The GRAPES is a fully compressible, non-hydrostatic numerical weather model that employs a semi-implicit, semi-Lagrangian discretisation scheme (Chen et al., 2008; Xu et al., 2008; Zhang and Shen, 2008; Wang et al., 2022). Its physical parameterisation packages include cumulus convection, single-moment cloud microphysics, radiation, land surface processes, and boundary layer processes. CUACE is a regional chemical weather forecasting system developed by Gong and Zhang (2008), coupled online with GRAPES (Wang et al., 2010). It is capable of simulating seven aerosol species of sulfate, nitrate, ammonium, black carbon, organic carbon, sea salt, and dust (Zhou et al., 2008, 2012; Wang et al., 2015). The sectional dust emission scheme is by Marticorena and Bergametti (1995) and Alfaro and Gomes (2001), which has been improved by surface dust flux observations and desertification in East Asia (Gong et al., 2003), and a new desertification map and soil texture samples from Chinese deserts (Zhou et al., 2019, 2024). The aerosol size spectra have been divided into 12 size bins with a radius range of 0.005–0.01, 0.01–0.02, 0.02–0.04, 0.04–0.08, 0.08–0.16, 0.16–0.32, 0.32–0.64, 0.64–1.28, 1.28–2.56, 2.56–5.12, 5.12–10.24, and 10.24–20.48 µm. GRAPES/CUACE has a horizontal resolution of 0.15° and 31 vertical levels extending to approximately 28.6 km.

In this study, we select the WDM6 microphysics scheme in GRAPES to simulate precipitation (Hong et al., 2004; Zhang et al., 2022). The WDM6 scheme simulates the mass mixing ratio of water vapour (Qv), as well as the mass and number concentrations of cloud water (Qc) and rainwater (Qr) in warm clouds. For icy clouds, it includes the mass mixing ratios of cloud ice (Qi), snow (Qs), and graupel (Qg). A double-moment cloud ice scheme by Park and Lim (2023) is incorporated into the WDM6 scheme, enabling explicit prediction of cloud ice number concentration. A sectional CCN-activated scheme has been introduced in WDM6 in GRAPES/CUACE, connecting the multi-component, multi-section aerosols from CUACE to the WDM6 microphysics and the sub-grid convective parameterisation scheme via newly activated CCN at each time step (Zhou et al., 2016).

In the original WDM6 scheme, when the temperature is below 0 °C, the increase in cloud ice mass concentration arises from two processes: heterogeneous nucleation (Pigen) and deposition–sublimation of cloud ice (Pidep, when positive). Both consume water vapour to form ice clouds. The abbreviations for the remaining cloud microphysical processes are listed in Table 2. The IN concentration, Nice (m⁻³), is calculated by a classical ice nuclei nucleation scheme, which is an empirical function of temperature and does not account for the influence of atmospheric aerosols (Hong et al., 2004): 1Nice=103e0.1(T0-Tk) Where, Tk is atmospheric temperature, T0 is the freezing point (273.15 K).

This study implements an online aerosol-IN nucleation scheme in GRAPES/CUACE that accounts for heterogeneous ice nucleation processes influenced by atmospheric aerosols. Heterogeneous nucleation mechanisms are generally classified into immersion freezing, condensation freezing, deposition nucleation, and contact freezing (Hiranuma et al., 2015; Ilotoviz et al., 2016; Lee et al., 2017). Among these mechanisms, immersion freezing, condensation freezing, and deposition nucleation are selected, as they are relatively well developed. This selection is based on the fact that dust aerosols primarily affect ice nucleation at temperatures below 258.15 K through these three mechanisms (Cantrell et al., 2013; Patnaude et al., 2025), whereas the efficiency of contact freezing by dust particles is relatively low (Niehaus et al., 2014).

Immersion freezing is a heterogeneous ice nucleation process with the existence of liquid drops at temperatures between 233.15 and 273.15 K, in which an ice nucleus is immersed in a supercooled droplet, thereby triggering freezing into an ice crystal (Boose et al., 2016). Immersion freezing consumes water vapour to form cloud ice. The initial size of the ice crystal is influenced by the size of the liquid droplet (Fan et al., 2014; Gibbons et al., 2018), therefore the cloud ice formation through this mechanism is relatively easier compared to other nucleation mechanisms. The selected DeMott et al. (2015),immersion-freezing nucleation scheme here is developed by DeMott et al. (2015) and is based on continuous-flow diffusion-chamber measurements. The number concentration of ice nuclei, Nicenui (m⁻³), activated via immersion freezing is given by: 2Nicenui=3⋅naer,0.51.25⋅e(0.46⋅273.16-Tk-11.6) Where, naer,0.51.25 is the number concentration of insoluble aerosol particles with diameters exceeding 0.5 µm, such as dust, black carbon and part of organic carbon.

Deposition and condensation freezing are both heterogeneous ice nucleation processes that occur at temperatures between 248.15 and 258.15 K (Chen et al., 2019). In condensation freezing, water vapour first condenses on the surface of IN and subsequently freezes to form an ice crystal, while in deposition nucleation, water vapour directly deposits onto the IN surface (Kanji et al., 2017). The ice formation through these two pathways is generally harder than that through immersion freezing (DeMott et al., 2015). The parameterisation used here follows the formulation of Chen et al. (2019). In Jiang et al. (2016), the ice-nucleating ability of dust aerosols was derived from measurements conducted at several sites in China (Yang et al., 2013; Jiang et al., 2015, 2016), using a static vacuum vapour diffusion chamber based on the FRIDGE (Frankfurt Ice Nuclei Deposition Freezing Experiment) design. Chen et al. (2019) further refined the parameterisation to explicitly represent deposition and condensation freezing processes within a specified temperature range. The number concentration of ice nuclei produced by deposition and condensation freezing, Nicenud (m⁻³), is calculated as follows: 3Nicenud=5.7×10-7naer,0.50.018273.16-Tk-0.007Si+0.342⋅(273.16-Tk)3.745⋅Si1.31 Where, Si is supersaturation with respect to ice.

WDM6 uses the formula ρqI0 (kg m⁻³) =4.92×10-11 Nice1.33 and Pigen (kg kg⁻¹ s⁻¹) =(qI0-qI)Δt to calculate newly nucleation of ice. Where, ρ denotes the newly-formed air density, and qI0 is the predicted ice mixing ratio (kg kg⁻¹). Δt is the integration time step. Production rate for heterogeneous nucleation is calculated as the difference between qI0 and the current ice mixing ratio (qI). However, it does not account for the influence of nucleated IN size or the specific characteristics of different heterogeneous ice nucleation mechanisms on ice crystal development.

Here, the mass production rate of cloud ice newly nucleated is calculated as follows: 4Pinud=4/3πρiρardf3Nicenud/ΔtPinui=4/3πρiρarif3Nicenui/Δt Where, Pinud (kg kg⁻¹ s⁻¹) is the mass production rate for deposition/condensation freezing, Pinui (kg kg⁻¹ s⁻¹) is for immersion freezing. Pinud depletes water vapour to form cloud ice, while Pinui depletes cloud water to form cloud ice. ρi is 500 kg m⁻³ (Park and Lim, 2023). rif represents the initial radius of cloud ice formed via immersion freezing, while rdf represents the initial radius of cloud ice formed through deposition and condensation freezing, respectively. Δt is the integration time step. In the new online scheme, the production rate for nucleated IN number concentration (Nigen) is the sum of Nicenui and Nicenud.

The typical range of ice crystal radius in East Asia is about 10–100 µm (Chen et al., 2021), droplet radius range is about 1–30 µm (Um et al., 2018; Yang et al., 2021). Considering ice crystals generally grow from smaller particles and the radius of initial ice crystal size are often smaller than observed values, and with reference to the bin sizes of aerosol particles in CUACE (Um et al., 2018; Chen et al., 2021; Yang et al., 2021), this study assumes the characteristic radius of ice crystals of rdf and rif to be: 5rdf=10µm(raer<10µm)rdf=30µm(raer>10µm)rif=30µm(raer<10µm)rif=50µm(raer>10µm)

Then, the original production rate for nucleation of ice from vapour Pigen in WDM6 is replaced by the Pinud and Pinui described above.

The typical dust-affected precipitation event

The typical dust-affected precipitation event spans from 00:00 UTC on 9 April to 00:00 UTC on 15 April 2018 and includes two dust storm events in East Asia. One is from 9 to 11 April, originating in Mongolia and affecting northern China. Numerous dust storm phenomena are observed in Mongolia, while blowing and floating dust phenomena are reported in central and western Inner Mongolia, central Gansu, Ningxia, northern Shaanxi, most parts of Shanxi, southern Hebei, northern Henan, and western Shandong in China (see Fig. S1 in the Supplement for locations). Another event is from 13 to 14 April. It also gains with widespread dust storms in Mongolia and central Inner Mongolia, and with blowing or floating dust observed in central Inner Mongolia, northern Shanxi, Beijing, Tianjin, and northern Hebei in China. Between the two dust storm events, the precipitation occurred from west to east, covering most of northern China extending to the Yangtze River area, from 00:00 UTC on 12 April to 00:00 UTC on 15 April, concentrated in Shaanxi, Henan, southern Hebei, and along the Yangtze River in Sichuan, Hubei, Anhui, and the Jiangsu-Zhejiang-Shanghai area.

Figure 1a presents the dust-affected areas by dust phenomenon from Meteorological stations and PM₁₀ from the National Environmental Monitoring Network of the Ministry of Environmental Protection. Based on the distribution of dust in this event, the domain bounded by 90–135° E and 20–54° N is defined as the major dust-affected area (DA, region 1 in Fig. 1). Together with the real precipitation distribution (Fig. 5a), the domain bounded by 103–130.5° E and 27.5–50° N is defined as the dust-affected precipitation (DP) area (DPA, region 2 in Fig. 1). The whole model domain covers 70–145° E and 15–64.5° N, containing the DA and DPA. To investigate the impact of dust on precipitation in regions distant from the dust source in Sect. 3.3, we calculate horizontal hydrometeor fluxes across 116° E (33–50° N) and 33° N (103–116° E) during 12:00 UTC on 12 April to 18:00 UTC on 13 April (Fig. 6). The area bounded by 103–116° E and 33–50° N is defined as the near-dust-source area (NDSA, region 3 in Fig. 1).

GRAPES/CUACE successfully reproduces both the spatial distribution and intensity of the dust events (Fig. 1b). Considering that many radar observations and model studies have indicated that dust mainly participates in heterogeneous ice nucleation as ice nuclei within the mid-tropospheric layer (-20–0°) (Haarig et al., 2019; He et al., 2021, 2023), which corresponds to altitudes between 4 and 7 km in the present case, Fig. 1c shows the simulated dust concentration within this layer.

The initial and boundary meteorological conditions for GRAPES/CUACE are obtained from the NCEP/NCAR Final Operational Global Analysis (FNL) data, with a temporal resolution of 6 hours and a spatial resolution of 0.25°. Dust observations are obtained from two sources: weather phenomena from the CMA surface meteorological observation network with a 3-hour temporal resolution, and PM₁₀ and PM_2.5 concentration data from the national environmental monitoring network of the Ministry of Ecology and Environment of China with a 1-hour temporal resolution. 6-hour rainfall data are also from the CMA surface meteorological observation network. As there are more than 2000 precipitation stations in DA, only 63 level-1 and level-2 stations are selected for evaluation, of which 43 are in DPA to avoid overfitting in the model outputs. Due to the complex sources of PM₁₀ and considering the relatively long atmospheric residence time of dust, we select precipitation stations where the PM2.5/PM10 ratio is less than 0.6 within 24 h prior to the precipitation event as representative of dust-influenced precipitation (DP) stations (Wang and Yan, 2007; Filonchyk et al., 2019).

Model performance is evaluated using mean absolute error (MAE), root mean square error (RMSE), and symmetric mean absolute percentage error (sMAPE) (Harmoko et al., 2025): 6MAE=∑i=1nrmi-roinRMSE=∑i=1n(rmi-roi)2nsMAPE=1n∑i=1nrmi-roirmi+roiaMAPE=rmi-roirmi+roi where rmi represents the simulated cumulative precipitation at station i, and roi denotes the observed precipitation. For MAE, RMSE and sMAPE, values closer to 0 indicate better simulation performance. The aMAPE is used to evaluate whether the simulated precipitation is overestimated or underestimated relative to observations. When aMAPE > 0, the precipitation is overestimated; when aMAPE < 0, the precipitation is underestimated.

The horizontal hydrometeor fluxes shown in Sect. 3.3 are calculated using a grid-based mass transport formulation. For each model layer, the flux is computed as 7F=ρairqxVnΔzΔs where F is the hydrometeor flux (kg s⁻¹), ρair is the air density (kg m⁻³), qx is the mass mixing ratio of the hydrometeor species (kg kg⁻¹), Vn is the wind component normal to the cross section (m s⁻¹). Specifically, for the north–south cross section along 116° E (33–50° N), Vn is taken as the zonal wind component; for the west–east cross section along 33° N (103–116° E), Vn is taken as the meridional wind component. Δz is the layer thickness (m), and Δs is the horizontal grid spacing along the cross section (m).

During the DP event, the implemented online aerosol–IN nucleation scheme enables dust aerosols to modify the nucleated IN number concentration. Figure 2a and b show the horizontal distribution of the maximum nucleated IN number concentration between 4 and 7 km above ground level at DP stations during the time period from 00:00 UTC on 11 April to 00:00 UTC on 15 April 2018 for T_CTL and T_IN, respectively. Figure 2c presents the vertical distribution of DP-event-averaged production rate for Nigen for T_CTL (red line) and T_IN (blue line). Figure 2d presents the vertical distribution of cloud ice mass production rate for heterogeneous ice nucleation for T_CTL and T_IN. Based on the variation characteristics, the vertical layer is divided into three parts: layer A, above 7 km (temperature below -18 °C); layer B, between 4 and 7 km (temperature approximately -18 to -1.5 °C); and layer C, below 4 km (temperature approximately -1.5 to 18 °C).

The online aerosol-IN nucleation scheme can correct the systematic underestimation of IN concentrations. The maximum nucleated IN number concentrations in T_CTL can reach 10² L⁻¹ in layer B during the DP event (Fig. 2a), showing a relatively uniform horizontal pattern, which is much lower than observed IN concentrations (10²–10⁴ L⁻¹) during East Asian dust events (Bi et al., 2019; Tobo et al., 2019; Chen et al., 2021; Hu et al., 2023). For example, Chen et al. (2021) measured immersion-mode INPs at Peking University Atmosphere Environment Monitoring Station during spring 2018–2019 and found that dust periods increased INP concentrations by approximately two orders of magnitude, reaching 10² L⁻¹ between -15 and -28°. The DP-event-averaged production rate for nucleated IN number concentration ranges 0.005–0.01 L⁻¹ s⁻¹ in layer B (Fig. 2c). In T_CTL, the production rate for nucleated IN number concentration increases with height (Fig. 2c), primarily due to the temperature-dependent nature of the original WDM6 scheme. As a result, cloud ice mass production rate due to heterogeneous ice nucleation peak near the -40 °C level (Fig. 2d). Above this layer, IN concentration continues to increase, but production rate of heterogeneously nucleated cloud ice begins to decline due to limited water vapour (Fig. 2d). In the real atmosphere, the number concentration of effective ice-nucleating particles often reaches a maximum in the mid-troposphere rather than at the highest altitudes (He et al., 2023), suggesting that the continuous increase of IN at higher altitudes in T_CTL may inconsistent with typical observed.

In T_IN, the maximum nucleated IN number concentrations can reach 104 L⁻¹ in layer B during the DP event (Fig. 2b), closer to those observed or simulated in other East Asian dust events (Bi et al., 2019; Tobo et al., 2019; Chen et al., 2021; Hu et al., 2023). The DP-event-averaged production rate for nucleated IN number concentration ranges from 0.2 to 3.7 L⁻¹ s⁻¹ in layer B (Fig. 2c), and the cloud ice mass production rate for heterogeneous ice nucleation also peaks in this layer, which is consistent with radar observations and other modelling studies (Haarig et al., 2019; He et al., 2021, 2023). As immersion freezing is the dominant heterogeneous nucleation mechanism (DeMott et al., 2015; Hiranuma et al., 2015), this study compares the number concentration of ice-nucleating particles activated by immersion freezing with those activated by deposition and condensation freezing. The DP-event-averaged results indicate that the activated IN number concentration from immersion freezing exceeds that from deposition and condensation freezing by approximately 4–5 orders of magnitude.

During the DP event, the introduction of the online aerosol-IN nucleation scheme allows dust aerosols to alter the distribution of cloud hydrometeors. Figure 3 shows the DP-event-averaged vertical distributions of hydrometeors in T_CTL and T_IN, averaged over the dust–precipitation period (00:00 UTC 11 April–00:00 UTC 15 April 2018) and over dust–precipitation stations, as well as their difference (T_IN–T_CTL), by using budget analysis. Figure 4 shows the differences in production rates among hydrometeors (T_IN–T_CTL). To further examine the thermodynamic conditions responsible for the weakened production rate of cloud droplet activation from CCN in T_IN in Fig. 4, the vertical profiles of temperature and water vapour were analyzed, averaged over the dust–precipitation stations in DPA and NDSA during the period when the dust impact was most pronounced (18:00 UTC 11 April to 18:00 UTC 12 April) (Fig. 5).

The online aerosol–IN nucleation scheme can modulate the spatial distribution of precipitation. Figure 6a shows the observed event-accumulated precipitation of DPA stations, and Fig. 6b shows the simulated event-accumulated precipitation of T_CTL. In T_CTL, 18 of 43 stations in DPA exhibit overestimated simulation precipitation compared to observations (overestimated stations), primarily located in areas near dust sources area such as Gansu, Ningxia, Shaanxi, and Inner Mongolia, as well as northeastern provinces including Shandong, Liaoning, Jilin, and Heilongjiang (Fig. 6b). At these overestimated stations, the observed mean accumulated precipitation is 11.49 mm, while the simulated mean accumulated precipitation is 25.55 mm (Fig. 7), with an average sMAPE of 45 %. The other 25 stations show underestimated simulated precipitation compared to observations (underestimated stations), mainly distributed across Hebei, Beijing, Henan, and the Yangtze River Basin downwind area of the dust events (Fig. 6b). At underestimated stations, the observed mean accumulated precipitation is 31.58 mm (Fig. 7), while the simulated value is only 4.63 mm, with an average sMAPE of -64 %.

In T_IN, the online aerosol–IN nucleation scheme does not alter the overall pattern of overestimation of precipitation north of 35° N and underestimation of precipitation south of 35° N in T_CTL (Fig. 6d). However, compared to T_CTL, notable improvements are mainly observed between 34 and 40° N. This is driven by the process discussed in Sect. 3.2, in which dust in layer C suppresses Pcact, thereby reducing the overestimation of precipitation near dust source areas. sMAPE is reduced by about 1 %–10 % in areas near the dust source, resulting in more accurate forecasts compared to both T_CTL (Fig. 6e, f).

Rather than being removed by precipitation or evaporation, the suppressed cloud hydrometeors are transported downstream in T_IN. We calculate horizontal hydrometeor fluxes across 116° E, 33–50 and 33° N, 103–116° E from 12:00 UTC on 12 April to 18:00 UTC on 13 April (Fig. 7). Over the entire 0–12 km layer, the total hydrometeor flux slightly increases to about 102 % of that in T_CTL.

Within the temperature range from 0 to -40°, the total horizontal hydrometeor flux decreases by about 11 %, primarily due to a substantial reduction in cloud ice flux, accompanied by increases in snow and graupel fluxes. In Layer A, the total hydrometeor flux is about 4.4×10-5 kg s⁻¹, corresponding to about 75 % of T_CTL. Cloud ice flux drops sharply to about 8 % of T_CTL, while snow and graupel fluxes increase markedly to about 19.8 times and 7.8 times, respectively. In Layer B, the total hydrometeor flux is about 2.6×10-6 kg s⁻¹, corresponding to about 93 % of T_CTL, with cloud ice flux reduced to about 28 % of T_CTL, and snow and graupel fluxes increased to about 2.3 times and about 1.8 times, respectively. At temperatures above 0°, the total horizontal hydrometeor flux increases to about 106 % of T_CTL, with cloud water and rainwater fluxes increasing to about 115 % and about 108 %, respectively.

These results indicate that although dust suppresses cold-cloud development in the upper and mid-troposphere, it enhances the downstream transport of liquid-phase hydrometeors near and below the melting layer, enhancing downstream precipitation.

Finally, for underestimation stations, the mean accumulated precipitation increases by 1.1 mm compared to T_CTL, and precipitation simulation improves by approximately 4 %, with little changes in MAE and RMSE (Fig. 8b). For overestimated stations, the mean accumulated precipitation decreases by 4.5 mm compared to T_CTL, and precipitation simulations improves by approximately 40 %, with MAE reduced by 1.4 and RMSE reduced by 4.1 (Fig. 8a).

In summary, because the reduction in cloud water in the 0–4 km layer is relatively small, the corresponding decrease in rainwater reaching the surface is also limited. As a result, the online aerosol–IN nucleation scheme exerts only a weak influence on the total precipitation amount. Nevertheless, it can modulate the spatial and temporal distribution of precipitation, impressing overestimates and altering underestimates to some degree, which is consistent with the findings of Park and Lim (2023) and Su and Fung (2018b).