Insight into seasonal aerosol concentrations and meteorological influence over a flood affected area using satellite data and statistical model simulation

Aerosol particles in the atmosphere are one of the many factors that might affect floods. One of India's most flood‐prone regions, Muzaffarpur district in Bihar, has been chosen as the study area. The time period considered for the satellite data on meteorological influence is from the year 2000 to 2021. The correlation coefficient between past forecasts and its confirming data is often used to assess the effectiveness of weather and climate forecasting systems. Therefore, changes in correlation can be utilized to gauge advancements in forecasting ability. In this study, the relationship between aerosol optical depth (AOD) 550 nm, temperature, relative humidity, wind speed, PM2.5 and precipitation are carried out with correlation co‐efficient. The average rainfall throughout the monsoon was found to be 162.5 mm, during the period 2000–2021. The descriptive statistical data for seasonal data were determined for AOD (550 nm), PM2.5, wind speed, relative humidity, and temperature values. It is inferred that there is a positive correlation between precipitation and AOD for the monsoon season. Hence the fitting of meteorological parameter AOD for the monsoon season are done with six different probability distributions Gamma (3P), Logistics, Lognormal (3P), Normal, Rayleigh (2P) and Weibull (3P). The parameters of these distributions are evaluated using the Maximum Likelihood Estimation and the goodness of fit is tested using the test statistics Kolmogorov Smirnov and Anderson Darling test. Among the six discussed distributions, Weibull (3P) distribution provides the best fit to model the meteorological data from the satellite, the flood prediction would be obtained from the model proposed.


| INTRODUCTION
Floods kill more people than any other weather-related calamity, the top five countries affected by flood on the list are: Netherlands, Bangladesh, Vietnam, Egypt and Myanmar (Conte, 2022).River floods accounted for approximately 80% of the total number of individuals affected, South Asia has the highest number of flood-prone countries, where the world's most flood-vulnerable population currently resides close to 1.81 billion people (World Bank, 2015).Estimates show that globally, 1.81 billion people (23% of the world population) live in locations that are exposed to a significant level of flood risk, facing inundation depths greater than 0.15 m in the event of a 1-in100-year flood, or at least medium risk.In other words, considering a global population of 7.9 billion, almost one in four of the world's people are exposed to significant flood risk (Ackerman et al., 2000).Floods affect both human and economic losses and continues to mount in nations around the world.Flood exposure estimates are viewed spatially, revealing that dangers within nations are concentrated in particular regions, such as the coast or river basins.There are a few subnational locations that stand out for having sizable, exposed populations, such the Ganges River along the Indian states of Bihar, Uttar Pradesh, and West Bengal, where 196 million people live in high-risk flood zones, making up 33%-53% of each state's respective populations.Aerosols may have a direct and indirect impact (Feingold et al., 2003) on the weather, the earth-atmosphere system's radiation balance is directly impacted by particles because they absorb and scatter solar radiation.The Indirect effects of aerosol optical depth (AOD) in Muzaffarpur can be categorized into two typesthe first type of indirect effect, also referred to as the Twomey effect (Chauhan & Singh, 2020, 2021) states that an increase in Aerosol concentration leads to an increase in the concentration of cloud (Kaufman et al., 2005) particles and a decrease in their radius, increasing the cloud's albedo and affecting the global radiation balance.The second type of indirect effect in Muzaffarpur, also referred to as the Cloud Lifespan Effect or Albrecht Effect, states that an increase in aerosol concentration causes an increase in cloud longevity, the global radiation budget is impacted by the lengthened cloud lifespan (Albrecht, 1989).
Recent research has also suggested that aerosols (Ramanathan et al., 2001) like black carbon (BC) or soot, which may absorb solar radiation and emit heat radiation outward, have a semi-direct effect on clouds.BC is also connected to numerous dangers (Twomey, 1977), the BC has a number of significant flaws, including its tiny size, unpredictable shape, and vast surface area.BC interacts with other air pollutants, frequently absorbing elements that cause cancer, such as Polycyclic Aromatic Hydrocarbons (PAHs) and volatile organic compounds (VOCs) (Kurwadkar et al., 2023).According to the research, Children and adults' health risks (Humbal et al., 2018) were evaluated, for the diesel exhaust, gasoline, biomass, and coal combustion are the main sources of 16 PAHs in the interior and outdoor atmosphere of urban slums and rural areas (Ambade, Kumar, & Sahu, 2021;Ambade, Sankar, et al., 2021).The atmosphere and clouds cause the cloud droplets (Khain et al., 2005) to evaporate, reducing the volume of clouds, shortening their duration, and decreasing their average albedo (IPCC, 2007).For Muzaffarpur district, floods are unwelcome guests, and each year, they claim numerous lives (Humbal et al., 2019) while washing away crops from more than one lakh hectare.People's and products' mobility is severely constrained during floods, flood has been a major challenge in Muzaffarpur district, since agriculture is the backbone for the people during the early twentieth century.Every Anchal in the Bagmati riparian zone is categorized as having more than 75% of its land subject to flooding.The entire Bagmati riparian area resembles a large sea during floods, with a few islands made up of communities situated on higher ground (District Development Plan-Muzaffarpur, 2019).Insight into seasonal aerosol concentrations and meteorological influence (Chen et al., 2017) over a flood affected area Muzaffarpur is done using satellite data.
An investigation is carried out to find the annual average of meteorological parameters, that is, temperature, relative humidity, Particulate Matter (PM2.5),wind speed and precipitation with AOD (Liu et al., 2011) and PM2.5 to predict the occurrence of flood due to rainfall.Seasonal analysis of the monthly mean temperatures, precipitation, PM2.5, wind speed, AOD for Muzaffarpur situated in the state of Bihar, Correlation analysis is done to find the relationship between the PM2.5 and AOD with meteorological parameters.Statistical modelling is performed to predict the occurrence of floods using a probability distribution model, which helps in forecasting future floods and urges the control of aerosol particles from various sources.We hope that the main findings of this study will improve our understanding of the causality between aerosols and precipitation.

| Muzaffarpur area investigations
Muzaffarpur district in Bihar is geographically large which has area of 3172 km 2 .The research region is located in the Indian state of Bihar between latitudes of 26 14 0 55 00 N and 25 59 0 41 00 N and longitudes of 85 11 0 15 00 E and 85 33 0 22 00 E. The district's northern and southern boundaries are formed by the districts of East Champaran and Sitamarhi, Vaishali, Darbhanga, and Samastipur (part), as well as Saran and a piece of Gopalganj, Muzaffarpur serves as the district's administrative centre.
The northern region of India is the study area under consideration.Muzaffarpur, Bihar, India, is the location chosen for the study of the relationship between precipitation and meteorological variables (Bisht et al., 2022).Muzaffarpur as shown in Figure 1 is located at 26.1197 N and 85.3910 E and is bordered by the Bagmati and Lakhandayee rivers as well as the Burhi Gandak River.
There are 5.439 million people living in the district (Census 2021), there were 906 women for every 1000 men overall.The district has a 90.7% rural population and a 9.3% urban population.Between 1981 and 1991, there was a decadal growth rate of 23.3%.The population density was 929 people per square kilometre.Within 2 miles of Muzaffarpur, there are 66% of artificial surfaces and 39% of cropland, 93% of cropland within 10 miles, and 94% of cropland within 50 miles.In Muzaffarpur, the dry season (Chelani & Gautam, 2022) is mainly clear and hot year-round, while the wet season is oppressive and mostly gloomy.The average annual temperature ranges between 49 and 99 F (9 to 37 C), rarely falling below 44 F (7 C) or rising above 107 F (42 C).

| Meteorological satellite data
Secondary data sets (i.e., aerosol and meteorological parameters) of the selected study area, have been collected for a period of 21 years  using NASA Giovani website.The data were presented as a time series, area-average, in the chosen region, and the coordinates for the precise location were listed.Aerosols (Gollakota et al., 2021) are picked from the disciplines, and AOD is chosen from the measurements, to gather the profiles.AOD and PM2.5 are provided by the MODIS Terra satellite with a 1-degree spatial resolution, 550 nm wavelengths, and daily temporal resolution; the PM2.5 and AOD 550 nm (Deep Blue, Land) dataset file can be downloaded in CSV format.
The daily data are chosen for temporal average and renewable energy for user community, the duration and the coordinates for the specific study area are updated.The data has been downloaded in CSV format once the parameters like temperature at 2 m, relative humidity at 2 m, wind speed at 50 m and precipitation (Tao et al., 2012) have been chosen from the Giovani website.The research software is used to execute the correlation coefficient, sort the gathered data, and determine whether there is a correlation between the yearly average and the monsoon average for a particular year through stochastic statistical analysis The properties of a data set are summarized and organized using descriptive statistics, data set is a collection of responses or observations from a sample or population as a whole.The initial step of statistical analysis in quantitative research (Ranjan et al., 2007) is to define the response characteristics, such as the average of one variable (e.g., precipitation) or the relationship between two variables (e.g., AOD and precipitation).
The positive square root of the variance is the standard deviation (SD), one of the most basic approaches of statistical analysis is SD.The standard deviation, abbreviated as SD and represented by the letter σ, indicates how far a value has varied from the mean value.A low SD indicates that the values are close to the mean, whereas a large SD indicates that the values are significantly different from the mean.
For each group, the median is the value in the middle, it's where half of the data is more and half of the data is less.The median makes it possible to represent a vast number of data points with just one (Rosenfeld et al., 2008).The median is the most straightforward statistical measure to compute.The data must be sorted in ascending order to calculate the median and the middlemost data point is the data's median.
The Standard Error of Measurement (SEM) is the SD of measurement errors that are linked to test scores from a certain group of examinees.Instead of using a single SEM number, it is advised that score bands be calculated using SEMs at several score levels (Harvill, 1991).The variability in a sample is calculated using sample variance, sample is a collection of observations drawn from a population that can entirely reflect that population.The sample variance is calculated in relation to the data set's mean, the calculation of skewness and kurtosis is required for a thorough examination of distribution shape.However, in the case of nonnormal distributions, their values are frequently skewed (Rosenfeld et al., 2008); that is, there may be a disparity between the real (theoretical) values or accepted standards of skewness and kurtosis measures for a given distribution and the observed (empirical) values.
Few primary research offered alternative estimators with the goal of eliminating this bias and used researcher's work in the analysis (Hogg, 1974;Micceri, 1989).The measure of correlation coefficient (r or R) provides information on closeness of two variables.Two correlation coefficients are typically used in applications: the Product Moment Correlation Coefficient and Pearson's and Spearman's Rank Correlation Coefficient (Senthilnathan, 2019).In contrast, the relationship between cloud droplet concentration and precipitation intensity is related to the liquid water path, and as the number of aerosols increases, the radar reflectance spectrum wideness and precipitation increase, while cloud droplet concentration decreases (Fan et al., 2019).

| RESULTS AND DISCUSSION
The results and discussion for collected data sets from the satellite have been analysed with the average annual value.The results and discussion consist of descriptive statistics for the annual average, average annual profile, and insight into the seasonal climate of the region under study.

| Descriptive statistics
The descriptive statistics for annual average are done for every year from 2000 to 2021, for the relative humidity, temperature, wind speed, AOD (550 nm), precipitation and PM2.5 is shown in the Tables 1-6 given as follows.  .

| Average annual profile
The average annual profile for the various parameters of the region are estimated and the statical analysis is done as follows.

| Relative humidity
It is a measurement of the actual amount of airborne water vapour in relation to the maximum amount of vapour that the atmosphere can support at the current temperature.The highest relative humidity value was 66.93% in the year 2020 (Figure 2).

| Temperature profile
The annual average temperature may be seen rising and falling in

| Aerosol concentration profile
AOD is a measurement of the amount of electromagnetic radiation that is absorbed by aerosols in an atmospheric column at a certain wavelength.From Figure 5, increasing trend from the past years in the level of AOD is observed.In the year 2015, the value reached its highest value of 0.94 nm; its lowest value of 0.49 nm during the F I G U R E 6 Annual average precipitation profile .
period of 2000 from the graph.This represents that as the years past; the amount of aerosols in the atmosphere is statistically increasing 30% over the years.

| PM2.5 profile
For the purposes of regulating air quality, particles are classified according to their diameter.It has been discovered that PM2.5 from the burning of fossil fuels, such as coal combustion or diesel-fuelled vehicle emissions, is one of the most dangerous types of PM2.5.
According to Figure 7, the PM 2.5 concentration reached its maximum level in 2018 at 0.091 g/m 3 , but it was also higher in 2002, 2004 and 2003, at 0.098, 0.082 and 0.081 g/m 3 , respectively.2020 saw the lowest figure of 0.049 g/m 3 , with 2007 seeing the second-lowest number.

| Insight of seasonal climate
The insight of the seasonal climate in the Muzaffarpur region, monsoon season has a higher PM2.5 value than any other season, the value is significantly lower during the monsoon, which may be because rains swept out the particulate particles.PM2.5 concentrations during the monsoon (0.022-0.12 g/m 3 ), in the years depicted from the Figure 8, the post-monsoon (0.012-0.07 g/m 3 ) and winter (0.02-0.06 g/m 3 ) seasons are found to be lower than the premonsoon (0.008-0.017 g/m 3 ) season.The AOD 550 nm value is higher in the winter and overlaps with itself in all other seasons, indicating that there is little seasonal variation.AOD concentration could increase because of the increasing atmospheric moisture content throughout the winter.The temperature was high prior to the monsoon season and low throughout the monsoon, due to the change in the climate, the temperature is also lesser in the winter.Relative humidity is observed to be high during the monsoon and postmonsoon seasons and low during the pre-monsoon season, with a range of roughly 28%-45%.In the monsoon season, the level of wind speed is observed to be higher between the years 2000 and 2012, and then there is some overlapping of values between the monsoon and pre-monsoon seasons after that.The data show a few peak levels in the post-monsoon, the precipitation value is found to be higher in the monsoon and then in the pre-monsoon season.
In Bihar's Muzaffar district, the maximum amounts of precipitation are analysed for the monsoon, pre-monsoon, post-monsoon, and winter seasons using AOD, PM2.5 and precipitation.In the year 2020 for the monsoon, it has been noticed that as the AOD 550 nm (0.89) increases, so does the daily rainfall (10.78 mm).Peak levels in the data for rainfall (2.48 mm/day) in the year 2021 coincided with the postmonsoon season, when the AOD 550 nm (0.87) and PM2.5 (0.07 g/m 3 ) increases.The backward trajectories indicated that air masses came from various heights and locations, according to BC (Ambade et al., 2022) research's study, particulate matter sources from north, northwest and east also the PM2.5 level is higher in post-monsoon season due to Industrialization and traffic load (Ambade & Sankar, 2021).
During the pre-monsoon season, the precipitation is observed to be 3.1 mm/day in the year 2021 and the PM2.5 (0.13 μg/m 3 ) and AOD (0.77) value is higher.The seasonal variation for the winter during 2003 for AOD (550 nm) and PM2.5 is observed to be lower (0.73 and 0.04 μg/m 3 ) and the precipitation is 0.04 (mm/day).

| Correlation analysis
Precipitation and AOD have a positive correlation with a correlation co-efficient of (r = 0.415) according to the monsoon season's correlation analysis from the metrological profile.Moreover, the monsoon season's r = 0.07 correlation coefficient between precipitation and PM2.5 is noted.Correlation analysis of the monsoon season from the metrological profile provides a positive correlation between precipitation and AOD with the correlation co-efficient.
The above Figure 9 demonstrates the relationship among AOD 550 nm, temperature, relative humidity, wind speed, PM2.5 with the precipitation for the study area.The correlations of AOD 550 nm with temperature, wind speed and precipitation have a positive correlation during the monsoon season, the relative humidity and PM2.5 with AOD shows negative correlation.According to (Ambade, Kumar, & Sahu, 2021;Ambade, Sankar, et al., 2021) research work on BC, the results suggested contrary results except for relative humidity.They observed an inverse correlation between BC and temperature (r = 0.92), wind speed (r = 0.61), precipitation (r = 0.60) and humidity (r = 0.52).This shows that the AOD can influence the rainfall in the particular area in the positive correlated manner.

| Stochastics statistical analysis
The stochastics statistical analysis of the meteorological profile (Amin et al., 2016) is carried out with the probability density where y (x, t) < ∞ for all the value of x and t: And for all x, F I G U R E 9 Correlation analyses of the meteorological profiles.AOD, aerosol optical depth.
F I G U R E 1 0 Kernal density plot for the average rainfall of Muzaffarpur.
By calculating the frequency of amount and intensity of rainfall during the seasonal wise, study carry out a test of normalcy on the annual amount of precipitation in the region.The following hypothesis is used to guide all tests: H0.The yearly average rainfall are normally distributed.
H1.The yearly average rainfall does not arise from a normal distribution.
All tests provide significant findings at ( p = .05),implying that the average annual rainfall for the seasonal profile of Northern India follows a normal distribution due to regular periodicities in the rainfall at each session as shown in Figure 10.
T A B L E 7 The probability density function (PDF), cumulative distribution function (CDF) and parameters of the discussed distributions.
F I G U R E 1 1 Fitting of aerosol optical depth (AOD) profile with various distributions.PDF, probability density function.

| Flood prediction model through PDF
The range of values and probabilities (Hogg et al., 1975) that a random  As a result, it can be observed that AOD is one of the suitable parameters for predicting potential rainfall in a certain location, and the Weibull (3P) distribution may be used to model the AOD profile and anticipate future rain fall.
The values in the years 2021, 2008 and 2007 were similarly higher, with readings of 64.68%, 64.52%, and 62.43%, respectively.The lowest figure was recorded in 2018, which is 50.42% lower than the values from the prior years, according to satellite data.

Figure 3 ,
Figure 3, the year 2008 saw the lowest temperature recorded at 17.79 C, and the year 2015 saw the highest temperature recorded at 20.17 C. As the density of the gases in this layer decreased with height, the air became thinner; therefore, the temperature in the region also decreased with height in response to the region.We can observe the fluctuation of the annual average temperature which indicate that it has an impact in the climate of the region.

Figure 6
Figure 6 shows the yearly average precipitation plotted against years.The highest recorded value was 4.66 mm per day in 2008, with the second highest recorded value being 4.01 mm per day in 2007.The year with the least amount of daily precipitation, 2018, received 1.8 mm.This explains, that there was a probability of flooding in the years 2007, 2008 and 2018, and as well as 2018 was a dry year.The amount of precipitation for the season, which is usually related to the amount of flooding in the area.The precipitation of 20% is increased from the observation during these years.
Season wise analysis of meteorological profiles.AOD, aerosol optical depth.function (PDF) f(x) assigns each value from the ith sample to point x i , the function K(x i , t) is known as a kernel function under the following conditions: b variable may have are explained by the cumulative distribution function (CDF) and PDF.Owing to the favourable link between precipitation during the monsoon season and the meteorological profile AOD, it was statistically modelled using Gamma (3P), Logistic, Lognormal (3P), Normal, Rayleigh (2P), and Weibull distributions (3P).The Maximum Likelihood Estimation (MLE)(Divya, 2018)  is used to evaluate the parameters of various distributions.The Anderson-Darling (AD) test and the Kolmogorov-Smirnov (KS) test are used to examine and compare the goodness of fit's quality.Table7includes a list of the PDF, CDF and parameters of the discussed distributions.

Figures
Figures 11 and 12 provide the graphical depiction of goodness of fit and its accompanying CDF curves.The CDF curve's goodness of fit is also evaluated for Gamma (3P), Lognormal (3P), Rayleigh (2P), Weibull (3P), Normal, and Logistics distributions.Among all these distributions, the Weibull (3P) distribution gives the best fit for the AOD profile.The results of goodness of fit tests are shown in Table8.It is observed that the Weibull (3P) distribution gives the best fit to the AOD profile under the both KS-test and AD-test of goodness of fit.
T A B L E 1 T A B L E 2 T A B L E 4 Descriptive statistical table for AOD (550 nm).in most of years the relative humidity is negatively skewed due to the high variance and also the relative humidity has less kurtosis.Table2shows that the lowest and highest annual average temperatures were recorded in the years 2008 and 2012, respectively.It has been noted that the low kurtosis and high variance indicate that the temperature is negatively skewed.Table3 revealsthat the years with the lowest the years 2018 and 2008.Precipitation has been observed to be positively skewed, as evidenced by the low variance and high kurtosis found in 2005.In Table 6, the years 2007 and 2020 have the lowest average PM2.5, while 2018 has the highest.The PM2.5 is positively skewed, as presented by the low variance and high kurtosis found in 2014.