1 Introduction

Aerosol particles interact with solar incoming short-wave and terrestrial outgoing long-wave radiation, thereby altering the earth’s energy budget (Horvath 1993; Kaufman et al. 2002). The aerosol’s direct effect is the scattering and absorption of insolation by atmospheric particles, resulting in a reduction in radiation flux at the surface (Charlson et al. 1992; Andreae et al. 2005). Aerosols also modify the cloud properties, which is signified as an indirect effect (Twomey 1977). Aerosols absorb solar energy, causing changes in the atmosphere's temperature profile, evaporation, and cloud features and are considered the semi-direct effect (Graßl 1979; Hansen et al. 1997; Lohmann and Feichter 2005). The aerosol’s interaction with solar radiation, which highlights their climatic role, strongly depends on their optical properties e.g. Ångström exponent (α), asymmetry parameter (g), and backscatter fraction (bf) (Hatzianastassiou and Katsoulis 2004; Hatzianastassiou et al. 2007). Ångström exponent, which is based on spectral wavelengths, is a broad indicator of the size distribution of aerosol particles (Eck et al. 1999; Kaskaoutis et al. 2007). Due to various reasons, the aerosol’s size distribution could be modified i.e., particle coagulation, the transformation of gas to particle phase, the non-homogeneous process in fog events, cloud formation, convection, etc. (Reid and Hobbs 1998; Levin et al. 2010). This distribution typically depends on the aerosol concentration, cloud area, relative humidity, etc., which significantly enhances the aerosol’s size distribution within hours to days (Reid and Hobbs 1998; Janhäll et al. 2010). The asymmetry parameter (g) is one of the important optical properties of aerosols apart from the aerosol optical depth (AOD), which is utilized in the radiative transfer model, climate model, and general circulation models (Bellouin et al. 2005). The asymmetry parameter explains the angular distribution of the scattered light and defines whether the light scattered by aerosol propagates in the forward or backward direction.

The backscattered light fraction or backscatter fraction (bf) is calculated as the proportion to the integral of the volume scattering function over the rear 2π (half solid angle) angle divided by the integral of the volume scattering function over the 4π (total solid angle) angle (Horvath et al. 2015). An integrating Nephelometer is being used to calculate the g. The g is a crucial parameter for measuring radiative transfer to acquire information on the impact of particulate matter on climate, weather, visibility, and various factors (Bellouin et al. 2005; Horvath et al. 2015). However, the g value of the atmospheric aerosols is limited and exist a correlation between g and bf, the lower the bf value, the higher the g value, or the more the asymmetric scattering (Bellouin et al. 2005; Horvath et al. 2015; Moosmüller and Orren 2017). The g relies on the aerosol’s size distribution and composition and is also a function of the relative humidity (Anderson and Ogren 1998). Parameterizations of the scattered light’s angular distribution or the aerosol phase functions of various particulate matters are used to assess radiative transfer (Moosmüller and Orren 2017). The backscattering ratio was established in response to the composition (organic content and particle size) of the aerosol in prior reports (Boss et al. 2004). bf and g are unaffected by the amount of aerosol in the atmosphere, instead, the parameters provide information about the properties of the particles (e.g., particle composition, mean size, shapes, etc.) (Horvath et al. 2015).

The study region is chosen because it is of genuine research importance due to the simultaneous existence of a range of both natural and anthropogenic aerosols (e.g., sand dust, marine, forest fire, industrial emission, etc.,) as reported in earlier works (Pathak et al. 2015; Kundu et al. 2018; Barman et al. 2018, 2019a) that makes the region hotspot for aerosol research. The station witnessed high precipitation throughout the monsoon every year and a larger water body nearby, causing a greater rate of evaporation/condensation over the study area. The evaporation/condensation processes have a significant impact on aerosol formation and size distribution (Levin et al. 2010; Sakamoto et al. 2016). Barman et al. (2021) demonstrated that mountain-valley wind movements have an impact on the meteorological parameters throughout the year except for the monsoon season.

In this study, total scatter and backward scatter data of Integrating Nephelometer 3563 is utilized for computation of α450-700 nm and bf. α450-700 nm and bf provide crude information about the aerosol particle size. To have detailed information about the aerosol particle size; g and particle radius (r) are the suitable parameters. Notably, it is challenging to draw conclusions about the parameters because the g and r cannot be directly determined from the Integrating Nephelometer. The prime objective is to estimate the g and r from the scattered data. To resolve the problem, Theoretical approximation (Kokhanovsky and Nauss 2006; Sviridenkov et al. 2017) and model simulation (MieTab and Mieplot) are utilized to estimate the g and r. Besides, the impact of mountain-valley wind flows and seasonal-long-range transportation of air mass on the aerosol characteristics at the station is also one of the major objectives.

2 Observational Site

In Shillong, Meghalaya, India (25°40′′ N, 91°54′ E), the measuring site is located on the grounds of the North Eastern Space Applications Centre (NESAC). The station is located 150 km south of the Himalayan Mountain range (altitudes > 5000 m), on a plateau at an elevation of roughly 1040 m above sea level. Bangladesh and the Brahmaputra Valley are seen from the Meghalaya plateau in the south and north, respectively. The summit is bordered by geological faults and fractures in all directions and has the appearance of a horst. Its elevation ranges from 150 m in its western half to 1961 m at Khasi Hill summit (Shillong Peak) in the mid-eastern zone (Dikshit and Dikshit 2014). The slope of the hilltop within a horizontal distance of 1 km is approximately 5°–6° towards the east and southeast. Pine trees predominately cover the slope and valley. A 1 km horizontal distance is the maximum for the slope towards the north, whereas a 2° slope exists towards the southwest, particularly for the upwind during the winter. In the southeast and southwest, trees are on average about 5.5 m tall. The Umiam Lake is running along the southwest direction, the site has a complex topography with a predominance of pine trees (Fig. 1c), 6.6 km2 in size and 1.35,108 m3 in storage volume, the Lake lies 900 m away from the station (Barman et al. 2019b).

Fig. 1
figure 1

a Google map of India, b Northeastern region of India and observation site (red star) on the map, c the station (red star) on the Google map

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3 Instrumentation and Methodology

3.1 Meteorological Parameter

An automatic weather station recorded the seasonal cumulative rainfall over the observation site during all the seasons (Table 1). It is noteworthy that the majority of northeast India receives more than 80% of its yearly precipitation during the monsoon season. During the winter and post-monsoon seasons, mean relative humidity (RH) values were lowest during the day and highest at night (Table 1). During the pre-monsoon period, the RH value is less during the day and soared at night. The higher and more frequent precipitation enhanced the moisture content in the atmosphere during the monsoon season. In monsoon, the RH value is less than 73% during the day and soared to 89% at night. RH values declined as the ambient temperature increased owing to surface heating during the day. The nighttime increment of RH value is greater during the winter and pre-monsoon seasons, and the minimum RH values are found during these seasons over the site during day hours. At the station, the air temperature is highest in monsoon and lowest during winter season (Table 1).

Table 1 Meteorological parameters at the station during all the season
Full size table

Four fast-response sonic anemometers were installed at 6-, 10-, 18-, and 30-m above the surface on a 31-m meteorological tower. The details about the ultra-sonic anemometer, data correction, and quality check are elaborated in Barman et al. (2019a, b), and CSAT3 (2014). The wind data at the 10-m level is utilized for the discussion of wind direction and wind speed in this study.

3.2 Integrating Nephelometer (Model-3563)

For scattering measurements of the aerosols, TSI’s Integrating Nephelometer (IN) 3563 is used. IN-3563 is dedicated to the long-term measurement of aerosol optical scattering properties (total and backscatter) in visible wavelengths (λ) (IN 3563 1995). It keeps track of the light scattering coefficient of atmospheric particles in real-time. An aerosol sample is drawn into the measurement volume during operation by a little turbine blower through the large diameter inlet port. A halogen light is used and it is guided through an optical and opal glass diffuser. The incident light falls on the aerosol sample at an angle of 7°–170° (IN 3563 1995). Three photomultiplier tubes (PMTs) collected the scattered light from the sample through a series of apertures fixed along the axis of the main instrument body. In the absence of a dark background, aerosol scattering occurs. The light trap, openings, and a very light-absorbing layer on all inner instrument sidewalls of the instrument lead to extremely high photon-absorbing surfaces (Ramachandran 2018). In front of the PMT detectors, high-pass and band-pass color filters divide the scattered light into three colors. Three forms of signal detection are provided by a reference rotor that rotates continuously (IN 3563 1995). The first mode is a measurement of the aerosol light-scattering signal made possible by an opening in the revolving shutter. The second mode completely prevents any light from being detected while measuring the PMT dark current, which is then subtracted from the measured signal (Ramachandran 2018). In the third mode, a transparent section of the shutter is inserted into the light's straight path to measure the illumination signal. This allows the device to adjust to variations in the light source. When in backscatter mode, the backscatter shutter slides in the direction of the light source to block light emitted between 7° and 90° angles (IN 3563 1995; Ramachandran 2018). Only light scattered in the rearward direction is sent to the PMT detectors when this component of the light is blocked. The total signal can be subtracted from the backscatter signal to determine the forward-scattering data. If this measurement is not important, the backscatter shutter can be “parked” at the total-scatter position. A high-efficiency filter can collect all the aerosol samples after an automated ball valve that is incorporated into the inlet is periodically triggered. This provides a gauge for the clean-air signal in the vicinity. To acquire only the component of the scatter signal that comes from the sample aerosol, this signal is deducted from the aerosol-scatter signal combined with the PMT dark-current signal (IN 3563 1995). The total and backscatter signals of all three wavelengths are continually averaged and transferred to a computer system for long-term archival. Condensation on the instrument walls brought on by humid aerosols is minimized by an integrated sample heater. Sulfates and sodium chloride, two air particles that absorb water, can go through phase changes at high humidity levels, this results in modifications to particle size, form, and refractive index. Using aerosol instruments in a climate-controlled environment frequently produces sample flows with relative humidity levels above 100% (IN 3563 1995). By raising the temperature of the chamber's walls to the same temperature as the incoming air sample, the heater provides resistance against this issue. As needed, the heating can be turned on or off.

The details about the data correction and calibration are elaborated in supplementary material section S.1. The total and backward scattering coefficients are estimated from IN-3563 at three wavelengths 450 nm (blue), 550 nm (green), and 700 nm (red) which are further used for the calculation of α, bf, g and Mie principle and calculation of the aerosol are elaborated in Sects. 4.1, 4.2, and 4.3. The measured data of IN 3563 (1995) has a truncation error which occurs due to the particle size; in this study, the truncation error is rectified by adopting the approach of Anderson and Ogren (1998) (S.1). A complete 1-year dataset of the year 2013 is utilized for the analysis and interpretation. The instrument operated only during day hours due to power problems (load shedding, and voltage fluctuation) at night hours. The instrument is calibrated with zero air and carbon dioxide before the data acquisition. As the station is in a remote area of northeast India, it is difficult to get frequent technical support from the manufacturer. Hence, every alternative year the instrument is used to be calibrated. An inlet particle filter with a size range of 0.01–2.5 μm is installed at the inlet pipe. The relation between backscattering, backscatter fraction, and asymmetry parameter is elaborated in Sect. 4.3.2.

3.3 Model Simulations

A verity of computer codes or software developed on Mie theory to estimate the light scattering and absorption of spherical particles e.g. MieTab, Mieplot, PyMieLab_V1.0, Scatla, Miepython, and PyMieScatt. In this study, the model-based light scattering simulations are performed by utilizing MieTab and Mieplot software. MieTab (Scattport 2023) and Mieplot (Philplaven 2021) software are used to estimate the value of g, and values are presented in the supplementary material. MieTab is a software for calculating the Mie Light Scattering parameters for a spherical particle in a transparent medium. This program was developed by August Miller (Scattport 2023). The MieTab program was also used for Mie scattering calculations for the development of Moderate Resolution Imaging Spectrometer (MODIS) reflectance data (ESIP 2009). Zhang et al. (2015) reported good agreement of the results of MieTab with a double precision Lorenz–Mie scattering code and a double precision T-matrix code for a lognormal particle size distribution. Similarly, Mieplot is a computer program for the scattering of light from a sphere using Mie theory and the Debye series (Philplaven 2021). In the nanoscience lab, the researcher used Mieplot to validate the experiment data (Phys 4970 2020). Similarly, Ma et al. (2022) demonstrated a comparison of estimated values from PyMieLab_V1.0 and the Mieplot program for validation of the PyMieLab_V1.0 software. The comparison of MieTab and Mieplot data is presented in the supplementary material Table S3.1–S3.7.

In this simulation, the aerosol particles are considered spherical in shape. Otto et al. (2009) and Klaver et al. (2011) demonstrated that the spherical/non-spherical differences only influence the single-scattering albedo by less than 1%. Different types of aerosol particles based on refractive index (m) and sizes are used in this study (Table S1). In the atmosphere, various types of aerosol particles hover all the time. These aerosols are made of different types of material and originated in different stages or conditions of burning. As the material of aerosol changes, their refractive indices also vary (real and imaginary parts). For example, Soot H25 is a graphite particle with a structure comprising 75% space a density of 625 kg m−3 (volume add-on is assumed for a pure substance of graphite and air) and its refractive index is 1.25–0.25i (Horvath 1993). Similarly, Soot H50 is a graphite particle with a structure containing 50% space have a density of 1250 kg m−3 (assumed as a homogeneous mixture of graphite and air, volume add-on) with refractive index 1.5–0.5i (Horvath 1993). Soot G is a carbon black with low porosity, a carbon content of > 97%, and a density of ≈1.85 g/cm3 (not graphitized) and is also known as Commercial carbon black with refractive index 2-1i (Janzen 1979). Several types of aerosol particles and their name and composition is listed in Table S1 in supplementary material and particle radius versus asymmetric parameters for various types of particles is shown in Fig. ten. For each type of aerosol profile, optical parameters are estimated with the help of MieTab and Mieplot at 550 nm wavelength (as standard) (Otto et al. 2009; Klaver et al. 2011). These estimated values are later compared with the observed values at the station. The aerosol sizes ranged from 0.015 to 2.5 μm (1000 subcategories) for the different types of material (varying m) and only 13 subcategories are presented in supplementary material Table S3.

3.4 Long-Range Air Mass Transportation

To comprehend the sources of the air masses above the study region, backward trajectory analysis based on the National Oceanic and Atmospheric Administration's (NOAA) HYbrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model is investigated. The HYSPLIT model helps to explain how aerosol particles were dynamically transported, distributed, and deposited by air mass over a site or a region. Combining the Lagrangian method with a running frame of reference, the model's calculation method computes advection and dispersion as the air mass moves away from the source. For the Eulerian technique to calculate pollutant mass concentrations, a specific 3-D framework is required (Stein et al. 2005). The model is run for 96 h duration at 50 m height backward trajectory of all weeks for the year 2013. For backward trajectory, the Global Data Assimilation System (GDAS) dataset is used with 1° × 1° gridded space. Quantum GIS (QGIS) software is utilized for the final backward trajectory map.

Monthly northward and eastward wind components at 50 m above displacement height data were utilized to create wind vector plots for various seasons over the area. Here, MERRA-2 (The Modern-Era Retrospective Analysis for Research and Applications, version 2) with 0.5°–0.625° spatial resolution is used to create the wind vector plot. Utilizing the atmospheric data assimilation technique of the Global Earth Observing System (GEOS), MERRA-2 is calculated. The Grid Point Statistical Interpolation (GSI) analytical scheme and the GEOS atmospheric model (Molod et al. 2015) are the two main components of the system (Wu et al. 2002; Kleist et al. 2009). Wind vector plots in this study indicated the predominant wind pattern over the region (Fig. S2).

3.5 Scattering Ångström Exponent (α sc)

Light Scattering coefficients measured at three wavelengths 450, 550, and 700 nm are utilized to compute the scattering Ångström exponent (αsc) (Reid and Hobbs 1998).

$${\alpha }_{sc}=-\frac{d{\text{ln}}\sigma }{d{\text{ln}}\lambda }=-\frac{{\text{ln}}\left(\frac{{\sigma }_{1}}{{\sigma }_{2}}\right)}{{\text{ln}}\left(\frac{{\lambda }_{1}}{{\lambda }_{2}}\right)}$$
(1)

\(\alpha \)sc is employed as a qualitative indicator of the size distribution of aerosol particles (Ångström 1929; Schuster et al. 2006). Characterizing and identifying different aerosol particle sources is made possible by calculating the αsc. The concentration of aerosol particles and particle size has an impact on the light scattering coefficient. Nevertheless, the light scattering efficiency is relatively low if the particle size is smaller than the used wavelength. As a result, the only particles that can be identified optically are those that determine the measured total light scattering coefficient. Small values (αsc < 1.5) indicate coarse mode particles (radii > 0.5 µm) that are associated with for instance sea salt and dust particles and large values (αsc ≥ 1.5) indicate fine mode particles (radii ≤ 0.5 µm) that are typically associated with biomass burning and anthropogenic emissions (Eck et al. 1999; Schuster et al. 2006; Ahmad et al. 2022).

3.6 Backscatter Fraction (bf)

The angle between the incident and dispersed waves determines how intensely a particle scatters light. The particle's size, shape, refractive index, and orientation all affect this angular dependence (Barber and Hill 1990). When dealing with three-dimensional particles, it is customary for the incident wave to travel in the direction of θ = 0°. Forward scattering refers to light scattered in and near the θ = 0° direction, while backscattering refers to light scattered in and close the θ = 180° direction (Barber and Hill 1990). The total scattering coefficient (\({\sigma }_{s})\) is estimated by integrating volume scattering function over the total solid angle (Eq. 3). When the integral of the volume scattering function over the rear 2π (half-solid angle) angle is divided by the integral of the volume scattering function over the 4π (whole solid angle) angle, the backscattering fraction (bf) is determined. (Horvath et al. 2015). The backscattering fraction is a very important parameter for defining the cooling potential of aerosol since it is an estimate of the amount scattered of solar radiation that gets back to space. The bf is weakly dependent on aerosol concentration and provides details on the properties of the aerosol material, such as the refractive index and the scattering angular dependence required to estimate aerosol scattered diffuse radiation that approaches the earth's surface (Horvath et al. 2015).

The total scattering coefficient (Tscf) and backward scattering coefficient (Bscf) are used to calculate the hemispheric backscatter fraction (bf). bf is defined as the ratio of light scattered into the backward scattering (Bscf) to total light scattering (Tscf) (Charlson et al. 1974). Bscf measured at 450, 550, and 700 nm is analyzed further to get an insight into the sizes of particles (smaller or bigger) that dominate the aerosol distribution.

3.7 Asymmetry Parameter (g)

3.7.1 Principle

The asymmetry parameter (g) varies in the range from − 1 (total backscatter) to + 1 (total forward scatter), the negative g values resulted only for tiny particles (Hansen and Travis 1974) and do not apply to the surrounding environment. Furthermore, the g value only is to be assumed between 0 for the symmetric scatter and + 1 for the total forward scatter.

3.7.2 Relation Between Backscattering and Asymmetry Parameter

For radiative transfer estimation, the g is a crucial input parameter to understand the impact of the atmospheric aerosol on the climate, screening, atmospheric visibility, etc. Inevitably, determining the g involves tedious effort. It ought to be clear that there is a relationship between the g and the bf (Horvath et al. 2015), the bigger the g, the more asymmetric the scattering, and the smaller the backscattered percentage.

A parallel light beam with flux density S incident on a volume element dv (Fig. 2). The light flux d2φ is scattered by the particles of this dv into an angular cone of dw in the direction represented by the scattering angle (θ). θ is the angle between the scattered light beam and the transmitted light beam. d2φ is estimated as follows

$$ d^{2} \varphi = S \cdot \gamma \left( \theta \right) \cdot dv \cdot dw $$
(2)

where \(\gamma \left(\theta \right)=\frac{{d}^{2}\varphi }{S.dv.d\omega }\) is the volume scattering function. Rotational symmetry around the direction of the incident light beam is assumed. This is the case for spherical particles or particles undergoing Brownian rotation.

Fig. 2
figure 2

Schematic diagram of light scattering

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The scattering coefficient (\({\sigma }_{s})\) is estimated by integrating \(\gamma \left(\theta \right)\) over the total solid angle.

$${\sigma }_{s}=\int \gamma \left(\theta \right)d\omega =2\pi {\int }_{0}^{\pi }\gamma \left(\theta \right)sin\theta .d\theta $$
(3)

Which represents the entirely scattered light by \(\gamma \left(\theta \right)\). The backward scattered light or hemispheric backscattering is estimated as

$$bf=\frac{2\pi {\int }_{\frac{\pi }{2}}^{\pi }\gamma \left(\theta \right)sin\theta .d\theta }{2\pi {\int }_{0}^{\pi }\gamma \left(\theta \right)sin\theta .d\theta }$$
(4)
$$bf=\frac{2\pi {\int }_{\frac{\pi }{2}}^{\pi }\gamma \left(\theta \right)sin\theta .d\theta }{{\sigma }_{s}}$$
(5)

g is estimated by weighing the \(\gamma \left(\theta \right)\) with the cosine of \(\theta \)

$$g=\frac{2\pi {\int }_{0}^{\pi }\gamma \left(\theta \right)sin\theta .cos\theta .d\theta }{{\sigma }_{s}}$$
(6)

For Rayleigh scattering (isotropic scattering or symmetric scattering), g = 0 and bf = 1/2; for forward scattering θ = 0, g = 1, and bf = 0, for backward scattering θ = π, g = ‒1 and bf = 1.

If the phase function \(P\left(\uptheta \right)=4\uppi \frac{\gamma (\uptheta )}{{\sigma }_{s}}\) is employed in Eqs. (5) and (6) and become as follows

$$g=2\pi {\int }_{0}^{\pi }P\left(\theta \right)sin\theta .cos\theta .d\theta $$
(7)
$$bf=\frac{1}{2}{\int }_{0}^{\pi }P\left(\theta \right)sin\theta .d\theta $$
(8)

In aerosol optical properties estimation, g, bf, and \(P\left(\uptheta \right)\) are crucial parameters. The correlation between bf and g relies on the particle size distribution, shape, and refractive index (m), and hence is difficult to explain (Marshall et al. 1995; Andrews et al. 2006). Henyey and Greenstein (1941) proposed a mathematical expression to estimate the phase function and is given below,

$$P\left(\theta \right)=\frac{1-{g}^{2}}{{(1+{g}^{2}-2gcos\theta )}^{1.5}}$$
(9)

the integration over the solid angle is possible and gives

$$bf=\frac{1-{g}^{2}}{2g} \left(\frac{1}{1+g}-\frac{1}{\sqrt{1+{g}^{2}}}\right)$$
(10)

Even though it is not a specific bf function, Wiscombe and Grams (1976) and Andrews et al. (2006) have provided parameterization to describe g as a function of bf. Kokhanovsky (2008) demonstrated an experimental expression for bigger-sized particles as

$$bf\approx \frac{1-g}{3} ,$$
(11)

Sviridenkov et al. (2017) analyzed a large set of integrating Nephelometer 3653 datasets and found the following relationship

$$C=\frac{1}{bf}-1,A=\frac{1}{1-g},$$

then

$$C\approx 1.1{A}^{1.85}$$

or

$$bf={\left[{1.1\left(\frac{1}{1-g}\right)}^{1.85}+1\right]}^{-1}$$
(12)

A third-order polynomial equation (gA_fit) was proposed by Andrews et al. (2006) and expressed as

$$ g_{A\_fit} = - 7.143889bf^{3} + 7.464439bf^{2} - 3.96356bf + 0.9893 $$
(13)

Equation (13) has a root-mean-square error (RMSE) of 0.0055. Although the range of g and bf for which this estimation is intended is not explicit, for 0 ≤ bf ≤ 0.5, leading to 0 ≤ g ≤ 1.

An improved third-order polynomial equation (g_fit) can estimate better results and is given as follows

$$ g_{\_fit} = - 6.347bf^{3} + 6.906bf^{2} - 3. \, 859bf + 0.9852 $$
(14)

Equation (14) has a root-mean-square error (RMSE) of 0.0051. This estimation is displayed in Fig. nine together with the other estimated values of g. The variations between the outputs of Eqs. (13) and (14) are negligible and would be difficult to recognize as gA_fit (Eq. 13) and g_fit (Eq. 14) would be plotted together in Fig. nine. Even so, g_fit is marginally perfect fit.

A linear relationship between bf and g was proposed by Sagan and pollack (1967) and expressed as following

$$ bf = \left( {1 - g} \right)/2 $$
(15)

Or

$$ g = 1 - 2bf $$
(16)

4 Results and Discussion

4.1 Hysplit Trajectory Analysis

The Hysplit backward trajectory analysis and wind vectors show that air masses were transported from the Indo-Gangetic plain (IGP) and the northwestern region of India to the measurement site at 50 m height during the winter season (Fig. 3a). The high-altitude trajectories indicate the transportation of long-range fine particles; the fine particle can reach the maximum altitude owing to the lower weight whereas the bigger particle with greater weight cannot reach a higher altitude owing to gravity. The air mass passed over the station throughout the winter seasons at elevations of 200 and 3000 m (Figs. S2a–b). Kundu et al. (2018) reported that the Brahmaputra River valley in the Northeastern Region of India is significantly affected by the prolonged dispersion of pollutants from the Indo-Gangetic plain during local winter and is burdened with a lot of natural and anthropogenic aerosol. Anthropogenic and natural events both contribute significantly to the evolution of aerosol particles over the area (Barman et al. 2018). The aerosol in north-east India comes from a variety of sources, including open agricultural fields and human activities, such as burning vegetation, combustion releases, brick kilns, coal mines, and oil wells (Pathak et al. 2015; Kundu et al. 2018; Barman et al. 2018). Because of the rugged topography in northeast India, aerosols are confined mostly to the Brahmaputra valley, where the air convergence phenomenon supports the ideal environment for the buildup of both transported and local pollutants (Pathak et al. 2015).

Fig. 3
figure 3

Backward trajectory at the station for different seasons a winter, b pre-monsoon (March in Black color, April in Orange color, and May in Brick red color), c monsoon, and d post-monsoon

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In pre-monsoon, the back trajectory shows a transition of air mass from the northwest direction to the south direction (Fig. 3b). In March, air mass is transported from the northwest direction (in black color Fig. 3b); during April, transportation occurred from south-west direction (in orange color Fig. 3b), while in May trajectories reach the station from the south direction (in brick red color Fig. 3b). In March and April, the pollutant is transported from both north-west and south-west, which indicates that both fine and coarse mode particles reach the station. During the pre-monsoon season, the air mass reached the station at a height variation of 0–3000 m (Figs. S2c, d). Due to the excessive pollution in Bangladesh and IGP, the atmosphere is laden with fine aerosol particles. Using ground-based equipment in campaign mode, Borgohain et al. (2019) examined the physical and optical characteristics of aerosols and noted considerable biomass burning along the sub-Himalayan terrains of the Northeastern Region of India in the winter and pre-monsoon seasons.

In the monsoon season, the bigger aerosol particles are transported from the lower altitude of 0–1000 m, which are highly driven by the higher wind velocity (Fig. 3c, Fig. S3c). Air masses carried coarse mode (sea salt and dust) particles from the Bay of Bengal (BoB) to the station from June to September. Back trajectory and wind vectors show that the air mass primarily came from the south direction during monsoon season over the station. The air mass is primarily brought in from BoB and Bangladesh's coastline region from heights of 0–1000 m (Fig. S2e–i). Sea salt and desert dust from the Arabian Sea and India are the prime aerosols influencing Bangladesh (Begum et al. 2011). The aerosols move over Iran and Afghanistan before entering Pakistan, due to the meteorological condition the divergence of air mass occurs towards Sri Lanka while entering India and Bangladesh (Hopke et al. 2008; Begum et al. 2011, 2013). In the open BoB, Satheesh et al. (2010) showed a larger loading of sea salt aerosol in the north–south gradient, which decreases as one moves farther north throughout the year. Most backward trajectories indicate that a regional aerosol transit to the station occurs largely from the east direction during the post-monsoon season (Fig. 3d, Fig. S3d).

4.2 Seasonal Wind Direction and Speed

The daily variability in the direction and speed of the seasonal wind over the measurement is described in Fig. 4. The variation in wind direction reflects a mountain-valley wind circulation at the site during the winter season. The wind is observed to be flowing from the south-west (200°‒330°) sector in the morning, while the dominant wind direction is from the east and the rest was from the south-east (25°‒170°) sector (Barman et al. 2019a). It is a unique periodic pattern, with an up-slope flow in the day and a down-slope flow in the nighttime. During the pre-monsoon season, the wind direction is constrained to the southeast (90°‒180°) direction; the wind speed also increases in comparison to the winter season (Barman et al. 2021). In the monsoon, the wind direction is restricted to the south direction (180°‒270°) in the day, indicating the superposition of the mountain-valley wind circulation. In the post-monsoon season, wind direction ranges from the northeast (45°) to the west direction (300°), indicating a mountain-valley wind circulation over the station (Barman et al. 2021).

Fig. 4
figure 4

Seasonal diurnal variation of a wind direction and b wind speed at the station for winter (in solid black line), pre-monsoon (in solid red line), monsoon (in solid blue line), and post-monsoon (in solid green line)

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4.3 Diurnal and Seasonal Variation of Aerosol Optical Properties

Figure 5 shows the seasonal diurnal variation of the total scattering coefficient (Tscf) and backward scattering coefficient (Bscf) at 550 nm wavelength over the station. The highest mean value is observed in the winter season in the afternoon period. While the monsoon season witnessed the lowest mean diurnal values throughout the day. In the winter, pre-monsoon, and post-monsoon seasons, a rise of Tscf and Bscf values is observed from the mid-day (1200–1300 IST). While in the monsoon season, the values remained almost unchanged throughout the day. A mountain-valley wind circulation is observed in the winter, pre-monsoon, and post-monsoon seasons over the station (Fig. 4a). In the morning, the wind flows from the southwest direction, while in the afternoon period, the wind flows from the valley (industrial area) and fresh emissions reach the measurement site, which could finally enhance the aerosols concentration. In the afternoon, as the Tscf increases, the Bscf also increases which signifies that the fine aerosol particles increased in the ambient environment. This fine particle settles down in the night hours and increases the concentration over the station. There is a difference between the morning and afternoon values of Tscf and Bscf values in all the seasons. Afternoon Tscf values were 32%, 44%, 8%, and 20% and Bscf values were 35%, 46%, 4%, and 16% higher than the morning values, in the winter, pre-monsoon, monsoon, and post-monsoon seasons, respectively.

Fig. 5
figure 5

Seasonal diurnal variation of a Tscf550 nm and b Bscf550 nm over the station for winter (in solid black line), pre-monsoon (in solid red line), monsoon (in solid blue line), and post-monsoon (in solid green line)

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In Fig. 6, the diurnal and seasonal variation of α450-700 nm over the station is shown. The mean α450-700 nm is utilized for the characterization of the aerosol particle source. The mean α450-700 nm values in the winter (1.47 ± 0.13) and pre-monsoon (1.74 ± 0.48) seasons were lower than the monsoon (1.88 ± 0.34) and post-monsoon (1.88 ± 0.35) seasons. In the winter, the α450-700 nm value is 16.8%, 24.5%, and 24.5% lower than in the pre-monsoon, monsoon, and post-monsoon seasons. α450-700 nm > 1.5 corresponds to new smoke particulate matter from biomass-burning sources, favoring the dominance of light-absorbing Brown Carbon (a type of Organic Carbon) (Szidat et al. 2007; Singh and Rastogi 2019; Kaskaoutis et al. 2020). The smaller aerosol particles (α450-700 nm ≥ 1.5) can be classified as a mixture of brown carbon or black carbon, but bigger ones (α450-700 nm < 1.5) may be a mixture of soil or desert dust, corresponding to the “dust-mix” type (Kaskaoutis et al. 2020). The aerosol type with α450-700 nm < 1.5 is characterized by large particles with low spectral absorption (Barman et al. 2018). In the winter season, the transported aerosols and locally produced aerosols contributed to the total concentration and resulted in smaller α450-700 nm (1.47 ± 0.13). In the pre-monsoon season, the forest fire or biomass burning increases and the contribution of biomass aerosol becomes higher which enhances the α450-700 nm value. The long-range transported aerosol particles from the northwest region of India also have an impact on the aerosol loading and the characteristics of the region. While in the monsoon and post-monsoon seasons, owing to the clean atmosphere, the local scale biomass burning (firewood) dominated the concentration of aerosol at the site and higher scattering occurred at 450 nm. The fresh biomass burning overloads the fine particles mixture of Brown Carbon and Black Carbon resulting in higher α450-700 nm (1.88 ± 0.34 and 1.88 ± 0.35). In monsoon and post-monsoon seasons, α450-700 nm values decrease from the morning to the evening hours (Fig. 6), however, during the winter and pre-monsoon seasons, α450-700 nm values increase from the morning to evening owing to the fresh fine particles from the industrial area (valley) southeast direction. According to an investigation undertaken in Athens between 2008 and 2018, Raptis et al. (2020) found that the Ångström exponent is around 1.25, 1.15, 1.47, and 1.30 during the winter, pre-monsoon, monsoon, and post-monsoon seasons. During the pre-monsoon season, Ramachandran and Rajesh (2008) found the α450-700 nm at various stations (Bhubaneshwar, Chennai, Trivandrum, and Goa) in India is ~ 1.84, 1.98, 1.77, and 1.82, respectively. Similarly, Kaskaoutis et al. (2020) reported α450-700 nm is 1.97, 1.88, 2.15, and 1.96 in winter, spring, summer, and autumn seasons over Athens during the period of 2016–2019. Here, the α450-700 nm is within the range of 1.5–1.9 (Table 2). It can be concluded that the aerosol particles over the station belong to the fine particle category with radii ≤ 0.5 µm that are typically associated with biomass burning, industrial emission, vehicular emission, and house hold burning.

Fig. 6
figure 6

The daytime variation at the station for winter (in solid black line), pre-monsoon (in solid red line), monsoon (in solid blue line), and post-monsoon (in solid green line)

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Table 2 Season wise estimated values of different parameters of aerosol’s optical properties
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4.4 Diurnal and Seasonal Variation of Backscattered Fraction (bf)

The annual variation of bf remained in the range of 0.11–0.13 at the wavelength 550 nm over the station (Table 2). The mean value of the bf is approximately equal to the median values of the parameters (Table S2 in Supplementary material). The mean and median values were nearly identical throughout the year, indicating that the number of smaller bf value is roughly equivalent to the number of higher bf value (Fig. 7).

Fig. 7
figure 7

Diurnal variation of a bf and b g at the station for winter (in solid black line), pre-monsoon (in solid red line), monsoon (in solid blue line), and post-monsoon (in solid green line)

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The bf is found in the 0.11–0.13 range over the station. The bf value in the winter season is 3.9%, 11.5%, and 3.9% higher than the bf values in the pre-monsoon, monsoon, and post-monsoon seasons. The bf value over the station is far smaller than the value over locations of the Indian continent found by Ramachandran and Rajesh (2008). Ramachandran and Rajesh (2008) reported that during pre-monsoon the column-averaged bf values at Bhubaneshwar, Chennai, Trivandrum, and Goa at 0.20 ± 0.03, 0.18 ± 0.01, 0.21 ± 0.04, and 0.24 ± 0.04, respectively. They also estimated that the near-surface mean bf values are 0.14, 0.15, 0.18, and 0.21 over Bhubaneshwar, Chennai, Trivandrum, and Goa, respectively. Here, all parameters were assessed at the surface level and compared with the surface values of bf with the other stations around India. The mean annual bf over the measurement location is 0.12 which is 15%, 22%, 40%, and 54% lower than the corresponding values of Bhubaneshwar, Chennai, Trivandrum, and Goa. The monthly mean bf value during the 1996–2000 period over the Southern Great Plains, Oklahoma was found to lie in the range of 0.10–0.15 with the annual mean bf value at about 0.13. According to Sheridan et al. (2001), bf showed a fall in the summertime and was associated with an enhancement in the fraction of courser atmospheric particulate matter over the Southern region. Kotchenruther and Hobbs (1998) reported that mean bf values were 0.131, 0.115, and 0.137 for the biomass-burning aerosols at Cuiabá, Porto Velho, and Marabá in the Amazon basin. The mean bf value (0.12) obtained in the current study indicated the dominance of smaller-size aerosols throughout the year. In winter, due to the dry atmospheric conditions, flam-dominated biomass burning produces more absorbing aerosol. The backward trajectory shows that the origin of the aerosol particles is from the IGP and north-western direction. In pre-monsoon season, the site is influenced by the local as well as the transported aerosol particles. Fresh black carbon aerosols are non-coated, according to Laborde et al. (2013), based on MEGAPOLI campaign results, whereas long-range transported black carbon aerosols have a larger coating of scattering material. Table 2 shows that the bf values were lower in the monsoon than in the other seasons, indicating that the particle size is greater than that of the winter season. According to the Table 2, the g value varies from 0.68 to 0.74 and after comparison of this value with the model simulated particle size, found that the radius varies from 0.17 to 0.21 µm approximately. Noteworthy that in the monsoon season, the prevailed aerosol radius is approximately 0.21 µm. In this season, Smouldering-dominated burnings emit more scattering aerosol (Megan et al. 2023), and the wet atmospheric conditions, also have a significant impact on aerosol formation and size distribution. Local biomass-burning aerosols prevailed over the station throughout the monsoon season, as evidenced by the smaller bf values.

4.5 Estimation of bf Different Approaches

The bf calculated from the model-estimated values of g for different substances (varying m) at 550 nm wavelength shown in Fig. 8 (the model-estimated values of g for varying r and m of the particle shown in supplementary material Table S1). The bf values are estimated by the following the approaches of Sviridenkov et al. (2017) and Kokhanovsky and Nauss (2006) and compared with the instrument’s measured value. The bf values abruptly fall from 0.47 to 0.33 and subsequently to 0.12 for the particle size range 0 < r < 0.2 µm for varying refractive index (Fig. 8a, b). The bf values vary to m above the particle size of 0.2 µm, the variation of bf is not significant for r < 0.2 µm. In both approximations, the lowest and highest bf value is shown by Soot H25 (m = 1.25–0.25i) and Soot G (m = 2-1i). For SiO2 and mineral dust particles, bf values are variant abnormally for the size range of 0.25 µm < r < 1.5 µm in both approaches. While the other species of particles follow a uniform path along with the size of the particle.

Fig. 8
figure 8

bf values estimated for the size range for various substances by following a Sviridenkov et al. (2017), b Kokhanovsky and Nauss (2006)

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4.6 Diurnal and Seasonal Variation of Asymmetric Parameter (g)

The annual variation of g remained in the range of 0.68–0.74 at the wavelength 550 nm over the station (Table 2). The mean values of the g are approximately equal to the median values of the parameters (Table S2 in Supplementary material). The mean and median values were nearly identical over the year, indicating that the number of smaller g values is roughly equivalent to the number of higher g values.

The asymmetric parameter increased from winter to monsoon season (Fig. 7b). g value in the winter season (0.68 ± 0.05) is 2.9%, 8.5%, and 2.9% smaller than the pre-monsoon (0.7 ± 0.02), monsoon (0.74 ± 0.07) and post-monsoon (0.7 ± 0.04) seasons (Table 2). The bf decreased from winter to monsoon season, but the g values enhanced, demonstrating a negative correlation. The bf value decreased owing to the lower backscatter and higher forward scatter for bigger particles from winter to monsoon. Thus, the g values were smaller for higher bf values associated with smaller aerosol particles and vice-versa. According to D’Almeida et al. (1991), g at a 500 nm wavelength varies from 0.64 to 0.83 depending on the kind of aerosol and the season, with a mean value of 0.67 at ambient relative humidity (RH). The g value of the US East Coast is 0.7 (Hartley and Hobbs 2001). Formenti et al. (2000) examined the Saharan dust aerosol and discovered that it had a value of 0.72–0.73 at North Atlantic. Ross et al. (1998) observed that biomass-burning aerosols have a g value of 0.54 in Brazil. The instrument-estimated bf values are used to calculate the g values in different approaches e.g., Sviridenkov et al. (2017), Andrews et al. (2006), and Sagan and Pollack (1967). Sviridenkov (1980) has proposed an approximation for the estimation of g that the dependence on the angle of the logarithm of the normalized scattering phase function can be accepted as a one-parameter dependency, which means that the asymmetric properties are connected to a single statistical parameter. One such parameter is the ratio of the partial scattering coefficients brought about by scattering into the forward and backward directions. Sviridenkov et al. (2017) analyzed a large set of Integrating Nephelometer 3653 with the assistance of Sviridenkov (1980) and proposed the empirical Eq. (12) for the estimation of g value from the scattering parameters considering bf as a function. Andrews et al. (2006) demonstrated a third-order polynomial equation (gA_fit) (Eq. 13) to estimate the g value. Equation (13) has a root-mean-square error (RMSE) of 0.0055. Although the range of g and bf for which this estimation is intended is not explicit, 0 ≤ bf ≤ 0.5, leads to 0 ≤ g ≤ 1. An improved third-order polynomial equation (g_fit) (Eq. 14) can estimate better results with a root-mean-square error (RMSE) of 0.0051. The variations between the outputs of Eqs. (13) and (14) are negligible and would be difficult to recognize as gA_fit (Eq. 13) and g_fit (Eq. 14) one be plotted together in Fig. 9. Even so, g_fit is a marginally perfect fit.

Fig. 9
figure 9

bf as a function of g estimated from various approaches i.e., Sviridenkow (2017) (black line), Sagan and Pollak (1967) (red line), gA_fit (blue line), and g_fit (pink line) third order-polynomial

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The Henyey-Greenstein approximation is generally adequate for size distributions, including super micron aerosol particles like dust and sea salt with a diameter of less than 10 mm and size distributions consisting primarily of submicron aerosol (e.g., continental, anthropogenic aerosol) (Andrews et al. 2006). The derived mean bf values in this study are in the range of 0.11–0.13, showing that smaller particles were more prevalent when the bf value is greater. Gopal et al. (2014) measured a ground-based Nephelometer for a year in Anantapur (a semi-arid area in south India) and found g between 0.53 and 0.65 at 550 nm. Ramachandran and Rajesh (2008) reported that the asymmetry parameter at 550 nm is in the order of 0.3–0.6 over India. At 550 nm wavelength, the median value of 0.57 is for free tropospheric particulate matter, while 0.65 is for marine particulate matter (Fiebig and Ogren 2006). According to Andrews et al. (2006), for normal weather conditions in 2003 IOP, a 10% decline of g yields a 19% reduction of the upper atmospheric aerosol radiative forcing.

4.7 Different Approaches for g Estimation

Here different approaches are utilized to estimate the g and the comparison is shown in Fig. 9. A linear relationship between bf and g was proposed by Sagan and Pollack (1967) (Eq. 16). The values of gS are 8.5% lower than gSP, and 15.4% higher than gA_fit and g_fit. The g value varies from maximum to minimum in different seasons and different approaches estimated different values e.g., 0.63 ≤ gs ≤ 0.75, 0.71 ≤ gsp ≤ 0.78, 0.55 ≤ gA_fit ≤ 0.64, and 0.55 ≤ g_fit ≤ 0.64. The g values estimated by Andrews et al. (2006) are smaller than the values estimated from the other approximations. Moosmüller and Orren (2017) found that Eq. (14) gave better g values than the Andrews et al. (2006), and Sagan and Pollack (1967).

The g can be calculated readily using the Mie theory for homogeneous spherical particles. In Fig. 10, g is plotted for the different-sized particles from 0.01 to 5 μm for various types of material. The estimated g for the observation site is 0.68–0.74 and this value indicates that the size of the particle is in the range of 0.17–0.21 μm radius (Table 2). The blue (1.25–0.25i or soot H25), black (1.5–0.5i or soot H50) and red (1.8–0.5i or soot B) lines in the plot pass through the estimated g values and mentioned refractive indexes represent three different particles. Sarpong et al. (2020) reported mean radii of particles of biomass burning (eucalyptus and olive) the refractive index was in the range of 1.31 ≤ n ≤ 1.56 and 0.045 ≤ k ≤ 0.468. The real and complex parts of m increased with rising particle mobility diameter. A grey absorption coefficient, as defined by Roach (1961), signifies that the n increases with λ, as it does for carbon and soot (Dalzell and Sarofim 1969). The complex part of the refractive index of urban aerosol continues to rise with λ (Fischer 1973). In a nutshell, the complex part of experimentally evaluated m increases with the λ. Nonetheless, there is a small trend for the g to grow when the k of m increases (Kokhanovsky and Nauss 2006). The g value reaches zero for sized parameters far less than one for all refractive indices; this is the standard symmetric scattering in the Rayleigh regime (Moosmüller and Arnott 2009). However, since scattering efficiencies (the ratio of scattering and geometric cross-section) in the Rayleigh regime are proportional to r4, very small particles (r <  < 1) do not contribute much to scattering compared to larger particles, these small values of the g do not lead to the scattering of a dispersed particle size distribution as seen in the atmosphere. The higher value of k of m indicates the attenuation of the light by the substance. Here, soot H25, soot H50, and soot B have the almost same g values for the particle range of 0.17 μm ≥ r ≥ 0.21 μm (in supplementary material Table S3.1, S3.2, and S3.3). For Soot A (1.9–0.66i) and Soot G (2-i), the g value reached the calculated value for the larger radius particles (0.2 μm < r < 0.25 μm) than the soot H25, soot H50, soot B (Table S3.4 and S3.5). From the estimated data and model simulation data, pure graphite particles witness over the station with a size range of 0.17 μm ≤ r ≤ 0.21 μm, which is also supported by the α450-700 nm (1.47˗1.88), bf (0.11˗0.13) and g (0.68˗0.74).

Fig. 10
figure 10

g as a function of the radius of the particles for different refractive indices with 550 nm incident wavelength

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5 Conclusion

The mountain valley wind circulation has an impact on the total aerosol scattering. Total scattering varied from morning to evening based on the wind direction at the station. The wind direction dependency is observed throughout the year except in the monsoon season. In pre-monsoon, the back trajectory shows a transition of air mass from the northwest direction to the south direction. In March, air mass is transported from the northwest direction; during April, transportation occurred from the southwest direction, while in May trajectories reach the station from the south direction. In March and April, the pollutant is transported from both north-west and south-west, which indicates that both fine and coarse mode particles reach the station. In the monsoon season, the biomass-burning aerosol prevailed at the station, whereas backward trajectories are transported from the South direction (BoB).

The Scattering Ångström exponent (α450-700 nm) varied from 1.5 to 1.9, indicating the aerosols are fine particles with a radius < 0.5 µm. In the pre-monsoon, local biomass burning increased compared to the winter, and the contribution of biomass aerosol is higher than that of long-range transported particles, which enhanced the α450-700 nm. In the monsoon and post-monsoon seasons, the local biomass burning and other emissions dominated the concentration of aerosol and caused higher α450-700 nm at the station. Fresh biomass burning contributed the fine particles to the mixture of brown and black carbon, resulting in a higher α450-700 nm. The other researcher carried out a similar kind of test in several Indian towns and Athens, and the results showed that the α450-700 nm ranged between 1.92–1.98 (during the pre-monsoon) and 1.97–2.15 all year long. Hysplit backward trajectory showed that particle size depends on the preponderance of locally burned biomass and long-range transportation. Smaller α450-700 nm is caused by the predominance of long-range transportation of particles over local emissions. Whereas local emissions predominated over long-range transportation, this resulted in higher α450-700 nm.

Over the station, the backscatter fraction (bf) and asymmetric parameter (g) are determined to be in the range of 0.11–0.13 and 0.68–0.74. From the winter to the monsoon season, the bf value decreased. The bf decreased from winter to monsoon season, but the g values enhanced, demonstrating a negative correlation. The bf value decreased owing to the lower backscatter and higher forward scatter for bigger particles from winter to monsoon. Thus, the g values are smaller for higher bf values associated with smaller aerosol particles. For various Indian cities and Cuiaba´, Porto Velho, researchers found bf value is in the range of 0.18–0.24 in pre-monsoon and 0.11–0.13 throughout the year. Similarly, researcher reported that g value is in the range of 0.64 -0.83 and 0.72–0.73 at US East Coast and North Atlantic. Upon comparing the g value with the simulated particle size model, it is noticed that the aerosol size falls between 0.17 and 0.21 µm for a given radius. Noteworthy that in the monsoon season, the prevailed aerosol radius is approximately 0.21 µm. The station’s bf value is much lower than the other stations over the Indian continent. The bf value is calculated from the model-estimated values of g for varying refractive index at 550 nm wavelength. The bf values vary for refractive index above the particle size of 0.2 µm, the variation of bf is not significant for tiny particles (r < 0.2 µm). The g value varies from maximum to minimum in different seasons and different theoretical simulations give different values. At the station, the estimated g value is 0.68–0.74 and this value indicates the size of the particle in the range of 0.15–0.2 μm radius. Here, soot H25, soot H50, and soot B have the almost same g values for the particle range 0.17 < r < 0.21, which indicates that the particles are a homogeneous mixture of graphite-air and dry ash. For Soot A and Soot G, the g value reached the calculated value for the larger radius particles.