High-resolution simulations are usually conducted for several days or weeks due to their high computational demand. Simulating full-scale aerosol–climate interactions including indirect effects adds further computational burdens. Therefore, considering our purpose, we conducted our model simulations using WRF-Chem at a cloud resolving spatial resolution of 1.5 km × 1.5 km for an entire month (August), of which the first 3 d were excluded from data analysis as the spin-up period. Most model evaluations and diagnostic calculations were performed for a reference year (August 2015) unless otherwise mentioned. Additional validations are carried out for August 2009 because aerosol size distributions and microphysical data from a field campaign were available during this period.

To obtain statistically meaningful calculations of the dust effect on rainfall, 10 years of simulations (2006–2015) were conducted specifically for August of each year. The simulations were conducted over the Red Sea coast outlined by the nested domain d03 (Fig. 1), in which the parent domains d02 (4.5 km ×4.5 km) and d01 (13.5 km ×13.5 km) cover the Arabian Peninsula–northeast Africa and the MENA region, respectively. August was chosen because during this month the Red Sea coast receives abundant rainfall and sea breezes are relatively strong, which plays an important role in moisture transport over the coastal plains (Mostamandi et al., 2022).

We use 6-hourly ECMWF operational data (F640) as initial and boundary conditions; these are some of the most accurate reanalysis data assimilating several observations. The sea surface temperature (SST) was also updated every 6 h using the skin temperature field from the same ECMWF dataset. We continue to use these data because they have worked well in our region (e.g., Parajuli et al., 2020; Mostamandi et al., 2022).

To better represent cloud processes, it is important to use well-developed aerosol chemistry and microphysical schemes (Zhang et al., 2016). Here, we adopted the Model for Simulating Aerosol Interactions and Chemistry (MOSAIC) scheme (Fast et al., 2006; Zaveri et al., 2008; Zhao et al., 2011) with eight sectional aerosol bins. The MOSAIC scheme is computationally intensive and generates large outputs, as all aerosol concentrations are reported for the eight MOSAIC bins for interstitial and in-cloud aerosols. Our simulations used chem_opt = 10, which couples the CBM-Z (Carbon Bond Mechanism version Z) gas phase chemical mechanism (Zaveri and Peters, 1999) with the MOSAIC aerosol scheme and is one of the most developed chemical mechanisms within WRF-Chem.

MOSAIC includes both interstitial and cloud-borne aerosols, cloud–aerosol interactions, activation/resuspension, nucleation, coagulation, aqueous chemistry, and wet removal (Fast et al., 2006; Gustafson et al., 2007). Here, we particularly focused on accurately representing dust aerosols because they are a specific characteristic of the region. MOSAIC includes all aerosols of interest including dust (included in other inorganic aerosols or “oin” because it is chemically inert), sea salt, sulfate, black carbon (BC), and organic carbon (OC) (Zhao et al., 2011; Zaveri et al., 2008). Within our model setup, aerosols affect clouds and clouds also affect aerosols, e.g., through in-cloud scavenging and by forming sulfate aerosols (Yang et al., 2012). Aerosol particles are assumed to be internally mixed, and Köhler's theory is used to relate the aerosol size distribution and composition to the activated CCN as a function of the maximum supersaturation (Abdul-Razzak and Ghan, 2002; Yang et al., 2012). Aerosol activation from the interstitial to in-cloud state is calculated based on a maximum supersaturation determined from a Gaussian spectrum of updraft velocities and internally mixed aerosol properties within each size bin (Chapman et al., 2009). When the hydrometeors evaporate, particles return to the original interstitial phase (Yang et al., 2012).

In MOSAIC, dust is treated as part of the internal mixture used across all aerosol species. All gas and aerosol processes (e.g., sulfate formation) operate within the mixture, but dust itself does not take part in the chemical reactions, although MOSAIC includes the chemical reaction of CaCO3 (a constituent of dust) with acids when the proportion of CaCO3 is provided (Zaveri et al., 2008). Dust itself is considered weakly hydrophilic in WRF-Chem with a hygroscopicity of 0.14 (Kawecki and Steiner, 2018). However, chemical processes within the aerosol mixture may affect the activation of CCN and/or IN, which ultimately affects precipitation (Abdelkader et al., 2017; Klingmüller et al., 2019). This is because interstitial aerosols are partially activated as CCN (in-cloud or cloud-borne aerosols) at each grid cell and time step by using a volume-weighted bulk hygroscopicity from all aerosol species (e.g., dust, sulfate, oin, sea salt) within each size bin (Kawecki and Steiner, 2018; Tuccella et al., 2015) as a function of the environmental supersaturation (Abdul-Razzak and Ghan, 2000). Reduction due to chemical and physical (e.g., coagulation) processes, as well as particle growth, will also cause particles to shift across different bins (Abdul-Razzak and Ghan, 2002; Chapman et al., 2009). The volume-average refractive index within a given size bin is used to calculate the optical properties using Mie theory (Tuccella et al., 2015). Therefore, dust can affect both direct and indirect aerosol feedback.

For cloud microphysics, we used the Morrison double-moment scheme (Morrison et al., 2009), which is one of the commonly used microphysics options in WRF. This scheme allows for the prognostic treatment of two moments of the hydrometeors (mixing ratios and number concentrations) for five species (cloud droplets, cloud ice, snow, rain, and graupel), while calculating key microphysical processes such as autoconversion, collection between hydrometeor species, melting–freezing, and mass transfer from snow to ice (Yang et al., 2011). Compared to the single-moment scheme, which only predicts mixing ratios, the double-moment approach can better represent precipitating convective clouds, particularly during heavy precipitation episodes (Lim and Hong, 2010). The size distribution of hydrometeors is prescribed from the predicted bulk number and mass mixing ratios of different hydrometeor types in an assumed gamma size distribution (Gao et al., 2016). The prognostic treatment of the CCN distribution improves the simulated cloud properties and radiative effects compared to a prescribed uniform CCN distribution, albeit at an increased computational cost (Gustafson et al., 2007). The physics and chemistry namelist options used in our WRF-Chem setup is summarized in Table 1.

We included sea salt emissions using a parameterization based on 10 m wind speed (Monahan et al., 1986; Gong, 2003). Anthropogenic aerosol emissions were also included in our simulations. The emission of sulfur dioxide (SO2), which chemically transforms to sulfate aerosols, is prescribed using OMI (Ozone Monitoring Instrument)-HTAP (Task Force Hemispheric Transport Air Pollution) data (Janssens-Maenhout et al., 2015) for 2015 developed by the National Aeronautics and Space Administration (NASA), as in Parajuli et al. (2020). Other emissions including BC and OC as well as SO2 ship emissions are prescribed using the EDGAR (Emission Database for Global Atmospheric Research) database v4.3.2 available at a 0.1∘ × 0.1∘ resolution (Crippa et al., 2018).

The cloud–aerosol interactions on shortwave (SW) radiation are represented by linking the cloud droplet number concentration predicted by the microphysics scheme with the RRTMG shortwave radiative scheme. Aerosol direct radiative effects through longwave (LW) radiation are also calculated using the RRTMG scheme (Iacono et al., 2000; Zhao et al., 2011). Aerosol indirect effects are calculated following Gustafson et al. (2007) to include both first and second indirect effects. Aerosol particles acting as CCN are coupled with the Morrison microphysics scheme, which allows aerosols to affect the cloud droplet number and cloud radiative properties, while also allowing clouds to alter aerosol size and composition through aqueous processes and wet scavenging (Gustafson et al., 2007). Note that we explicitly resolved the updrafts using a cloud-resolving spatial resolution in the inner domain (d03).

In MOSAIC, aerosol emissions are independently calculated within its own module in which the dust emission is calculated using the original GOCART dust scheme (Ginoux et al., 2001) as described by Zhao et al. (2010), which is called by setting dust_opt = 13. Note that this option was not implemented in the version of WRF-Chem used herein (3.8.1), but we ported this change into our setup (within the subroutine module_mosaic_addemiss.F). We also accounted for gravitational settling of aerosols in this work similar to Ukhov et al. (2021), which has not been implemented for the MOSAIC scheme in WRF-Chem.

To represent dust sources, we used the topographic source function developed by Ginoux et al. (2001), which is calibrated to match the simulated AOD with observed AOD as in Parajuli et al. (2020). To accurately simulate the effect of dust on cloud formation and rainfall, it is important to ensure that the simulated AOD is consistent with the observations. The AOD is highly sensitive to the size distribution of the dust particles (Ukhov et al., 2021). Therefore, we iteratively adjusted the emission size distribution to match the volume size distribution of aerosols obtained from AERONET as described by Ukhov et al. (2020). There are two places in which the dust size distributions can be adjusted within WRF-Chem. First is the size distribution of the “emitted dust” prescribed in five bins within the GOCART dust scheme, which is specified in phys/module_data_ gocart_dust.F. The second is the dust size fractions used by the MOSAIC aerosol scheme (eight bins) specified in chem/module_mosaic_addemiss.F. Both of these size fractions were modified to obtain a closer fit to the AERONET volume size distributions. The modified and the default size fractions are presented in Tables S1 and S2 in the Supplement.

Designing an appropriate experiment to determine the effect of dust in a model is challenging. For example, one can consider a “baseline” simulation with “clear” conditions without any aerosols and then add dust to see how it affects the rainfall. However, clear conditions are hardly ever observed, and thus it is unrealistic to design an experiment with zero rainfall. Therefore, we first considered a real-world scenario as a baseline by including all aerosols (dust, sea salt, sulfate, organic, and black carbon) similar to Klingmüller et al. (2019) (Table 2, F1). This baseline experiment (all_aer) is calibrated against MODIS/AERONET AOD data by changing the dust emission fractions and dust size fractions as mentioned previously in Sect. 2.3.1. The results of this baseline simulation were compared against observations, which exhibited a realistic aerosol distribution in terms of optical depth, PSD, and vertical profiles, as well as the rainfall pattern (see Sect. 3.2.1). The second experiment is the “no_dust” experiment (Table 2, F2) in which we assigned “zero” values to the source function in the dust emission equation (Parajuli et al., 2019), thereby effectively eliminating dust emissions from all grid cells in all three domains. Both of the aforementioned experiments include aerosol–radiation, aerosol–cloud, and microphysical interactions, and therefore they represent the total effect (both direct and indirect) of aerosols. From a practical perspective, the all_aer experiment represents a real-world scenario in which all aerosols including dust are included to obtain a realistic rainfall pattern, whereas the no_dust experiment represents rainfall in an idealized, dust-free world. We also conducted two additional experiments (F3 and F4) to separate the aerosol direct effects from indirect effects. In these two simulations, we restricted aerosol–radiation interactions (aer_rad_feedback = 0), in both all_aer (F3) and no_dust (F4) cases, while keeping all the model physics and domain settings the same as in the previous two experiments. Therefore, these latter two experiments essentially represent the indirect effects only.

The total effect (Δtot), indirect effect (Δindir), and direct effect (Δdir) of dust were then calculated with the following equations. 1Δtot=F1-F22Δindir=F3-F43Δdir=Δtot-Δindir=(F1-F2)-(F3-F4)

The physical processes through which dust affects breezes are difficult to understand when both direct and indirect effects are active. Additionally, the indirect effects are more complex, and their representation in the model is accompanied by a high degree of uncertainty. For these reasons, we additionally analyzed the direct effects of dust alone from an independent pair of simulations involving the dust direct effects only (F5, F6, Table 2) (i.e., without considering the indirect effects (chem_opt = 8)).

The dust direct effect is caused by both scattering and absorption of radiation in the SW bands. Therefore, to further understand the relative importance of shortwave cooling and warming resulting from direct effects, we conducted an additional pair of simulations (F7, F8, Table 2), in which we restricted the shortwave absorption of radiation by dust in the previous experiments F5 and F6. To achieve this, we changed the imaginary part of the refractive index for dust from the default value of 0.003 to 0.

The aforementioned effects were calculated for the domain-average daily-accumulated rainfall over the study period of 4–31 August for each year between 2006–2015 as the difference of rainfall amounts between the experiments all_aer (x) and no_dust (y). The statistical significance of the effect was determined from the entire 10 years of simulations by creating a uniform sample of domain-average daily-accumulated rainfall data consisting of 280 (10×28 d) data points. Statistical analyses were then conducted by separating the data into two categories: extreme and normal rainfall events. This separation is meaningful because extreme rainfall events are more influenced by synoptic features whereas normal rainfall events are more influenced by diurnal-scale sea breeze circulation. High- and low-rainfall regimes are also known to respond differently to a given aerosol loading (Li et al., 2011; Choobari, 2018). Extreme rainfall events were separated from normal rainfall events using the 90th percentile value of the rainfall data from F1 experiment, which was 1.33 mm. Specifically, days with domain-average daily-accumulated rainfall values greater than or equal to 1.33 mm were considered extreme rainfall events, whereas those with values below 1.33 mm were considered normal rainfall events. With this criterion, the effective numbers of samples (days) available for statistical analysis were 31 and 243 for extreme and normal rainfall events, respectively. Using MATLAB, the statistical significance of the effects was determined with the Wilcoxon signed-rank test (Hollander and Wolfe, 1999; Gibbons and Chakraborti, 2011), which is recommended for data with non-normal distributions such as rainfall. The null hypothesis of the test considered that the difference (all_aer (x) - no_dust (y)) comes from a distribution with zero median. The same method was applied to identify significant effects among other parameters including 2 m air temperature, 10 m winds, and 2 m water vapor mixing ratio.

Figure 13a, b, c show the dust effects on 2 m air temperature. Dust induces a total cooling effect over the lands (Fig. 13a), which appear to be dominated by the direct effects (Fig. 13c) rather than the indirect effects (Fig. 13b). Dust also induces warming in some inland areas and over the ocean, which is affected by both the indirect and direct effects (Fig. 13b and c). The total and direct effects were largely statistically significant (black dots), but the indirect effects were significant only over the lands.

In turn, the cooling and warming of the land surface affects the winds. Figure 13d, e, f show the effects of dust on surface winds. As with surface temperature, the direct effects had a stronger influence compared to the indirect effects on winds as well. The direct effects on winds were statistically significant along the coast, which confirms the impact of dust's direct effects on sea breezes.

A high positive moisture anomaly was observed over the land (Fig. 13g, h, i), particularly with the direct effect (Fig. 13i). The moisture increase over the land caused by the direct effect is further amplified by the weaker indirect effect, making the total effect more widespread. The increased moisture due to the direct and total effect was statistically significant for both. The reason for the positive moisture anomaly over the land in relation to sea breeze is explained in the section below.

Table 3 summarizes the effects of dust on rainfall for extreme and normal rainfall events calculated in terms of a 10-year average daily-accumulated rainfall over the study domain (d03) during the month of August. For the extreme rainfall events, the total effect (0.140 mm), indirect effect (0.105 mm), and direct effect (0.035 mm) were all positive (enhancement). The total, indirect, and direct effects in terms of percentage of average rainfall are 6.05 %, 4.54 %, and 1.51 %, respectively. The total and indirect effects are significant at the assumed 5 % significance level but not the direct effect. The direct effect, although small and statistically insignificant, contributed to the larger indirect effect, making the total effect statistically significant.

For the normal-rainfall events, the change in rainfall amount due to total, indirect, and direct effects is -0.003, 0.014, and -0.017 mm, respectively. The rainfall changes from both the indirect effect (positive) and the direct effect (negative) were statistically significant at the assumed 5 % significance level. The total, indirect, and direct effects in terms of percentage of average rainfall were -1.02 %, 4.76 %, and -5.78 %, respectively. The indirect and direct effects, which are opposite in sign and nearly equal in magnitude, cancel each other out, making the total effect small and statistically insignificant. However, note that the total effect could be considered significant if the significance level was increased to 10 % (p=0.083).

Although the domain-average rainfall change caused by dust averaged over multiple years (2006–2015) appeared small, the effect can be large at different locations and times. For example, for the year 2015, the accumulated rainfall changes (total effect) for August at the grid point maxima and minima within the domain were 92.0 mm (190.0 %) and -70.0 mm (-46.6 %), respectively.

The total, indirect, and direct effects were also calculated for the total number of wet days (average daily-accumulated rainfall ≥1 mm). The number of wet days increased by 3 due to the indirect effects but decreased by 4 by the direct effects, resulting in a total net increase of 1 d.

Table 3 summarizes the dust direct effect (Δdir) calculated using the standard method mentioned in Sect. 2.3.2 (i.e., by subtracting the indirect effect (Δindir) from the total effect (Δtot)). To verify the validity of this method, we compared the results obtained from this method with the direct effect calculated from direct-effects-only experiments (F5, F6, Table 2) for August 2015. The direct-effects-only experiments allow us to more directly calculate effects of dust on rainfall induced by land surface cooling or warming using the same model but with simpler settings without the indirect effects. The dust direct effect calculated from these direct-effects-only simulations (-0.046 mm) agreed very well with the results obtained from the standard method (-0.045 mm). The consistency of these two results confirms the robustness of our results.

The results of the direct-effects-only simulations (F5, F6, Table 2) are presented in Fig. 14 (left two columns). The cooling effect was dominant in the coastal areas, whereas warming was also observed in some inland areas, particularly in the southern region (Fig. 14b). Figure 14d demonstrates that the breezes are weakening and even reversing from land to sea in the areas of cooling (∼ 22∘ N) due to the dust direct effects. However, in the areas that exhibited warming (∼ 18.5∘ N), sea breezes strengthened as the land warming further increased the land–sea thermal contrast.

A strong positive moisture anomaly was observed over the land in the direct-effects-only simulations (Fig. 14f, left two columns). This is intriguing because we expected a reduction in moisture transport over the land due to the dust direct effects as a result of land surface cooling and a subsequent weakening of the sea breezes (Mostamandi et al., 2022). Figure 14 also shows the results of the additional experiments in which the SW absorption was restricted (F7, F8), as mentioned in Sect. 2.3.2. Given that the SW absorption was eliminated, this experiment allows us to better understand the effect of dust on sea breezes via the cooling effect alone (i.e., without warming effects). However, note that the effect of dust is complex as it warms the atmosphere and cools the surface (Choobari et al., 2014). Nevertheless, this elimination of SW absorption removed the dust-induced warming observed earlier over the land (compare Fig. 14b left and right panels). Since the cooling effect becomes dominant, sea breezes are now weaker, and therefore the landward moisture transport is considerably reduced, which is evident by comparing the left and right panels of Fig. 15f. These results confirm that the high positive moisture anomaly over the land by dust direct effects is caused by the strengthening of sea breezes as a result of dust-induced warming. Although it is generally understood that SW absorption decreases the radiation reaching the surface and thus cools the surface (e.g., Choobari et al., 2014), we observed surface warming because most of the atmospheric dust here lies very close to the surface (Parajuli et al., 2020), which is evident in Fig. 3b. The observed effects on breezes are broadly consistent with those of Mostamandi et al. (2022), who also observed a weakening of albedo-induced land cooling on sea breezes associated with the strong land cooling, which reduces the thermal contrast between the land and the ocean.