Correlation analyses between downward longwave radiation particulate matters, aerosol optical depth, and metrological variables under non-dusty and cloudless conditions

This study used downward longwave (LW) radiation measurements, air temperature (T), particulate matter (PM) concentrations of fine (PM 2.5) and coarse (PM10) particles, aerosol optical depth (AOD), wind speed (WS), and precipitable water vapor (PWV) data from Riyadh, an arid site in central Saudi Arabia, between 2014 and 2019 to characterize their variations and investigate the influence of these variables on the measured downward LW radiation under non-dusty, clear sky conditions. The LW radiation and air temperature, it was found, attain their maximum in summer and minimum in winter. Conversely, the PM mean concentrations and AOD showed their maximum in spring and minimum in winter. PWV features an increasing trend during spring, summer, and fall, whereas it features a decreasing trend during the winter. The monthly variation of WS shows low monthly values during fall and winter and considerably higher monthly mean variation during spring and summer. Apart from wind speed, which does not affect the LW radiation, correlation analyses demonstrated that the LW correlates positively with the remainder of the considered variables. The strength and degree of association between the LW radiation and these variables differ from one variable to another, with air temperature having the strongest correlation (correlation coefficient = 0.98) with the LW radiation, followed by the AOD (correlation coefficient = 0.69), with a correlation coefficient of 0.36 with the PWV. Similarly, the relationships between the LW radiation and both PM10 and PM2.5 had the same correlation coefficient of 0.32. The effect of the meteorological variables (mainly air temperature, relative humidity, and wind speed) on the PM concentrations was investigated using the regression analyses. The results showed a significant positive relationship with air temperature and wind speed and a negative relationship with RH.

This radiation results from the absorption and re-emission of the infrared (IR) radiation emitted from the Earth's surface due to the presence of greenhouse gases in the atmosphere. This absorption/emission in the atmosphere is caused primarily by water vapor (below 7.6 μm, between 13 μm and 16 μm, and beyond 22 μm), carbon dioxide (from 14 μm to 16 μm), and, to a lesser extent, ozone (between 9 and 10 μm). Trace gases, such as methane, nitrous oxides, and carbon monoxide, also absorb and emit in the IR wavelengths. The remaining unabsorbed portion of the Earth's radiation escapes into outer space through the atmospheric window, which lies between 8 and 14 μm (e.g., Idso and Jackson, 1969;Ruckstuhl et al., 2007;Maghrabi 2012;Viudez-Mora et al., 2009).
Atmospheric aerosols directly influence the radiation balance through the absorption and scattering of both solar and atmospheric radiation. Moreover, aerosol particles affect cloud formations and distributions, which affect, indirectly, the energy budget and, thereby, the climate. The aerosol effects vary in importance according to several factors, such as wavelength, concentrations, and atmospheric conditions (Liu and Ou, 1990;Smirnov et al., 2002;Xia et al., 2007).
Atmospheric aerosols, termed particulate matter (PM), consist of solid particles, liquid droplets, or mixed-phase particles varying in size from tens of nanometers to hundreds of microns. PM includes both the coarse PM 10 (diameter of 2.5 to 10 μm) and the fine PM 2.5 (diameter less than 2.5 μm). The sources of PM 10 and PM 2.5 can be natural, such as windborne dust or anthropogenic, such as the combustion of fuels (Harrison, et al., 2004;Barkan et al., 2004;Hueglin, et al., 2005;Alharbi, 2009;Begum, et al., 2011;Chantara, et al., 2012;Chen, et al., 2018).
Despite the importance of atmospheric aerosols/PM and their impact on solar and LW atmospheric radiation, there has been less work conducted in this part of the world to study their effect on LW atmospheric radiation. In light of this, this paper aims to characterize LW radiation's variations, screen level temperature, precipitable water vapor, wind speed, atmospheric aerosol (PM 10 , PM 2.5 ) concentrations, and atmospheric aerosol optical depth and investigate their relative impact on the cloudless LW radiation in Riyadh.

Data sources and methodology
Riyadh, Saudi Arabia's capital, owing to fast urbanization and industrialization, is one of the country's most polluted cities. It has more than 7 million inhabitants with great heating, industrial, and traffic activities within cities in Saudi Arabia. These factors, among others, result in a high number of particulate matters of different sizes in Riyadh. Since Riyadh is located in the middle of the Arabian Peninsula and surrounded to the east and west by the two corridors of the Ad-Dahna sand belt and many regional dust sources, dust storms, in addition to local sources, can be considered a major natural source of atmospheric aerosols (Alharbi 2009).
The dataset used here consists of downward longwave (LW) atmospheric radiation measurements, particulate matter concentrations (PM 10 , PM 2.5 ), meteorological data, and aerosol optical depth data. Apart from aerosol optical depth data, all the measurements were taken using a radiometric and weather station installed on January 2014 on the rooftop of the radiation detector laboratory building at the King Abdulaziz City for Science and Technology (KACST) campus (Riyadh,central Saudi Arabia;lat. 24 43;long. 46 40;alt. 613 m). The data covered the period from 1 March 2014 to 30 September 2019.
The LW radiation data were measured using a Kipp and Zonen pyrgeometer model CGR3 (CG3 handbook Kipp & Zonen, 2015). It has a 150° field of view and records broadband infrared flux in the wavelength range of 4-50 µm. The specifications of this detector and its calibration processes can be found on the Kipp and Zonen website.
Meteorological data such as atmospheric pressure, relative humidity, wind speed and directions, and air temperature were measured using the Skye Mini Metstation (Skye instrument, 2015) that incorporates different meteorological sensors. Dataloggers CR23X and CR10X were programmed at 30-and 10-s sampling rates, respectively, and both provided measurements at every 10-and 60-min integration time.
The total integrated water content, namely the PWV, is the amount of liquid water that would be obtained if the entire vapor in the atmosphere within the vertical column was compressed to the point of condensation. PWV is the most important greenhouse gas and significantly influences many atmospheric processes and plays a major role in climate variability. It is a physical parameter that is difficult to measure with adequate spatial and time resolution due to its considerable variations with prevailing conditions. Moreover, the measurement of the PWV requires costly equipment (e.g., radiosonde, LIDAR systems, and GPS satellites) which is not easily available (e.g., Maghrabi and Clay, 2010 references therein). In situations, where the PWV data are correspondingly scarce, the use of empirical models, which are based on the statistical fit between the PWV data and screen-level parameters, is a common practice.
In this work, the PWV was calculated using the model developed by Maghrabi and Al dajani (2013). As per this model, the PWV data obtained from the radiosonde observations, for Riyadh for the period between 1985 and 2007, were correlated with the measurements of the vapor pressure and air temperature. The obtained model was: Here, eo and T are the ground level values of vapor pressure (in hPa) and air temperature (in C) respectively. This multilinear model can predict the PWV with a mean bias error (MBE) of − 0.06 mm, and a root mean square error (RMSE) of approximately 2.80 mm (Maghrabi and Al dajani, 2013).
The concentrations of PM 10 and PM 2.5 were measured using beta attenuation monitors (BAM 1020, Met One Instruments) based on the principle of the beta ray attenuation method. In this study, two monitors were used, with each one featuring a size-selective inlet, a beta radiation (1) PWW = 2.72 + 1.32 × eo + 0.21 × T source and detector, and a filter tape. PM 10 and PM 2.5 were sampled through the respective size-selective inlet installed in each monitor and deposited on a single point on a filter tape. The mass of deposited PM 10 and PM 2.5 was determined by calculating the difference between the beta radiation transmitted through the filter tape before and after taking the PM 10 and PM 2.5 samples.
The aerosol optical depth at 500 nm (AOD 500 ) data between 1 March 2014 and August 2015 from the AER-ONET solar village site located 15 km north-west of KACST was used. The hourly averaged level 1.5 products were utilized, which were cloud-screened and quality assured (Holben et al., 2001). The instrumentation, data acquisition, retrieval algorithms, and calibration procedure for the used instruments are described in detail in several studies (e.g., Holben et al., 2001;Maghrabi and Alotaib, 2011).
Due to some technical issues, there was a lack of observation data during the study period. However, the observation data covered all the expected atmospheric and environmental conditions experienced in Riyadh.
The clear sky times were selected based on the cloud information provided by the Saudi Presidency of the Environment (SPE). The cloud coverage was required to be less than two octa during the course of measurements. Dusty periods were excluded using the synoptic information provided by the Saudi Presidency of the Environment (SPE). Additionally, dusty periods were excluded using the procedures developed by Alharbi (2003).
Using the above-mentioned quality control procedures, a total of 16,022 h of clear sky measurements during the study period are selected, and their basic statistical values are presented in Table 1.
The aerosol optical depth data were recorded between March 2014 and August 2015.
The LW atmospheric radiation ranges between 238.55 and 505.29 Wm 2 with a mean of 383.99 ± 69.75 Wm 2 and a median of 389.9 Wm 2 . The PM 10 ranges between 8 and 442 µg/m 3 with a mean value of 141.67 ± 71.9 µg/ m 3 and median of 129 µg/m 3 . PM 2.5 on the other hand has a mean of 39.9 ± 29.3 µg/m 3 , median of 34 µg/m 3 , maximum of 98.51 µg/m 3 , and minimum of 1 µg/m3. The precipitable water vapor and air temperature range between 6.35 and 38.50 mm and 3.41 and 46.22 °C, respectively, with mean values of 19.02 ± 4.35% for the former and 29.2 1 ± 9.34 °C for the latter. The wind speed reaches a maximum of 5.49 m/s and has a minimum of zero and a mean of 1.89 ± 1.50 m/s. The monthly variations in the LW radiation, PM 10 , PM 2.5 , air temperature, PWV, and wind speed were 26%, 38%, 44%, 59%, 33%, and 40%, respectively. LW radiation displays a minimum in February (317 W/m 2 ); between February and March, it increases by about 32 W/m 2 and then increases gradually until it reaches a maximum (about 430 W/m 2 ) in July.

Characterization of the considered variables
The PM mean concentrations showed their maximum in the spring season and minimum in winter. The PM 10 and PM 2.5 concentrations increase dramatically from 110 to 166 µg/m 3 for the former and from 29 to 43 µg/m 3 for the latter between February and March. The PM 10 remains around this value until May, and it dropped to 140 µg/m 3 in June. Between June and July, the PM 10 jumped from 140 to 180 µg/m 3 and dropped to 140 µg/m 3 in August and remained between 140 and 135 µg/m 3 between August and October and decreased to 110 µg/m 3 by November. Then, it reached 140 µg/m 3 by December and decreased to its minimum in February. From its maximum, PM 2.5 decreased gradually in March to reach its minimum of 30 µg/m 3 in November. This period is characterized by a dramatic drop of about 16% between July and August and by 21% between October and November with no major changes observed between August and October.
The monthly variation of the atmospheric column of atmospheric aerosols, represented by aerosol optical depth (AOD), is indicated in Fig. 1d, which shows that AOD during the March-August period (spring and summer) features a considerably higher monthly mean variation than during the September-February period (fall and winter). It increases from its lowest mean value in January (0.11) until they reach its maximum in April (0.7). Between March and April, the AOD value rises due to the high aerosol loads brought to the region by dust storms from local, regional, and global sources (Kutiel and Furman 2003;Alharbi et al., 2013). Subsequently, the AOD value decreases to 0.38 in July. In August, the AOD reaches a value of 0.5 and then decreases steadily until January. The August increase may be due to the high temperature during this month, and its influence on the boundary layer which, in consequence, affects the aerosol loads from anthropogenic sources (e.g., Gröbner et al., 2009;Maghrabi and Alotaibi 2017). The air temperature (Fig. 1e) increases gradually from its minimum value of 16 °C in February to reach its maximum of 39 °C in July. Between June and August, the monthly temperature varies by about 1.5 °C. The temperature decreases gradually subsequently to attain its minimum. Figure 1f shows that the monthly mean variation of the estimated PWV features an increasing trend during spring, summer, and fall, whereas the variation features a decreasing trend during winter. The increasing trends during spring and summer are comparable. The monthly mean variation of the estimated PWV decreased to its lowest value of ∼ 14.3 mm in February and increased to its highest value of ∼ 22 mm in November. The decrease in the PWV in June-July can be explained as follows. As the surface heating progressively intensifies during these times, changes in patterns of pressure systems and moisture advection over the study area occur resulting in a transport pattern featuring a moisture transport relatively lower than that during April-May period.
The monthly pattern of the WS curve (Fig. 1g) features low monthly mean variation during fall and winter and a much higher monthly mean variation during spring and summer. The mean near-surface wind speed decreased to its lowest value of ∼ 1.5 m/s in October and increased to its peak value of ∼ 2.7 m/s in July.

Correlation analyses between LW and the considered variables
Regression analyses between the downward LW radiation and independent variables (meteorological variables, PM 10 , PM 2.5 , and AOD) were performed and established. The significance of the proposed regressions was tested using F-tests and t-statistic student test. The results have been presented in Table 2. Figure 2 shows the relationship between the daily mean values of the LW radiation and the considered meteorological variables. The magnitude and the strength of the correlations were different from one variable to another.   The AOD data is from 2014 to August 2015. All the correlations are statistically tested and showed significant correlations.

LW radiation and metrological variables
The relationship between LW radiation and air temperature (Fig. 2a) is much clearer, stronger, and extended over the wider ranges of temperature values. The data are less scattered and confined within no more than 1.5 standard deviation. The correlation coefficient, standard deviation, and the slope of the regression between T and LW were 0.98, 27.61 Wm 2 , and 6.85 Wm 2 /C, respectively.
While there is a spread in the data, the LW radiation increases as the total atmospheric water content (PWV) increases. This relationship has a correlation coefficient of 0.36 and a standard deviation of about 37.7 Wm 2 . The LW increases by about 5.10 Wm 2 per 1 mm increase in the PWV. The regression analyses between the wind speed and LW radiation showed no significant correlation between the two variables. The scatter in the data of both PM 10 and PM 2.5 showed a positive correlation with the LW radiation. The PMs that exist in the atmosphere are capable of absorbing and re-emitting the LW radiation; hence, the LW radiation increases as the PM concentrations increase. The mechanism of longwave absorption and emission by aerosols in different conditions has been described by Dufresne et al. (2002).

LW radiation and PM concentrations
There are obvious spreads in the data; for e.g., for a certain value of PM values, there are several measurements of different values of the LW radiation. The PM concentration could be increased and affected by different factors, including traffic activities, population intensity, and topography. The long-range transportation of atmospheric aerosols may be another factor that affects the region. The effect of other atmospheric, environmental, and meteorological factors on the LW radiation may contribute to the spread in this relationship. Moreover, the PM concentrations represent the particulate matters with sizes below or equal to the 10 μm measured at ~ 30 m above ground, whereas the atmospheric AOD is integrated for the whole atmospheric column, which is more suitable to represent the total atmospheric extinction.
The LW when correlated with the PM 10 has a correlation coefficient of 0.32, a standard deviation of 39.29 Wm 2 , and a slope of 53.05 Wm 2 per 1 increase in 1 µg/m 3 . It increased by 0.55.79 Wm 2 per 1 µg/m 3 of PM 2.5 with a correlation coefficient of 0.32 and a standard deviation of 38.42 Wm 2 .

LW radiation and atmospheric AOD
Atmospheric AOD is more suitable to represent the total atmospheric extinction since it is integrated for the whole atmospheric column rather than being a representation at a low level near the ground. Figure 4 is a scatter plot that illustrates the relationship between LW radiation and AOD. Although there is some scatter in the data, the AOD is obviously correlated better with the LW radiation when compared to the PM concentrations.
According to the regression analyses, the LW radiation increased significantly by about 46.26 Wm 2 per 1 increase in AOD. This relationship has a correlation coefficient of 0.69 and a standard deviation of 34.73 Wm 2 .

Discussions
The positive relationship between air temperature and LW radiation found in this study is comparable with previous research. The positive correlation between these two variables indicates that the infrared emission in the part of the atmosphere where the radiation originates is correlated via some combination of radiation, turbulence, and advective process with the surface temperature (e.g., Maghrabi 2012).
Similarly, the dependence of the LW atmospheric radiation on the PWV arises from the strong absorption and reemission of the infrared radiation in the atmospheric window (8-14 μm), vibro-rotational, and rotational absorption bands of water molecules. However, the strength of the relationship between the LW radiation and the PWV is not stronger than expected. This may be attributed to several causes. These include the use of the empirical model to calculate the PWV, where this model may have its own uncertainties. In practice, the PWV values measured with the radiosondes or GPS receivers are most useful (e.g., Bevis, et al., 1992;Maghrabi and Clay 2010). However, such data are usually not available. Moreover, the effect of other atmospheric conditions may also contribute to the spread in the relationship between LW radiation and PWV.
Interesting results were found by studying the effect of the atmospheric aerosols on LW radiation. Such correlations between the LW radiation and, particularly, PM concentrations are rarely available in the literature, and this work is the first to present such an investigation. The LW radiation was found to increase with an increase in the atmospheric aerosols represented by PM 10 , PM 2.5 , and AOD. The relationship between the atmospheric aerosols and the downward atmospheric radiation is due to the absorption and reemission of the LW radiation (atmospheric warming) emitted by the aerosol particles, which increases with an increase in aerosol loading (e.g., Dufresne et al., 2002). The absorption of the LW radiation by atmospheric aerosols and the resultant increase in the LW radiation is an important factor to be considered particularly in energy budget studies and climate change modeling. The LW radiation showed stronger dependence on the AOD than the PM concentrations, which is partially because the AOD accounts for all the air/particles found in the atmospheric column, whereas the PM concentrations represent the atmospheric aerosols only at the screen level. The dependence of the LW radiation on the fine (PM 2.5 ) and coarse particles (PM 10 ) has the same statistical indicators. The spread in the relationship between the PM concentrations and the LW radiation may be attributed to several factors. These include the prevailing atmospheric and environmental conditions (Easter, et al., 1994;Querol, et al., 2001;Vardoulakis and Kassomenos, 2008;Streets et al., 2009;Akyüz and Cabuk, 2009;Tian, et al., 2012;Dominick, et al., 2012;Jayamurugan, et al., 2013;Wang and Ogawa, 2015;Klingmüller, et al., 2016Li, et al., 2017Phairuang, et al., 2017;Fernandes, et al., 2017). For example, the source and sinks of trace gases and aerosol particles in the atmosphere are, indirectly, affected by the variations of air temperature and the water vapor and wind speed at the screen level.
To study this hypothesis, regression analyses between the air temperature, relative humidity, and wind speed and the PM concentrations are conducted as presented in Fig. 5. The correlation results were statistically tested and showed that the PM concentrations (PM 10 and PM 2.5 ) correlated significantly with the air temperature and wind speed and negatively with the RH. The increase in the air temperature can promote the evaporation of aerosols, whereas an increase in the RH increases the rate of absorption of particulates in the atmosphere. It is also expected that the AOD may be affected by metrological variations, but based on the obtained results, these effects may be small when compared to PM concentrations. Studying the influence of metrological variables and the PM requires detailed investigations beyond the scope of this study, and it is the subject of an ongoing research project. Although limited studies have been conducted to determine the interactions between meteorological factors and air pollutants in an arid environment, one that is characterized by extreme heat during sunshine and an abrupt drop in temperature at night, extremely low rainfall and extremely high evapotranspiration rates, the obtained results are consistent with those previously conducted and established associations between meteorological conditions and the parameters of air pollutants and quality (Alharbi 2009).

Conclusions
In this study, downward and longwave (LW) radiation measurements, air temperature, particulate matter (PM) concentrations of fine and coarse aerosols, and the aerosol optical depth at 500 nm and the precipitable water vapor from Riyadh, an arid site in central Saudi Arabia, were used to  1-LW radiation follows the trend in temperature, which reaches a maximum in summer and a minimum in winter. 2-The monthly variations in the LW radiation, PM 10 , PM 2.5 , air temperature, PWV, and wind speed were 26%, 38%, 44, 59%, 33%, and 40%, respectively. 3-The screen temperature shows a better correlation with LW radiation with a correlations coefficient and an RMSE of 0.98 and 8.09 Wm −2 respectively. 4-Although water vapor is considered one of the most important greenhouse gases, the correlation between LW and PWV found in this study was reasonable. This may be due to the empirical nature of calculating the PWV. However, the physical relationship between PWV and LW radiation is evident. 5-The PM mean concentrations and AOD showed their maximum in spring and minimum in winter. 6-The relationship between the atmospheric aerosols and the downward atmospheric radiation showed that the LW radiation increases with increased aerosol loading. This is due to the absorption and reemission due to atmospheric aerosols. 7-The effect of the atmospheric aerosols on the LW radiation occurs mainly in the atmospheric window and is controlled by several factors such as the wavelength, weather, and atmospheric conditions. 8-The regression analyses between LW radiation and AOD showed strong positive correlations between the two variables in comparisons with the PM concentration in Riyadh under cloudless and non-dusty conditions. 9-The correlations coefficient between AOD and LW radiation was 0.69, whereas, it was 0.32 when the LW radiation was correlated with PM concentrations. 10-The strong relation between AOD and LW is, partially, due to the fact the AOD represents the total atmospheric extinction integrated for the whole atmospheric column rather than being a representation at a low level near the ground. Moreover, the PM concentrations are more affected by atmospheric and environmental conditions at the screen level. 11-The correlation analyses between the PM concentrations (PM 10 and PM 2.5 ) showed positive relationship with the