of radiation. $T_{s}$ is the
surface temperature of the surface having emissivity $\epsilon_{s}$.

###  3.1 Inclusion of aerosol-radiation interactions

The vertical profile of the aerosols close to the ground plays a key role via
a change in radiative flux divergence [46, 47]. From laboratory experiments,
Mukund et al. [47] showed that the LTM intensity decreases with decrease in
aerosol concentrations in the test section, and it disappears when the aerosol
concentrations in the test section are reduced significantly by filtering
aerosols or by blocking radiation interaction in the test section with a thick
opaque sheet. Noting the experimental observations of Mukund et al. [47], we
have developed an extension to the corrected version of the model Ponnulakshmi
et al. [54, 55] by including aerosol-radiation effects. The extent to which a
spherical aerosol particle ($s$) of radius $r$ and refractive index
$n+k\textit{i}$, interacts with radiation at wavenumber $\nu$ is given by the
extinction cross-section $\sigma_{ext}^{s}(\nu,r)$ [69, 34]. Effect of the
hygroscopic growth of aerosols on radiation has been accounted via a change in
refractive index when RH changes [30]. For simplicity, the shape of aerosols
is considered to be spherical, and independent scattering dominates for
typical aerosol concentrations in the atmosphere [41]. Under these conditions,
extinction efficiency ($\sigma_{ext}^{s}(\nu,z)$) at wavenumber $\nu$ for an
aerosol species $s$ having distribution $N_{s}(r,z)$ at height $z$ is given by

$\sigma_{ext}^{s}(\nu,z)=\sum_{r}\sigma_{ext}^{s}(\nu,r)N_{s}(r,z)$ (6)

where $N_{s}(r,z)$ follow log-normal distribution at height $z$ [30] and is
given by

$\frac{dN_{s}(r,z)}{dr}=\frac{N_{s}(z)}{\sqrt{2\pi}r\log\sigma_{i}\ln{10}}exp\bigg{[}-\frac{1}{2}\bigg{(}\frac{\log
r-\log r_{modN,s}}{\log\sigma_{i}}\bigg{)}^{2}\bigg{]}$ (7)

where $N_{s}(z)$ is the total number density of aerosol species $s$ at height
$z$; $\sigma$ and $r_{modN,s}$ are distribution parameters.
$\sigma_{ext}^{s}(\nu,r)$ is calculated from the standard BHMIE code [5] and
$\sigma_{ext}^{s}(\nu,z)$ is summed for all aerosol species ($s$) and sub-band
interval $i$ to get total extinction efficiency in band $j$ at height $z$

$\sigma_{ext}^{j}(z)=\sum_{\nu=\nu_{ij}}\sum_{s=1}^{S}\sigma_{ext}^{s}(\nu,z)$
(8)

The diffuse transmission function for the aerosol in band $j$, at level $z$ is
given by Liou [41]

$\tau_{j}^{aer}(z)=exp\bigg{(}-d\int_{0}^{z}\sigma_{ext}^{j}(z^{\prime})dz^{\prime}\bigg{)}$
(9)

When water vapor and aerosols are both present, the transmission function for
a band $j$ is given by:

$\tau_{j}(eff)=\tau_{j}^{wv}\tau_{j}^{aer}$ (10)

where $\tau_{j}^{wv}$ is given by

$\tau_{j}^{wv}=\sum_{i=1}^{m_{j}}c_{i}^{j}\tau_{j}^{i}$ (11)

where $\tau_{j}^{i}$ is given by

$\tau_{j}^{i}=exp\bigg{[}-d\int_{0}^{z}k_{j}^{i}\bigg{(}\frac{P}{P_{r}}\bigg{)}^{m}f_{j}(T,T_{r})\rho_{w}dz^{\prime}\bigg{]}$
(12)

From Eqs. (9, 10, 11, 12), $\tau_{j}^{i}(eff)$ is given by

$\tau_{j}^{i}(eff)=exp\Bigg{[}-d\int_{0}^{z}\bigg{(}\sigma_{ext}^{j}(z^{\prime})+k_{j}^{i}\bigg{(}\frac{P}{P_{r}}\bigg{)}^{m}f_{j}(T,T_{r})\rho_{w}\bigg{)}dz^{\prime}\Bigg{]}$
(13)

To account for the role of aerosols, $A_{j}^{i}$ is updated in the model by
using Equation (13) as

$A_{j}^{i}=d\bigg{[}\sigma_{ext}^{j}(z)+k_{j}^{i}\bigg{(}\frac{P}{P_{r}}\bigg{)}^{m}f_{j}(T,T_{r})\rho_{w}\bigg{]}$
(14)

Inserting the updated expression of $A_{j}^{i}$ from Equation (14), we get the
updated radiation model, which accounts for aerosol-radiation interactions. In
this updated model, Equation (1, 2, 4 and 11) remains the same along with the
updated Equation (14).

From Equation (1) and (2), total radiative flux divergence at level z is given
by

$\frac{dF}{dz}=\sum_{i}\sum_{j}\bigg{(}\frac{dF_{ij}^{\uparrow}}{dz}-\frac{dF_{ij}^{\downarrow}}{dz}\bigg{)}$
(15)

Equation (15) becomes the source term in the 1-dimensional radiation-
conduction equation which is given by:

$\frac{\partial T(t,z)}{\partial t}=\alpha\frac{\partial^{2}T(T,z)}{\partial
z^{2}}-\frac{1}{\rho C_{p}}\frac{dF}{dz}$ (16)

where $z\in(0,H)$ and $t>0$. $H$ is the height of the atmosphere, and $\alpha$
is the molecular thermal diffusivity of air. Equation (16) is solved using the
Thomas Algorithm [56] to get the temperature and radiative flux evolution in
the atmosphere in the presence of water vapor and aerosols.

###  3.2 Aerosol concentrations and profile

Due to the unavailability of aerosol data at the observation site,
representative aerosol properties have been taken from the OPAC (Optical
Properties of Aerosols and Clouds) database to account for the role of
aerosols in the model [30]. Although this database contains diverse aerosol
profiles for different atmospheric conditions, the considered radiation model
has been integrated with urban aerosols (which consists of insoluble; INSO,
water-soluble; WASO and soot; SOOT particles) because flight operations and
other construction-work close to the observation site emit a massive amount of
aerosol particles in the atmosphere. Note that only WASO particles show
hygroscopic growth as a function of RH [30], which has been accounted for in
all simulations. The parameters for the size distribution and refractive index
for the different aerosol components at different RH have been taken from the
same database where all components follow log-normal distribution as shown in
Equation (7).

Hess et al. [30] has considered the roughly uniform concentration of aerosols
(scale height of 8 km) in the ABL, which has not been observed in Indian
tropical regions [12, 13, 6]. Devara and Raj [12] and Devara et al. [13] have
reported a decrease in the aerosol concentration with an increase in height
(measured above 40 m AGL) from long-term lidar observations at a tropical
site. Chate and Pranesha [6] has shown uniform aerosol concentration within 1
m AGL in the range of $10^{4}$–$10^{5}$ cm-3, which is 10-100 times higher
compared to the concentration measured above 40 m. Hence, we use the aerosol
concentration profile, based on the measurements by Devara and Raj [12],
Devara et al. [13], Chate and Pranesha [6], and we use the properties of
aerosol species as provided by the OPAC database [30].

Mukund et al. [46] fitted the Rouse profile to the aerosols profile from
Devara and Raj [12] and arrived at the functional profile as in Equation (17)
for the variation of aerosol number density with height. Taking into account
the observations of Chate and Pranesha [6] and Mukund et al. [47]
calculations, we use different equations for aerosol concentrations above 1 m
and below 1 m differently (Equation 17, 18 and 19)

$N_{i}(z)=N_{i0}\bigg{(}\frac{z}{Z}\bigg{)}^{-p},z>1m$ (17)

$N_{i}(z)=N_{c}exp(-z+1),z\leq 1m$ (18)

$N_{c}=N_{1m+}(1.0+10^{-6})$ (19)

where $p=0.74$ and $z=50$ m and $N_{i0}$ is total concentration at height $z$
[46, 30].

Figure 2: Comparison of upward, downward, and net flux, with the radiation
model by Varghese et al. [72], (this model produces correct result at
$\epsilon_{s}=1$) and FASCODE [10] for $\epsilon_{s}=1$. In these models,
Midlatitude summer atmosphere with water vapor absorption has been used to
calculate fluxes.

Figure 3:  Vertical profile of aerosol concentration (accumulation and coarse
mode only): concentration of water-soluble (WASO) and soot particles (SOOT)
are significantly higher than that of insoluble particles (INSO), and
concentrations are roughly uniform below 1 m AGL.

Since direct measurements of aerosol concentration profile and its properties
are not available at the observation site, we have tested 1 to 7 times of the
reported concentration in Hess et al. [30] in the present work to account for
the uncertainties in spatial and temporal variability of aerosol particle
concentrations and properties [30, 73, 19, 75]. If we take the same aerosol
concentrations as reported in Hess et al. [30], the steady-state simulated LTM
intensity is less than 0.2 K, which is weaker compared to our field
observations as well as other field observations [47]. Instead, if we consider
six times (6x) higher concentration of aerosols compared to the reported
concentration in Hess et al. [30] (Figure 3), the LTM and LHR obtained from
the simulations are in good agreement with our field observations. Note that
aerosol particles of diameter less than 0.1 $\mu$m (ultra-fine particles) are
not relevant to optical interactions [64], hence aerosol concentration
presented here consists of accumulation and coarse mode only. With this
profile, the total aerosol concentration at 1 m AGL is 3.3$\times 10^{5}$
cm-3, whereas it is 2.15$\times 10^{4}$ cm-3 at 40 m AGL, which is in the same
order of magnitude, reported from many field observations [75]. Hence, we will
use aerosol concentration profiles shown in Figure 3 for all further analysis.
In Section 5, we will discuss the implications of higher concentrations of
aerosols close to the ground.

###  3.3 Validation of the model

Although the radiation model by Varghese et al. [72] produces a spurious
cooling near the ground due to incorrect handling of reflected term, such
spurious cooling does not occur for $\epsilon_{s}=1$ because the reflected
component of downward radiative flux vanishes (Equation 4). Hence, the present
model has been validated against the model by Varghese et al. [72] and the
line-by-line Fast Atmospheric Signature Code (FASCODE) by Clough et al. [10]
for $\epsilon_{s}=1$ for the Mid Latitude Summer (MLS) standard atmosphere
with water vapor line absorption only. Figure 2 shows the comparison of
upward, downward, and net flux with the radiation model by Varghese et al.
[72] model and FASCODE. At the top of the atmosphere, offset in upward fluxes
in the present model goes up to 7 W m-2 as compared to FASCODE, and a similar
offset in upward fluxes has also been observed between the model by Varghese
et al. [72] and FASCODE [72]. Near ground, the relative offset of fluxes in
the present model is less than 2 W m-2 compared to the model by Varghese et
al. [72] and FASCODE.

###  3.4 Initialization of radiation model

Vertical profile of temperature and water vapor mixing ratio with respect to
pressure and height and aerosols profiles are required to initialize the
model. To get the temperature and humidity profile from the surface to 50 km
AGL, data from three different sources have been concatenated according to the
height: surface to 2 m data from the mast observations, 2 m to 10 m data from
MW radiometer measurements, and 10 km to 50 km from spatially interpolated
ERA5 reanalysis dataset [16]. Since, true vertical resolution of the retrieved
water vapor profile is coarse [4], we have performed sensitivity analysis by
$\pm$20% change in mixing ratio at all heights ($\pm$1.2 g/kg change at 10 m
AGL), magnitude of change in temperature is less than 0.2 K at any height. It
is one order of magnitude smaller compared to observed LTM intensity (Section
6), also variation of the mixing ratio alone in this range will not produce an
LTM type profile. Hence, we will use the observed mixing ratio profiles from
the MW radiometer. To resolve LTM and radiation divergence, the vertical
resolution of the present model is kept at 0.4 mm within 1 m AGL, and later,
it gradually coarsens to 18 m at 50 km AGL, which counts a total of 32771
vertical grid points in the model. All simulations have been performed with
and without aerosol profiles for all the considered days at this resolution.

For the bottom boundary condition, we have used observed/estimated surface
temperature ($T_{s}$). We don’t have a direct measurement of $T_{s}$ for the
initial 44-days of analysis, and hence, we have estimated it using the
radiosity Equation (20), whenever required. The estimated surface temperature
has been validated against the observed surface temperature (mounted later in
January 2023), which is available for the last 36-days of the analysis. Here,
it is to be noted that with a surface emissivity of $\epsilon_{s}=0.95$, the
mean and standard deviation of the absolute error between estimated and
observed $T_{s}$ from local sunset to sunrise time is 0.42 K and 0.3 K,
respectively. This discrepancy is 5–6 times smaller than the observed LTM
intensity derived from direct $T_{s}$ observations.(See supplementary figure
S1).

$F^{\uparrow}_{s}=\epsilon_{s}\sigma
T_{s}^{4}+(1-\epsilon_{s})F^{\downarrow}_{s}$ (20)

where $F^{\uparrow}_{s}$ and $F^{\downarrow}_{s}$ are upward and downward LW
flux respectively.

Each day, simulation begins with a concatenated temperature and water vapor
mixing ratio profile, initiated two hours before local sunset as a model spin-
up. After 5–6 hours post local sunset, mist forms, reducing visibility to less
than 5 km for most days (Figure 4a). This can lead to sensor wetting and
measurement errors when relative humidity (RH) exceeds 80%. Therefore,
analysis and simulation are primarily restricted to within 4 hours after local
sunset when RH remains below 75%. However, when discussing fog/cloud effects
on LTM (Subsection 4.4), mast-temperature observations during fog are
approached with caution. Significant changes in CNR at 50 m AGL occur with
mist or fog presence, attributed to variations in micron-sized particle (water
droplet) concentration or size distribution not considered in the current
model. As aerosol concentrations remain constant over time in simulations,
analysis is limited to 4 hours post local sunset to mitigate observed mist or
fog effects at the site and condensation-induced measurement errors.

##  4 Results

###  4.1 LTM observations

A temperature profile within 2 m AGL is considered an LTM profile if the
minimum temperature between 10 cm to 55 cm AGL is lower than the surface
temperature and the temperature between 1.6 m and 2 m by at least 0.3 K. Note
that in the absence of direct observations for ground surface temperature, we
have used temperature measured at 4.5 cm to quantify LTM occurrence. Threshold
of 0.3 K is chosen to avoid the spurious observation of LTM whereas the
threshold for upper and lower limit of LTM height is taken from Blay-Carreras
et al. [3] and Oke [53].

####  4.1.1 LTM occurrence and characteristics

Although it has been speculated that LTM would not appear in cloudy conditions
or it disappears when cloud/fog appear [47, 3], the behavior of LTM due to
change in the downward LW flux in foggy conditions has not been reported
quantitatively through observations. From the simultaneous measurement of LW
flux during LTM occurrences and fog events from our field experiments, we show
that downward LW flux changes substantially with the appearance of fog (Figure
4b). In this plot, downward LW flux obtained from the radiation sensor mounted
at 1.14 m AGL has been overlapped with LTM (orange marker) and fog occurrence
(red marker) to observe LTM behavior in different atmospheric conditions.
Since on all considered days show similar behavior (for eighty days, covering
two fog seasons), data from only five days have been shown for brevity. It can
be observed that downward LW flux shows a distinctive diurnal variation
(except when fog appears), indicating that the sky is free from convective
system. Also, the precipitation sensor has not recorded any precipitation (not
shown). However, mild fluctuations in the downward LW flux during the local
afternoon on some days indicate the presence of fair-weather cumulus clouds
associated with local convection.

Figure 4: Observations of LTM over a few days (a) Change in CNR at 50 m AGL in
the presence of mist and fog indicates a change in concentration or
distribution of micron-size water droplets in the atmosphere. (b) LTM appears
during evening transitions and maintains for hours before fog occurs. LTM is
not observed during day hours, local conditions are based on METAR
notification and reported minimum-visibility on 17th, 18th, 19th, 20th and
21st December , 2021 are 96 m, 800 m, 193 m, 48 m and 48 m respectively.

We note that, LTM is absent during the daytime but emerges as the evening
transition progresses, persisting for several hours on clear nights or
intermittently if local conditions are unfavorable. When fog develops in the
early morning, LTM disappears, which is also accompanied by a sharp increase
in downward longwave (LW) flux (except on 18th December 2021). It should be
noted that temperature from the mast sensors and, hence, LTM occurrence might
not be accurate because of sensor wetting, but a similar observation, like
disappearance of LTM in the presence of fog/cloud has been reported in other
field experiments [47, 3]. We will further look at this aspect from idealized
simulations in Section 4.4. From METAR observations, fog reported on $18^{th}$
December 2021 was mild, having a minimum visibility of 804 m (possibly an
optically thin layer of fog). Because of the thin layer of the fog, downward
LW flux as well as divergence does not change sharply, and LTM persists during
this fog event. When sunlight causes the dissipation of fog in the morning,
downward LW flux, as well as radiation divergence, returns to its diurnal
cycle. However, because of solar heating, local convection close to the
surface dominates and does not allow sustenance of LTM. Hence, LTM is not
observed during daytime in spite of the sky being cloud-free.

Based on eighty days of observations spanning two winter and two spring
seasons, we find that LTM characteristics remain consistent across seasons.
During winter, LTM intensity averages $2.3\pm 0.7$ K, while in spring it is
$2.0\pm 0.5$ K (mean and one standard deviation). Likewise, LTM height
measures $0.30\pm 0.10$ m in winter and $0.32\pm 0.12$ m in spring. Overall,
across the eighty-days analysis period, LTM intensity averages 2.2$\pm$0.6 K,
with a height of 0.31$\pm$0.11 m. These findings align well with previous
studies (Mukund et al. [47], Blay-Carreras et al. [3]). Our observations
indicate slightly higher LTM intensity compared to Blay-Carreras et al. [3]
and lower than Mukund et al. [47]. Minor differences in LTM characteristics
across different field experiments may stem from variations in favorable
conditions such as calm, clear skies, ground properties, and aerosol
characteristics.

####  4.1.2 Parameters that control LTM

Calm and clear sky conditions are favorable for LTM occurrence, which implies
that wind speed, TKE, and downward and upward LW flux are important parameters
that control the LTM characteristics [39, 47, 3]. Further, Apart from aerosol
characteristics near the ground, SHF at the soil surface controls the surface
temperature evolution and hence, LTM intensity. Histogram of these
meteorological factors with and without LTM occurrence from local sunset to
the next 4 hours are shown in Figure 5. Unfortunately, since the wind sensor
was not functioning during the winter and spring seasons of 2022-23, we have
used initial 44 days of wind data from season 2021-22 for analysis (Figure 5a
and 5b).

Low wind speed and fluctuations introduce minimal disturbances so that an LTM
profile can sustain. Wind speed measured 2 m above the ground level is $<$ 6 m
s-1 indicate the calm condition during the observation period (Figure 5a). We
observe that LTM occurrence strongly depends on the wind speed. Most ($>$ 80
%) of the LTM occurrence is when the wind speed is less than 2 m s-1.
Moreover, LTM does not appear or sustain if wind speed is more than 3 m s-1. A
drop in frequency of LTM occurrence with the increase in wind speed rules out
the role of advection or drainage flow in LTM development, which is also
reported in other field experiments [47, 3].

Figure 5:  Histogram of different meteorological factors with and without LTM.
(a) Wind speed and (b) TKE at 2 m AGL; (c) downward and (d) upward LW flux at
1.14 m AGL; (e) Surface sensible heat flux (SHF) at 0.05 m below ground.

Apart from mean wind characteristics, turbulence is another key parameter in
LTM development [48, 47, 3, 35]. Since turbulent kinetic energy (TKE) is a
quantitative measure of the intensity of turbulence, we calculate it from
horizontal wind measured at 2 m AGL using Equation 21.

$TKE=\frac{1}{2}\big{(}\overline{u^{\prime 2}}+\overline{v^{\prime 2}}\big{)}$
(21)

where $u$ and $v$ are easterly and northerly components of wind, respectively,
sampled at the interval of 1 second. Velocity fluctuation is calculated as
$u^{\prime}=u-\overline{u}$, $v^{\prime}=v-\overline{v}$, and all averaging
have been done over 5 minutes. Figure 5b shows TKE variation with and without
LTM. Although TKE varies up to 0.5 m2 s-2, TKE $>$0.2 m2 s-2 is observed for
less than 8% of the observations, which indicates that the boundary layer near
the ground is not highly turbulent. Further, note that most ($\sim$ 95 %) of
the LTM occurrence is when the TKE is $<0.1$ m2 s-2 and LTM is not observed
when TKE is $>$ 0.3 m2 s-2. It signifies the requirement of low-turbulent
conditions within a few meters from ground for the occurrence of LTM. Since
low wind speed and TKE provide favorable conditions for LTM occurrence but do
not interact directly with LTM evolution, we observe that LTM intensity is
poorly correlated with wind speed and LTM intensity.

Figures 5c and 5d show histograms of observed radiative fluxes with and
without LTM. Unlike wind-speed and TKE, we note that LTM appears for all
observed values of LW radiative fluxes. However, the frequency of LTM
occurrence increases with the decrease in upward and downward LW fluxes. It
indicates that LTM occurrence, not only depends on cloud-free sky, but it also
depends on the state of the local atmosphere, which can modulate the incoming
LW fluxes. These factors include vertical distribution of water vapor and
thermal state of the atmosphere, which can change the incoming LW radiation
depending on how it is distributed vertically. Since LTM intensity depends on
radiation divergence, not on radiative fluxes (Subsection 4.2), we observe
that LTM intensity and LW fluxes are weakly anti-correlated ($r<-0.2$).

Sensible heat flux (SHF) and surface temperature exhibit a strong correlation
and are pivotal in determining the occurrence and characteristics of the LTM.
Figure 5e illustrates that the occurrence of LTM decreases with an increase in
SHF. When LTM is observed, assuming other fluxes remain constant, a reduction
in SHF diminishes the surface cooling rate, potentially resulting in a
relatively higher surface temperature, thus intensifying LTM. We find a
moderate negative correlation between SHF and LTM intensity ($r=-0.36$,
p-values $<$ .001). Similar relationships between surface SHF and radiative
cooling have been documented by Gentine et al. [25]. In summary, LTM
occurrence tends to increase with decreasing wind speed, Turbulent Kinetic
Energy, upward and downward Longwave fluxes, as well as sensible heat flux.

###  4.2 LTM in 1-D model and comparison with field observations

Figure 6:  Mean relative temperature profiles (line plots) from observations
(green) and simulations with aerosols (blue) and without aerosols (orange).
Shading represents ($\pm 1\sigma$) variability in the profiles for each cases.
(a) day-to-day variability in 4-hourly mean profiles (from local sunset to
next 4-hours) observed over 80 days spanning two fog-seasons and (b) temporal
variability of the vertical temperature profile observed during the 4 hours
period after the local sunset for the same dataset. The green, dotted lines in
observations represent the transition from mast-data (up to 2 m) to microwave
radiometer data beyond 10 m. Note here vertical axis has hybrid-scale, a
logarithmic scale above 1 m AGL, and a linear scale from the surface to 1 m
AGL.

Mukund et al. [47] demonstrated through laboratory experiments the necessity
of aerosols, for getting observed temperature profiles and radiative cooling.
However, both laboratory and field experiments conducted by Mukund et al.
[47], were limited to a height within two meters close to the ground. For
various atmospheric phenomena, such as fog occurrence, temperature and
humidity profiles extending several hundred meters above ground level are
crucial. In this context, utilizing our dataset, we investigate the
significance of aerosols in determining vertical temperature profiles within
the nocturnal atmospheric boundary layer. For all eighty-days of observations,
numerical simulations were conducted with and without aerosols, for a four-
hours period from sunset. Initial and boundary conditions are derived from
observations as discussed in Subsection 3.4. Given that ground-level
temperatures vary diurnally and daily, we present relative temperature
profiles with respect to the ground surface. Results from this analysis are
depicted in Figure 6. It is evident that, there exists a substantial disparity
between observed and simulated profiles without aerosols, both in profile
shape and mean temperatures ($\sim$ 2–5°C). Incorporating aerosols into the
simulations largely mitigates these temperature differences, resulting in
simulated vertical profiles resembling LTM as observed in this field study.
Also, the impact of including aerosols in radiative processes extends several
hundred meters into the boundary layer. However, still a significant offset in
temperature (more than 2oC) occurs above 20 m, this might be due to large-
scale temperature advection (see supplementary figure S2) and day-to-day
variations as discussed below.

In Figure 6, we present two types of averaging both for simulations and field
observations. These plots elucidate two types of variabilities in the
temperature profile. We have considered observations and simulated data at
five-minutes time interval, starting from local sunset time to the next four
hours on each of the eighty days. For this part of the discussion, concentrate
on observed profiles (green color) and simulated profiles with aerosols (blue
color). The mean temperature profiles in Figures 6a and 6b, are represented by
solid green-lines (observation) and dashed blue-lines for simulations. Day-to-
Day variability in the temperature profiles for eighty days is depicted in
Figure 6a. For this plot, temperature measurements for each day within the
4-hour window following local sunset are averaged to obtain a single mean
temperature profile for that day. This process is repeated for eighty-days in
the dataset, resulting in a collection of eighty-mean temperature profiles.
Now the average of these eighty profiles is the solid green-line (for
observation) and dashed blue-line (for simulation with aerosols) in Figure 6a.
Green-shaded region is obtained by calculating variability ($\pm 1\sigma$) of
observed temperature at each height from the mean value of observation at that
height. Shaded region indicates day-to-day variability of temperature in
observation, resulting from the prevailing atmospheric conditions. Similarly
blue-shaded region indicates day-to-day variability of simulated temperature
profile for given input temperature initialization and observed boundary
condition.

We can also investigate temporal variability of the temperature profiles (see
Figure 6b). For this analysis, we consider five-minute interval separated 48
(4 hr x 12/hr) temperature profiles on each day for eighty-days. Here, we take
averages across eighty-days for corresponding time profiles, we get a set of
48-mean temperature profiles. The average of these 48-profile is same as the
one we got previously and is plotted as solid green-line (observation) and
dashed blue-line (for simulation with aerosols). As above, for the set of
48-temperature profiles calculating the variability ($\pm 1\sigma$) of
temperature at each height from the mean value at that height, we have plotted
the shaded green (observation) region and shaded blue (for simulation with
aerosols) region. It is evident that, in the surface layer up to 20–30 m, the
day-to-day variability (in Figure 6a) is many times greater than the temporal
variability (in Figure 6b). The result indicates that, time to establish
observed temperature profile on a given day is very short, and most of the
variation originates from the day-to-day variation in the atmospheric
conditions including temperature, water vapor in the atmosphere, diurnal
history of solar insolation and probably even the aerosol distribution.

Figure 7: Mean radiative flux and its divergence with and without aerosols
from local sunset to next 4 hours over the daily mean profiles of 80 days
analysis. (a) Net LW radiative flux with and without aerosols from
simulations. Flux measurements from the field experiments are also marked. (b)
Vertical variation of radiation, conduction, and net divergence without
aerosols and (c) with aerosols. Here, absolute divergence less than 0.01 W m-3
has been shown as $\pm 10^{-2}$ W m-3. Spread at any height is one standard
deviation over 4 hours from sunset (shading around line plot).

Scattering, absorption, and emission of radiation from aerosols change the net
radiative flux and net radiation divergence, leading to different temperature
profiles in the atmosphere [41]. 4-hour (from sunset) mean net radiative flux
with/without aerosols, as well as net LW flux obtained from radiation sensors,
have been presented in Figure 7a (green marker). The shaded region shows one
standard deviation spread over 4 hours. The maximum spread in both simulations
and observations is less than 6 W m-2 at 1.14 m AGL, which signifies that
simulations and observations follow similar variability over the evolution.
Downward LW fluxes obtained from both radiation sensors show an offset of 4 W
m-2, a possible relative uncertainty in radiative flux measurement. However,
net radiative flux from simulations is 100 W m-2 higher than the observed one
if aerosols are not accounted for, and the above difference reduces to 40–50 W
m-2 if aerosols are accounted for in the model. These offsets in downward LW
flux can be further reduced if other major greenhouse gases like Carbon
Dioxide (CO2) and Ozone (O3) are accounted for in the radiation model.

Radiation, conduction, and net divergence with/without aerosols are shown in
Figure 7b, c (Equation 16). When aerosols are not accounted for in the model,
radiation divergence induces heating within a few decimeters above the
surface, but conduction divergence causes cooling. In this region, cooling
induced by conduction divergence dominates over warming induced by radiation
divergence and produces net cooling close to the surface. After a few
decimeters above the surface, conduction divergence weakens, and radiation
divergence dominates over the remaining column of the atmosphere. Overall, in
the absence of aerosols, radiation and conduction divergence together lead to
net divergence (cooling) of the whole column, but net divergence decreases
monotonically with height and does not cause any preferential cooling, which
is required for the development of LTM.

In the presence of aerosols, radiation divergence is substantial near the
surface and dominates over conduction divergence over the whole column (Figure
7c). However, as heating induced by conduction divergence decreases rapidly
away from the surface and cooling caused by radiation divergence dominates
(Equation 16). It leads to locally enhanced net divergence between 0.5 to 2 m
above the surface and makes the net divergence profile non-monotonous with
height. This enhanced net divergence causes preferential cooling, which leads
to LTM development. Interplay of these flux divergence terms, at the surface,
is further complicated by the presence of penetrative convection system (see
Kaushal et al. [36]) driven by radiative cooling. We also observe that
aerosol-induced radiation divergence (net cooling) after a few decimeters from
the surface is higher than the no-aerosols conditions, extending for a few
hundred meters. Although the net divergence (cooling) decreases with height,
it can induce significant temperature change over the night in ABL.

Figure 8: Temporal variation in mean LHR from local sunset to next 4 hours up
to 1 km (a) Without aerosols: when aerosol-radiation interactions are not
accounted for in the model (b) With aerosols: When aerosol-radiation
interactions are accounted for, (c) Observations; derived LHR from observed
temperature profiles using Equation 16. Derived LHR from observations are in
better agreement with aerosol-accounted LHR, compared to without-aerosol LHR.

###  4.3 Longwave heating rate (LHR) after sunset

Temporal variation in day-to-day mean LHR over 80 days from local sunset to
the next 4 hours are shown in Figure 8. Since the net heating rate and
conduction heating rate can be directly estimated from the temperature
profile, LHR profiles have been derived using Equation (16) under the
assumption of negligible horizontal advection and vertical mixing. When
aerosols are not accounted for, the mean LHR near the surface is weaker
compared to the LHR from the field observations and aerosol-accounted
simulations (Figure 8). Simulations without aerosols show positive LHR and,
hence, radiative warming within a few centimeters from the surface. Above the
warming region, radiative cooling of $\approx$2 K/h is observed near the
ground. A comparable radiative cooling rate has also been reported without
aerosols in HA and Mahrt [29] and Steeneveld et al. [66]. In contrast,
observations and aerosols-accounted models show intense cooling within 1 m AGL
where LHR goes less than -10 K/h. Similar values of LHR of several K/h during
sunset have also been reported by Steeneveld et al. [68], but all LW radiation
models systematically underestimate radiative cooling by one order of
magnitude, which could be attributed to the absence of aerosols-radiation
interaction in the models. Further, when we don’t account for aerosols in the
models, it can lead to an offset of $\approx 4$ K in the model (Figure 6),
which can affect the onset, growth, and intensity of fog. Here, we show that
LHR profiles from simulations and field experiments are of the same order only
if aerosols-radiation interactions are allowed in the model.

The temporal and vertical evolution of LHR profiles from aerosol-accounted
simulations is in good agreement with derived profiles from field observations
(Figure 8). During local sunset, radiative cooling of more than 1 K h-1 is
observed up to 10 m AGL in aerosol-accounted models as well as in field
observations, which causes intense cooling close to the ground. Further, LHR
decreases sharply with height, but a weak negative LHR can be observed till a
few hundred meters. We believe that LHR fluctuations in derived LHR are due to
the advection of temperature and humidity profiles, which has not been
accounted for in the present model. Although LHR spread in observations is
large compared to simulations, mean LHR from aerosol-accounted simulations is
in better agreement with the observed mean LHR compared to simulations.
Moreover, it is clear from derived LHR and aerosol-accounted simulation that
LHR can be lower than -5 K h-1 very close to the ground which might play an
important role in land-atmosphere coupling.

###  4.4 Radiation divergence and LTM in the presence of fog/cloud

Based on the past field observations, it has been speculated that LTM
disappears if cloud passes over it [60, 53, 47, 3]. We also observe that LTM
disappears in most of the fog events but sustains in one fog event (Figure 4,
on 18th December). Hence, to investigate the role of different thicknesses as
well as different base heights of fog on LTM, we have considered four
idealized layers of fog/cloud in simulations. These layers are located
between; surface to 10 m (T1), surface to 90 m (T2), 10 m–100 m (T3), and 300
m–390 m (T4). Although T1 and T2 both represent fog touching the ground, T1 is
shallower than T2. T3 and T4 both represent fog/cloud whose thickness is the
same, but its base height is different. Further, the size distribution and
concentration of fog are not site-specific and are taken from the OPAC
database [30]. For the sake of simplicity, the concentration and size
distribution of fog do not change within a fog layer and show sharp changes
across the boundary. In this set of analysis, aerosol profile considered is
same as earlier (Figure 3), in addition, fog droplets were considered with a
modified gamma distribution having a total concentration of 15 cm-3.

For each fog thickness, we have simulated the growth and dissipation of LTM
profiles, radiative flux, and its divergence in the presence of the fog layer.
In all three simulations, the initial 2 hours of the simulations are run
without the fog layer to allow the LTM to develop. After 2 hours of
simulations, the fog layer is activated, where the evolution of different
parameters like temperature, radiative flux, and divergence under the combined
effect of aerosols and fog are observed for the next 2 hours of simulation.

Figure 9: Vertical profiles of (a) relative temperature and (b) radiative
divergence in the presence of different fog layers.

Figure 9(a) shows relative temperature profiles compared to the surface
temperature in the presence of different fog/cloud layers as well as without
it. Without any fog/cloud, we observe LTM profiles of 2 K, usually observed in
our field experiments. However, LTM intensity and height increase in the
presence of shallow fog of 2 m thickness (Case T1) due to enhanced radiation
divergence near the ground (Figure 9(b)). It is due to an increase in
radiation interaction with fog droplets and clear skies. A similar case, like
maintenance of LTM in fog has been observed during a fog event (Figure 4). At
the fog top and bottom, we notice a sharp change in temperature profiles and
radiative divergence, which is due to idealized boundary conditions, i.e., the
sharp change in fog concentration at the boundary. After the fog top,
temperature and radiative divergence tend towards without fog condition. With
an increase in fog thickness (Case T2), the optical thickness of fog becomes
so large that it behaves like an opaque sheet for the air layer near the
ground. Hence, radiative flux evolution becomes practically independent above
the fog layer and near the ground, and LTM does not appear. We have observed
an increase in downward LW radiation in the presence of fog in the simulations
(not shown here), which has also been observed in the field experiments
(Figure 4). Hence, we observe an inversion profile rather than an LTM profile.
Further, with an increase in the cloud base height, keeping the same thickness
(Case T3 and T4), we observe that radiation divergence weakens near the
ground, which results into an inversion profile of higher intensity.

We observe a significant temperature drop at the fog top. Many field
observations and simulations have reported intense fog top cooling [63, 49,
37, 77], but we note here that the present model is one-dimensional and does
not account for gravitational settling, downward draft, and mixing due to
turbulent convection (because of negative buoyancy). With such limitations,
temperature drop within the fog layer or fog top/bottom indicated here can be
significant. Further, vertical mixing induced by fog top cooling might lead to
temperature convergence within the fog layer [57]. Moreover, the energy
released during phase change in foggy conditions offsets the cooling caused by
radiation divergence. As fog top height increases, cooling caused by radiation
divergence extends across the fog layer, which results in reduced observable
cooling within the fog layer. If fog top height is substantial and fog
duration is brief, temperature drop because of fog top cooling is not
significantly noticeable (See supplementary figure S3). However, our interest
here is to test the radiative effect of the fog layer, especially the impact
of fog on radiation divergence and the sustenance of LTM. Therefore, fog
micro-physics and related dynamics will not be discussed here. We observe that
enhanced radiation divergence at the fog top is responsible for the intense
cooling at the fog top.

##  5 Discussions

LTM characteristics vary significantly across different field experiments [53,
47, 3]. In the present field experiments, the observed mean LTM height is
close to the height observed by Mukund et al. [47], whereas the observed
intensity is lower. Mukund et al. [47], who studied LTM at one location with
modified surface properties, have shown that LTM height does not depend
significantly on the surface type. We expect that it strongly depends on other
parameters, especially the aerosol concentration profiles, which have high
spatial and temporal variability [75]. An extensive field experiment with
simultaneous profiling of aerosols and LTM would unravel the direct
correlation between aerosol vertical distribution and variation in LTM height
as reported in field observations [53, 47, 3].

The results obtained from the one-dimensional conduction-radiation model,
which incorporates radiation interactions with a representative aerosol
profile, closely agree with the observed temperature profiles after the
evening transitions. This agreement also extends to predicted and measured
radiation divergence during the evening transition in the present study and
other field observations [68]. However, considerable variability in aerosol
vertical distribution, particle concentrations, sizes, chemical composition,
and their intricate interactions with radiation is reported by [19]. In this
survey, the total aerosol concentration at a few sites was found to exceed
$10^{5}$ cm-3, but most of these observations have been performed a few meters
away from the ground, and aerosols within 1–2 m above surface have not been
investigated. However, aerosol concentration within 1 m can be 10-100 times
higher than the concentration measured a few meters above the ground [13, 6].

Overall, in light of significant uncertainties associated with spatial and
temporal variability of aerosol particle concentrations and properties, we use
aerosol concentration, profile, and properties presented in Section 3.2.
However, detailed profiling of aerosols at the observation site might further
reduce the offset in LTM height and offset in temperature profiles at
different vertical levels away from the surface. Despite uncertainties in the
aerosol profile, we demonstrate that LTM simulations appear in good agreement
with the field observations only when aerosols are included. It is also
consistent with laboratory-scale LTM observations by Mukund et al. [47] that
LTM intensity decreases with a decrease in aerosol concentration in the test
section. Moreover, the evolution of radiative flux, divergence, and
temperature are in better agreement with field observations if aerosols are
accounted for in the model. Therefore, results presented here clearly
emphasise the need to include aerosol-induced radiative cooling in current
radiation models used in stable, nocturnal ABL.

The model employed in this study is a one-dimensional conduction-radiation
model that considers aerosols. However, it does not incorporate horizontal
advection, vertical convection/mixing, or other dynamical processes. Hence,
the model has limitations in accounting for the changes in the temperature
profile due to horizontal advection and vertical mixing. Although we show from
current field observations that radiation divergence plays a crucial role in
LTM development and its decay, a better comparison with simulations and field
observations can be achieved if other dynamical processes like vertical mixing
in unstable layer near the ground are also accounted for in the model [43].

A basic calculation shows that a 0.5 W m-3 radiation divergence can lead to a
cooling rate of 1.8 K/h, which can influence many meteorological phenomena
after sunset like near-surface temperature inversion, fog, pollution
dispersal, drainage flow, and nocturnal jet in the NBL. Since occurrence,
dissipation, and intensity of fog and drainage flow are sensitive to small
temperature changes, prediction of these phenomena can be improved if
aerosols-radiation interaction in the LW region is accounted for in the
current forecasting model.

##  6 Conclusions

During evening transition and later in the night, radiative cooling strongly
modulates the thermal structure of the ABL near ground which has significant
implications in micro-meteorology and agriculture. Most of the radiation
models are not able to produce it satisfactorily [68, 65] which might be due
to missing aerosol-radiation interaction in LW region [79, 11, 1, 46]. In this
paper, we have presented results that elucidate the role of radiative cooling
due to aerosols on the thermal structure of the ABL during and after evening
transitions through extensive field observations and numerical simulations.
From our field experiments, we have demonstrated that the Lifted Temperature
Minimum (LTM) generally occurs in the nocturnal boundary layer under calm and
clear sky conditions, typically appearing during the evening transition and
intermittently disappearing during the night. The persistence of LTM depends
on specific conditions and it is not observed during the daytime when solar
heating and convection dominate.

Our field observations reveal that LTM occurrence are strongly influenced by
factors like mean wind speed, turbulent kinetic energy, downward and upward
longwave fluxes, as well as sensible heat flux. The probability of occurrence
of LTM occurrence increases with a decrease in the above parameters. Notably,
LTM’s disappearance with increasing wind speed suggests that near-surface
advection is not the primary cause. Further, LTM is observed in both seasons
(winter and spring), and there is no significant change in its characteristics
across the seasons. Observed LTM intensity and height are 2.2$\pm$0.6 K and
0.31$\pm$0.11 m (mean and one standard deviation), respectively. These values
are in a similar range as reported by Mukund et al. [47] and Blay-Carreras et
al. [3].

Simulations using a one-dimensional, conduction-radiation model that accounts
for aerosols show that LTM cannot form in the absence of aerosols, even under
favorable conditions. Without aerosols, the net divergence of longwave
radiation decreases monotonically with height, leading to a typical
temperature inversion profile. However, the presence of aerosols results in a
non-monotonic net divergence, causing preferential cooling near the ground and
leading to LTM development. Simulated LTM height and intensity match with
field observations when aerosols are considered. Further analysis with
idealized fog layer simulations reveals that the presence of fog modulates
downward longwave flux and radiation divergence depending upon the fog base
height and thickness. In case of shallow fog near the ground, LTM strengthens
with an increase in radiation divergence. Both radiation divergence and LTM
intensity decrease with an increase in fog thickness, and if the fog becomes
optically thick, LTM disappears completely, and we observe an inversion
profile. This behavior aligns with observations in the field, supporting the
model’s microphysics of radiative transfer.

We have also investigated the reasons for the underestimation of longwave
heating rate (LHR) by radiation models during evening transitions, as reported
by Steeneveld et al. [68]. Our findings, along with simulations with and
without aerosols, demonstrate that LHR from simulations and field experiments
better agree when aerosols are considered in the model. Aerosol-induced LHR is
not limited to LTM occurrence during evening transitions; its effects extend
several hundred meters above ground level and can influence various
meteorological phenomena such as the development of the nocturnal boundary
layer, temperature inversion, mist, fog, and pollution dispersion, ultimately
affecting the stability of the boundary layer. Incorporating aerosol-radiation
interactions in longwave radiation models will lead to improved forecasts of
these phenomena.

Although we have shown the role of aerosols in radiation divergence as well as
LTM occurrence in calm and clear sky conditions from 1-dimensional model, its
parameterized version needs to be developed and tested in NWP models. Further,
current study does not account for dynamical modeling which can be important
near the ground. Although penetrative convection formed near the ground due to
radiative cooling has been studied by Kaushal et al. [36], LTM maintenance
against convective instability and turbulent flux divergence in the unstable
layer of LTM needs to be investigated in future. Other LTM characteristics
like its transient behavior, appearing and disappearing nature during night
are currently under investigation from observations and simulations.

##  7 Acknowledgements

We thank the Department of Science and Technology, Government of India, for
co-funding this project through the Technical Research Centre (TRC) program at
JNCASR, Bengaluru, India. Additionally, we extend our thanks to Bangalore
International Airport Limited (BIAL), Bengaluru, India, for co-funding this
project and for granting access to the runway area at Kempegowda International
Airport Bengaluru (KIAB) to establish our observation site, as well as
providing other logistical support. Furthermore, we acknowledge the National
Supercomputing Mission (NSM) program at JNCASR for providing the computational
facility necessary for this research project.

##  8 Conflict of interest

We herewith declare that we do not have any conflict of interest in the work
reported in this paper.

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