Where does the dust deposited over the Sierra Nevada snow come from?

. Mineral dust contributes up to one-half of surface aerosol loading in spring over the southwestern United States, posing an environmental challenge that threatens human health and the ecosystem. Using self-organizing map (SOM) analysis with dust deposition and ﬂux data from WRF-Chem and Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2), we identify four typical dust transport patterns across the Sierra Nevada, associated with the mesoscale winds, Sierra barrier jet (SBJ), North Paciﬁc High (NPH), and long-range cross-Paciﬁc westerlies, respectively. We ﬁnd that dust emitted from the Central Valley is persistently transported eastward, while dust from the Mojave Desert and Great Basin inﬂuences the Sierra Nevada during mesoscale transport occurring


Introduction
The emission, transport, and deposition of mineral dust (hereafter dust) are processes receiving increasing interest from the scientific community (Sarangi et al., 2020). Dust emission is an integral part of aridification and mirrors the effects of climatic change and anthropogenic land use on global drylands (Duniway et al., 2019). Airborne dust interacts with Earth's climate system by altering the radiation budget and cloud lifetime and amount (Forster et al., 2007;Haywood et al., 2005;Huang et al., 2019;Liu et al., 2022b). Research has indicated that exposure to dust particles can cause respiratory infections, heart disease, and chronic obstructive pulmonary disease (COPD) (Laden et al., 2006;Lim et al., 2012;Crooks et al., 2016). A significant asso-ciation between dust exposure and increased mortality has been reported, but there is no consensus in this regard to date (Giannadaki et al., 2014). The deposition of dust on snow surface influences snow albedo, further contributing to anthropogenic climate change as early as the 1970s (Qian et al., 2009(Qian et al., , 2014Skiles et al., 2018).
Dust over the southwestern United States, particularly in California and Nevada states, is an important aerosol type contributing to more than half of surface aerosol concentrations in spring (Kim et al., 2021). Covered by dry soil with large gaps and sparse vegetation, the surrounding Mojave Desert, Sonoran Desert, and Great Basin are susceptible to wind erosion (Okin et al., 2006;Duniway et al., 2019). The dry or ephemeral lakes in the deserts produce very fine dust containing toxic inorganic constituents (Goldstein et al., 2017). In addition, anthropogenic land-use practices, e.g., agriculture and human settlement, have greatly disturbed crustal biomass and produced windblown dust along the west coast (Pappagianis and Einstein, 1978;Clausnitzer and Singer, 2000;Neff et al., 2008). Furthermore, cross-Pacific dust transported from Asia and Africa to the Sierra Nevada range is widely reported (Ault et al., 2011;Creamean et al., 2014Creamean et al., , 2013. The surface dust concentration has been found to increase in the past 2 decades during spring at sites across the southwest (Tong et al., 2017;Hand et al., 2017;Brahney et al., 2013), and the onset of dust season is shifting earlier in response to climate change (Hand et al., 2016). The elevated dust emission and earlier dust season are supposed to lead to a spectrum of environmental and societal impacts in the most populated US state. In particular, the resultant dust deposition on mountain snow decreases snow albedo and produces a radiation forcing of 0-14.6 W m −2 during the melting season (Huang et al., 2022a), shifting snowmelt timing to earlier dates and further increasing California's vulnerability to water resource fluctuations (Wu et al., 2018;Huang et al., 2022b). With its complex terrains, frequently varying microclimate, and coexisting sources from both local and remote regions, the Sierra Nevada area is an interesting region for studying dust transport and its response to climate change.
Characterization of dust emission, transport, and deposition across the Sierra Nevada has been investigated using various data. Isotopic analyses (i.e., concentrations of Pb and Nd) are widely used to distinguish and quantify the respective contribution of dust emission from local (dried Owens Lake), regional (Central Valley and the Mojave Desert), and global sources (Asia and Africa) on the dust deposition on the mountain (Muhs et al., 2007;Jardine et al., 2021;Aciego et al., 2017;Aarons et al., 2019). Their source attribution has been generally confirmed by the analyses of dust particle size and composition (Creamean et al., 2014(Creamean et al., , 2013Reheis and Kihl, 1995). The isotopic and composition analyses have been commonly used with back-trajectory modeling to further identify the dust transport pathway from the source to the deposition location (Vicars and Sickman, 2011;Creamean et al., 2014Creamean et al., , 2013). Yet, these analyses generally retrieve dust sources in a short time and at a specific location. Alternatively, ground-based measurement networks were established in the 1990s and provide long-term trends of dust concentrations and the interannual variability across multiple sites (Hand et al., 2017;Achakulwisut et al., 2017;Hand et al., 2016). However, they do not contain information on dust origins and atmospheric conditions responsible for dust transport. Satellite retrievals were less commonly used to study dust characteristics across the Sierra Nevada (Lei and Wang, 2014), mainly due to the poor data coverage caused by cloud contamination in the region. Global and regional climate-chemistry models have been widely used to understand the drivers of the variability of dust and quantify the role of regional and remote transport, filling the gaps in the observations (Chin et al., 2002(Chin et al., , 2007Kim et al., 2021;Wu et al., 2017). While dust emissions and transport have been generally studied, a connection between dust emissions from the source region and the timing, location, and amount of dust deposition to the Sierra Nevada snow is lacking. The isotopic and composition analyses attribute dust sources at a few sites. But to the best of our knowledge, no regional characterization has been conducted on how dust is transported to the Sierra Nevada after emissions from adjacent drylands and remote continents and when, where, and how many depositions occur for dust transported through different pathways. The connection between dust emissions, transport pathways, and deposition to snow would facilitate the prediction of future changes in dust regimes and the corresponding climate impact, enabling more efficient management practices. With a focus on the dust that influences the Sierra Nevada, this study investigates the following questions. (1) Where does the dust come from? (2) How is dust transported to the mountain from the sources? (3) How is the dust deposited on the Sierra Nevada during spring, when the dust in snow largely influences snow albedo and snowmelt? We integrate models and observations to understand how the dust deposition is linked to a specific source both surrounding and far from the Sierra Nevada.

WRF-Chem configuration
We used the WRF-Chem version 3.9 to study dust emission and transport across the Sierra Nevada. The model setups (Table 1), including the physical schemes and emission inventory, follow Huang et al. (2022a), which showed that the model captures the distribution and variation in aerosols reasonably well in the study domain (126.12-112.86 • W, 32.3-43.0 • N). The Model of Ozone and Related chemical Tracers (MOZART) chemistry module (Emmons et al., 2020) and the Model for Simulating Aerosol Interactions and Chemistry with four bins (MOSAIC 4-bin) aerosol model (Zaveri and Peters, 1999) were applied, and dust emissions were calculated online using the GOCART dust scheme (Ginoux et al., 2001). The meteorological initial and lateral boundary conditions (IC and LBCs) were derived from the ECMWF Reanalysis v5 (ERA5) at 0.25 • horizontal resolution and 6 h temporal intervals (Hersbach et al., 2020). Spectral nudging was employed with a timescale of 6 h above the PBL to reduce the drift between ERA5 reanalysis data and WRF's internal tendencies (Von Storch et al., 2000). The chemical initial and boundary conditions were provided by CAM-Chem . We applied the model to two nested domains (Fig. 1). Domain 1 (126.12-112.86 • W, 32.3-43.0 • N) was configured to cover all of California, Nevada, and part of the surrounding states with 110 × 120 grid cells at 10 km × 10 km horizontal resolution; the nested domain 2 covered the Sierra  Nevada and surrounding regions with a 2 km × 2 km resolution. The cumulus scheme is turned off in domain 2 with convection-permitting resolution. We used 35 vertical model layers from the surface to 10 hPa with denser layers at lower altitudes to resolve the PBL. The simulation period ranged from 20 September 2018 to 31 August 2019, while we only used output from February to June in consideration of both dust emission season and mountain snow existence (Hand et al., 2016;Kim et al., 2021;Achakulwisut et al., 2017).
ERA5 provides assimilated wind fields at a 0.25 • × 0.25 • horizontal resolution at 137 hybrid sigma/pressure levels from 1979 to near-real time (Hersbach et al., 2020). This study obtained the 3-hourly meridional and zonal wind field from February to June 2019 from 1000 to 500 hPa. The ERA5 wind reanalyses were used with satellite-retrieved dust optical depth (DOD) to evaluate the classified dust emission and transport patterns from the model.

Satellite observations for validation
The Infrared Atmospheric Sounding Interferometer (IASI) on board the European Meteorological Operation (MetOp) satellite series measures infrared radiation in 8461 spectral channels between 3.63 and 15.5 µm. The instrument has provided near-global coverage with a spatial resolution of 12 km at nadir (Hilton et al., 2012) since 2007. IASI is primarily sensitive to coarse-mode dust particles, and thus the retrieved AOD at the wavelength of 10 µm can represent the DOD (Yu et al., 2019). Note that the thermal infrared (IR) AOD reported by IASI is usually significantly smaller than the visible AOD in MODIS because of the spectral dependence of dust extinction (Zheng et al., 2022). We use the version 2.2 AOD product developed at the Centre National de la Recherche Scientifique Laboratoire de Météorologie Dynamique from https://iasi.aeris-data.fr/dust-aod/ (last access: February 2022) (Capelle et al., 2014). The 0.3 • × 0.3 • daily AOD data covering California were produced by aggregating day and night retrievals at the satellite pixel resolution (Capelle et al., 2018), in consideration of both data completeness and fine features. The 1.0 • × 1.0 • daily AOD was produced in a similar way to investigate dust transport from Asia across the North Pacific.
The MIDAS (ModIs Dust AeroSol) dataset provides global fine-resolution (0.1 • × 0.1 • ) daily DOD between 2003 and 2017 using quality-filtered AOD from MODIS Aqua and DOD-to-AOD ratios from MERRA-2 reanalyses (Gkikas et al., 2021). Despite the uncertainties in modeled DOD-to-AOD ratios, the validations of the MIDAS dataset against the AERONET dust-like AOD and the LIdar climatology of Vertical Aerosol Structure for space-based lidar simulation (LIVAS) DOD reveal a high level of agreement at both global and station level (Gkikas et al., 2022). Compared with other MODIS-derived DOD products (Song et al., 2021;Voss and Evan, 2020;Ginoux et al., 2012;Pu and Ginoux, 2018), MIDAS has finer spatial and temporal resolutions over both land and ocean, which is particularly applicable in this study focusing on a small region and a few cases at daily scale. The dataset has been extended to near-real time to match our study year.
Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) is a two-wavelength (532 and 1064 nm) polarization lidar on board the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite . Since June 2006, the lidar has been collecting an almost continuous record of high-resolution profiles of aerosol and clouds as fine as 30 m in the vertical, covering 82 • N to 82 • S (Winker et al., 2010;Winker et al., 2009). This study used clear-sky data from the CALIOP Version 4, level-2 aerosol profile product (Young et al., 2018), to investigate the vertical profile of the elevated dust layer, especially from remote transport. When there were large DOD values shown in IASI and MIDAS, we examined the vertical profiles of dust by identifying the "dust," "polluted dust," and "dusty marine" species in the CALIOP data (Kim et al., 2018)

SOM analysis
We applied self-organizing map (SOM) analysis, a clustering method developed in the field of artificial neural networks, to recognize different weather features associated with dust transport and deposition. SOMs have been widely used in atmospheric sciences to recognize spatially organized sets of patterns in the data (Reusch et al., 2007;Bao and Wallace, 2015;Liu et al., 2022a;Song et al., 2019). Before the machine-learning process, we assign a few two-dimensional arrays of initial nodes randomly or more efficiently from the leading empirical orthogonal functions (EOFs). During the training phase, the Euclidean distance between each input pattern and the initiation nodes is calculated to begin an iterative procedure. The best-matching node or the "winning" node is the one with the smallest distance between the initiation nodes and the input vector. Then the winning node and the neighborhood nodes around the winner are updated to adjust themselves toward the input vector. Since this process is iterated and fine-tuned, the nodes are self-organizing. The final SOM nodes represent typical dust transport and deposition patterns across the Sierra Nevada.
Here, we first used five variables from the WRF-Chem inner domain (D02) in the SOM clustering, including dust deposition flux at the Sierra Nevada, the low-level meridional and zonal dust transport fluxes, and the mid-level meridional and zonal dust transport fluxes surrounding the Sierra Nevada. The original fields were used without any filtering methods to consider the extreme cases. The 3-hourly model outputs during February-June 2019 are used to count for the spatial distribution and temporal evolution of dust transport and deposition. For WRF-Chem, we averaged the zonal and meridional dust fluxes in model levels 3-5 (roughly 900-950 hPa over coastal California and 650-700 hPa over the Sierra Nevada) to acquire the low-level transport features. We averaged 200-700 hPa fluxes to acquire the mid-level transport features. Levels 3-5 were selected to focus on airborne particulate matter entrained above the planetary boundary layer and transported on the regional scale. Remote transport of Asian and African dust is mostly found around 600-200 hPa, which flows downward to the lower troposphere along the post-cold isentropic surface into the atmospheric river (AR) environment (Voss et al., 2021). By selecting levels between 200-700 hPa, we were able to include all cross-Pacific remote transport in the middle level.
We tested the number of clusters (k) that ranges in 3, 4, 5, 6, 8, 9, and 16 to assess the distinctiveness and robustness of different k. For each k, the robustness of the clusters was measured by a classifiability index (CI) (Vigaud and Robertson, 2017;Vigaud et al., 2018;Hannachi, 2010) constructed using the minimum spatial correlation coefficient between the clusters obtained from the full data and many random halves of the data (100 halves used here) (Hannachi, 2010). Therefore, the CI measured the reproductivity of the k clusters partitioning (Visbeck et al., 2001), with perfect partitioning leading to 1. Figure S1 shows the CI as a function of the number of clusters using WRF-Chem output for 2019. With the highest CI, the four-cluster partitioning represents distinct dust transport and deposition patterns over the Sierra Nevada well and is used in this study.
To verify the recognized transport patterns based on WRF-Chem, we conducted SOM analyses using variables from MERRA-2. We first remapped the same five variables using bilinear interpolation from 0.5 • × 0.625 • to 10 km, the res-olution of the WRF-Chem outer domain, before clustering. The vertical levels of low-level and mid-level dust transport fluxes were selected to approximately match the WRF-Chem pressure level. Four nodes were identified and arranged to make a direct comparison with those from WRF-Chem. To further investigate if transport patterns recognized from SOM vary significantly with years, we applied SOM analyses over 2001-2021 using MERRA-2 extended records of dust fluxes and deposition.

Dust emission sources around the Sierra Nevada
We find four emission source regions surrounding the Sierra Nevada where dust emissions could potentially influence the mountain snow impurities between February and June (Fig. 2). The Mojave Desert, located southeast of the Sierra Nevada, is characterized by low annual precipitation, sparse vegetation, and dried fine soil. Airborne dust loading over the desert can reach 30 000 µ m −2 averaged over our study period (Fig. 2a). It is generally transported eastward but can also be transported westward, influencing the southern part of the mountain (Neff et al., 2008). Dust produced in the northern (Sacramento Valley) and the southern part (San Joaquin and Tulare basins) of the Central Valley is often transported eastward to the mountains. With high soil aridity and a higher fraction of dry sand (Duniway et al., 2019), the southern Central Valley is more erodible and emits a higher amount of fine dust. The Great Basin dust is relatively weak in magnitude but located at a higher altitude. Therefore, it can easily ride along wind currents upward along the east slope of the mountain. The column dust loading in MERRA-2 confirms our results in WRF-Chem (Fig. 2b), despite it showing a stronger dust emission in the Great Basin while a weaker one in the Sacramento Valley. The IASI shows the strongest IR DOD in the Mojave Desert, followed by the southern Central Valley, but smaller dust emissions from the Sacramento Valley as compared with model output (Fig. 2c). The smaller magnitude is largely due to the fact that IASI measures the radiation at IR wavelengths, which is more sensitive to coarse-mode dust particles (Yu et al., 2019), whereas the fine dust produced in the Central Valley has a negligible contribution to DOD at 10 µm. In contrast, MIDAS captures dust emissions from the Great Basin, the southern and northern Central Valley ( Fig. 2d) but not the Mojave Desert. MIDAS is reported to underestimate DOD from the Mojave Desert compared to AERONET DOD, which might be caused by the lower dust amounts simulated in MERRA-2 (Gkikas et al., 2021) and the underestimation of MODIS AOD over the deserts as compared to ground observations (Tao et al., 2017).

Dust transport across the Sierra Nevada
This section introduces the features of dust transport patterns discerned from WRF-Chem and evaluates them against satellite observations over the period of February to June 2019. Figure 3 shows the WRF-Chem dust concentration and wind in the low levels and middle levels averaged for each of the four types acquired from the SOM analyses. The dust transport pattern represented in SOM type 1 accounts for 35.8 % of hours from February to June (Fig. 3a), especially in February (43 %) and March (57 %) (Fig. 4a). Type 2 occurs in 24.2 % of the whole study period and contributes to more than 50 % in February and then decreases with the month. In contrast, types 3 and 4 account for 17.8 % and 22.3 %, respectively, with the occurrence increasing with the month. The maximum occurrence is found in June for type 3 (40 %) and April for type 4 (34 %), respectively.

Mesoscale regional (MSR) transport
In type 1, dust is transported from northwest to southeast in the Central Valley at the low level (roughly 875-925 hPa over the California coast). A vortex (Schultz eddy) was found in the northern Central Valley (Fig. 3a), circulating counterclockwise and confining dust to the local environment (Bao et al., 2008). The air inflow from the ocean is relatively weak and obstructed by the terrain. The Great Basin is dominated by the northwesterlies. The emitted dust is transported southeastward and blocked by the mountain, depositing dust on the east slope. Dust emitted from the Mojave Desert can be elevated to the middle level (Fig. 3b). The cross-section further shows a vertical circulation where the Mojave Desert dust is blown away from the Sierra Nevada at the low level and towards the mountain at 600-700 hPa (Fig. 5a). A weaker mid-level cross-Pacific flow is found in type 1 than in other types (Fig. 6a), with no signals of remote transport reaching the Sierra Nevada (Fig. 3b). Type 1 generally corresponds to the dust transport in lack of prevailing large-scale weather systems. The high peaks of the Sierra Nevada produce mesoscale circulations and prevent the Central Valley and Great Basin dust from being transported to the other side of the mountain. It is referred to as "mesoscale regional (MSR) transport" hereafter. We validate the features of type 1 from WRF-Chem using satellite-retrieved DOD and wind vectors from ERA5. The cloud contamination results in many missing satellite pixels in our study domain, making the transport patterns hard to discern on a single day. DOD and winds belonging to the same SOM type on consecutive days are averaged to maximize the data completeness. One typical example for each type is presented based on their representativeness and the maximum spatial coverage. Figure 7a-b present dust emission and transport patterns during 10-12 May, a typical case for MSR transport. In IASI, we find peak IR DOD (>0.2) over the Mojave Desert and the southern Central Val- ley and moderate values in the Sacramento Basin related to the Schultz eddy (Fig. 5a), resembling the relative magnitude of dust concentrations in regional source regions in WRF-Chem (Fig. 3a). MIDAS shows another evidence of dust transport pathways within the Central Valley with a higher resolution, although the maximum DOD shifts slightly towards the mountain range (Fig. 7b). Dust emissions from the Great Basin are weaker than those from the southern Central Valley.

Sierra-barrier-jet-related (SBJ-related) transport
In type 2, the low-level winds turn to the north above the western slope of the Sierra Nevada (Fig. 3c), which resembles the terrain-locked Sierra barrier jets (SBJs) typically observed during the presence of ARs (Neiman et al., 2013). The large-scale pattern consists of a low 500 hPa geopotential height (GPH) center in the North Pacific (Fig. 6b). The meridional gradient produces intense storm tracks from the Kuroshio Current towards Alaska (Rodionov et al., 2007). Indeed, we find extensive precipitation in type 2 (not shown), which produces more wet deposition along the mountain's windward (west-and south-facing) slopes and result in cleaner air in the Central Valley (Fig. 3c). The dust layer at the Central Valley is found below 700 hPa, mostly blocked by the high mountain peaks, and is hardly transported to the lee-side (east) slope of the mountain (Fig. 5b), despite the cross-barrier westerlies found in the middle level. Dominated by SBJs, dust generated in the Great Basin and the Mojave Desert is blown away from the mountain. No clear signal of remote transport is found on the California coast (Fig. 3d). The dust transport from all sources is closely connected to SBJ; therefore, type 2 is referred to as the "SBJ-related transport". In both IASI and MIDAS, we find more missing pixels for SBJ-related transport than any other type caused by cloud contamination (Fig. 7c-d). The AR-related landfalling pre-  cipitation from 25 February to 2 March removes the airborne dust particles. A cleaner atmosphere might be induced, but it is hard to confirm considering the missing pixels over the continent.

North Pacific High-related (NPH-related) transport
Type 3 has northwestern winds in both Central Valley and the Great Basin (Fig. 3e), transporting Central Valley dust to the southwest part of the Sierra Nevada in early summer. It is known as the "North Pacific High-related (NPH-related) transport", during which the North Pacific High (NPH) built up in the north Pacific 130 • W produces the northwestsoutheast wind direction along the California coast (Fig. 6c), influencing the transport patterns for dust emitted from the surrounding sources. At the middle level, we observe a meridional mid-level dust transport pathway (Fig. 3f), which appears at 400-500 hPa in the northern Sierra Nevada and descends to 700 hPa at 36-37 • N, the top of the southern Sierra Nevada (Fig. 5c). The MERRA-2 reanalysis DOD (Fig. 6c) further shows that dust originating from Asia is transported towards North America following the isobars and wind patterns (discussed further in Sect. 3.2.3). The dust emitted from the Great Basin is transported by the southward winds to the east slope of the mountains, while emissions from the Mojave Desert are transported away from the mountain range.
The simulated dust concentration and transport in the NPH-related transport are confirmed by DOD observations during 7-9 May, with the transport pathway parallel to the California coast (Fig. 7e-f). Studies have shown two main pathways of Asian dust transport to North America during the spring months: (1) meridional excursions north into Alaska and then south along the US west coast and (2) zonal transport over the North Pacific Ocean (Creamean et al., 2014). With north-south dust transport at the middle level, the NPH-related transport characterizes the first pathway. To examine this hypothesis, we averaged the IR DOD and 500 hPa wind field over the North Pacific during 2-9 May. We included a few days before the event (Fig. 8a) as it takes 7-10 d for dust to be transported from Asia to North America (Ault et al., 2011;Creamean et al., 2013). The dust transport pathway shows that after being emitted from East Asia and the Gobi Desert, dust is transported zonally to 150 • W, excursing north into Alaska/Canada and then traveling south along the US west coast. Similar conclusions can be drawn with more evident pathways using DOD from MERRA-2 reanalyses (Fig. 8e). An elevated dust belt from 8 to 12 km is discerned over the North American coast (27 to 60 • N) from the CALIOP data, denoting the north-south transport of a thin dust layer through the middle level (Fig. 8c).

Cross-Pacific zonal (CPZ) transport
Air inflows from the ocean enter California and diverge to the northern and southern branches in type 4, transporting dust eastward across the Sierra Nevada (Fig. 3g). At the middle level, the low-GPH center recedes in April, and the isobars become straighter than in boreal winter, which facilitates the zonal transport of dust emitted from middle Asia over the North Pacific Ocean (Fig. 6d). The cross-section further shows that an elevated dust layer is transported from the ocean at around 700-500 hPa (Fig. 5d). The concentrations are much stronger and the altitude also lower than the NPH-related transport (Fig. 5c). The remotely transported dust descends to low altitudes when reaching the California coast and converges with the dust from the Central Valley at around 800 hPa. A portion of dust is compacted to the windward slopes at higher elevations, and the remaining across the mountains affects the east slope. Dust emitted from the Great Basin and the Mojave Desert is transported away from the mountains. Type 4 is denoted "cross-Pacific zonal (CPZ) transport" to reflect the strong cross-Pacific dust transport.
The period of 5-9 April, a typical case for the CPZ transport, clearly shows the north and south branches of dust transport over the Central Valley (Fig. 7g-h). Different from the NPH-related transport pathway, the large-scale DOD and winds at 500 hPa (averaged over 1-9 April) show that dust emitted from East Asia is being transported eastward, with a belt of IR DOD >0.1 evident around 25-40 • N (Fig. 8b). The DOD from MERRA-2 confirms the zonal pathways of dust transport with a smaller magnitude (Fig. 8d). The vertical distribution shows an elevated dust layer at 2-4 km above ground level, reaching the higher elevation of the mountain (Fig. 8f).  We calculated the mid-level dust remote transport, defined as the dust influxes from the north and west boundaries of the 200-700 hPa of WRF-Chem modeling domain 1, and investigated how the top 10 % largest remote transport distribute in each SOM (Fig. 4b). Among all the large remote transport, CPZ transport accounts for 48 %, while NPH-related transport accounts for 32 %, indicating that the zonal pathway plays a more important role in the cross-Pacific transport. Most remote transport is found in April and May, the former dominated by the meridional transport in the exis-tence of the NPH, while the latter is led by the CPZ transport. The remaining two types contribute to a fairly small portion, consistent with the clean atmosphere in the middle levels (Fig. 3b, d).

Dust emissions and transport in back-trajectory analyses
We discern four types of dust transport patterns across the Sierra Nevada using the SOM clustering method. MSR trans- port represents the local dust transport, which contributes to more than 20 % of the time each month during February-June (Fig. 4a) in the absence of prevailing weather systems. The SBJ-related air inflows transport dust eastward and are closely related to the AR, during which the GPH and storm tracks at 500 hPa feature a typical large-scale pattern during the boreal winter (Rodionov et al., 2007). As time evolves, the GPH center recedes, and the isobars become more straight zonally in April, bringing dust from Asia and Africa to the western US coast (CPZ transport). In early summer, the buildup of NPH in the east Pacific corresponds to north-south winds along the California coast, transporting dust along the Sierra Nevada (NPH-related transport). We further conducted air mass back-trajectory (AMBT) simulations to evaluate the dust emission sources and transport pathways identified using SOM analyses. The backtrajectory simulation was conducted using the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model with meteorological forcings from the North American Mesoscale Forecast System. We selected typical days for the four SOM types as in Fig. 7 and three sites located at the central Sierra Nevada (38 • N, 120.3 • W), southern Sierra Nevada (36.5 • N, 119 • W), and eastern Sierra Nevada (37 • N, 117 • W), to represent dust deposition at different subregions.
The 12 h and 7 d AMBT results corroborate the identified local and long-range transport pathways for each type. The transport pathways generally follow the wind directions shown in Fig. 7. Multiple emission source regions are found in type 1, including the Central Valley where dust is transported eastward to the windward slopes and the Great Basin where dust is transported westward to the lee-side slopes (Fig. S2). In type 2, dust deposited in all three sites comes from the Central Valley (Fig. S2), and the transport corresponds to the direction of SBJ during the AR (Fig. 7c). Types 3 and 4 are affected by both local and remote transport. Locally, dust mainly comes from northern California and the Great Basin in type 3, while it comes from the Central Valley in type 4. Remotely, in type 3, we find dust emitted from Asia and North Africa excurses meridionally to Alaska at 135 • W and then travels southward along the US west coast (Fig. S3a). In contrast, dust emitted from East Asia is transported zonally across the Pacific, reaching the Sierra Nevada from the west (Fig. S3b).

Dust deposition over the Sierra Nevada
The averaged dust deposition and low-level dust transport for each type are shown in Fig. 9, including both dry and wet depositions. The dry depositions consider the diffusion and gravitational effects, while wet depositions describe incloud removal (rainout) and below-cloud removal (washout) by grid-resolved stratiform precipitation as well as the subgrid wet scavenging (Chapman et al., 2009;Easter et al., 2004). In all SOM types, extensive depositions are found on the west slope in all types, generally decreasing with elevation.
MSR transport has the smallest deposition among the four types (Fig. 9a). Large depositions are found in the southern Sierra Nevada and Lake Tahoe. Dust contributing to the deposition mainly originates from the Mojave Desert and the Great Basin dryland. In contrast, large depositions found in the southern and eastern parts of the mountains in NPHrelated transport may be produced in agricultural land from the southern Central Valley, as we find a persistent eastward transport pathway in the low level (Fig. 9c). The remote transported dust plays a minor role as it is located above 8 km in altitude.
While SBJ-related transport has the lowest low-level dust concentration over the Central Valley, it produces the largest deposition along the west slope (Fig. 9b). Most eastward transport in the southern Sierra Nevada is obstructed by the high mountain peaks, resulting in large depositions below 2900 m. The SBJ turns eastward in the Sacramento basin and climbs through the mountain north of 38 • N, producing a relatively homogenous deposition in the northern part. The combination of dust transport and deposition indicates that dust influencing the mountain snow impurities mostly comes from the Central Valley. Compared with the other SOM types, SBJ-related transport has large depositions at elevations higher than 2500 m (discuss later). Large depositions are also found in the CPZ transport (Fig. 9d), with the largest value occurring on the west slope of the central and southern Sierra Nevada, contributed by both Asian dust and Central Valley dust. Compared to MSR and NPH-related transport, the large-scale westerlies in the Central Valley (SBJ-related and cross-Pacific transport) produce larger deposition, probably because of the more efficient removal of particles by collision with terrestrial surfaces at higher elevations (Fig. 5d).
To quantify the relative importance of wet and dry depositions in each 3-hourly total deposition data, we calculate the fraction of wet depositions to total depositions averaged over the Sierra Nevada: wet deposition wet deposition+dry deposition . The contribution of dry deposition is defined in a similar way. We find that the wet deposition accounts for 40 % in frequency in the SBJ-related type. The landfalling precipitation has deposited large amounts of airborne dust on the snow surface, producing a cleaner atmosphere, as we have found in Fig. 3c. The frequent wet depositions also explain the larger depositions in high elevations (Fig. 9b): dust particles reaching the high mountains are small in size and difficult to deposit through gravitational effects. Wet deposition is a more efficient way of depositing small particles as they collect dust in raindrops. In contrast, dry depositions play predominant roles (more than 80 % in frequency) in all the other types (Fig. 10a). creases with deposition intensity. The averaged contribution of wet depositions in magnitude increases from 19 % in all events to 29 % in the top 10 percentile, 36 % in the top 5 percentile, and 56 % in the top 1 percentile largest events, supporting our conclusion that wet deposition is a more efficient way of dust deposition.

Features of the dust transport in MERRA-2
We repeated the SOM analyses using 2019 MERRA-2 data to examine the WRF-Chem model performance and interannual variability. We conducted additional SOM analyses using 2001-2021 climatology MERRA-2 data to investigate the interannual variability of the transport patterns. The low-level and mid-level dust transport features identified in  are similar to their corresponding types in WRF-Chem (Fig. 3), with types 1, 2, 3, and 4 representing MSR, SBJ-related, NPH-related, and CPZ transport, respectively (Fig. 11). Additionally, north-south transport occurs in the middle layer in type 3 and west-east transport in type 4, despite the slight difference in the peak region (Fig. 12).
The relative contribution of each transport type in MERRA-2 (SBJ-related > MSR > CPZ > NPH-related) is generally consistent with the results in WRF-Chem (MSR > SBJ-related > CPZ > NPH-related), except that MSR transport occurs less frequently in MERRA-2. The difference is largely caused by the spatial resolution of the two datasets. With a resolution of 0.5 • × 0.625 • , MERRA-2 has smooth topography information and cannot resolve the high peaks of the Sierra Nevada, which produce the MSR winds and transport. Consequently, MSR transport contributes to a smaller fraction in the MERRA-2. The coarser-resolution MERRA-2 also produces a more homogeneous dust concentration at low levels than 2 km WRF-Chem.
Similar dust concentrations and transport patterns are found in the 21-year SOM analysis (Fig. 13), indicating that the four patterns identified in 2019 are representative of the  climatological conditions. In climatology, the SBJ is weaker, and air inflows hit the California coast at a latitude further north (about 40 • N; Fig. 13b), which is reasonable as 2019 is an El Niño year with a stronger AR reaching California further south than usual. The changes in the transport patterns reflect the interannual variations of large-scale forcings and regional weather conditions, which are investigated using the frequency of each type in a year during 2001-2021 (Fig. S4). Types 1 and 4 have a negative correlation coefficient (R = −0.75) in their frequency, indicating the competing impact between remote transport and local emissions on dust concentrations over the Sierra Nevada. In particular, type 4 tends to occur more frequently during La Niña years, while it occurs less frequently during El Niño years. An opposite conclusion can be drawn for type 1. We further examine the dust transport pattern and the frequency of the four SOM types during three La Niña (2008, 2011, and 2021) and three El Niño (2015, 2016, and 2019) years. We find that the La Niña years have larger dust concentrations than El Niño years in both lower levels and middle levels (Figs. S5-S8), due to suppressed precipitation and drier soil in the southwestern United States. Meanwhile, the frequencies of types 3 and 4 are higher in El Niño years, reflecting the increased contribution of cross-Pacific transport to dust loading over California. The increase of remote transport weakens the relative importance of local emissions, decreasing the frequency of type 1.

Conclusions and discussion
With a focus on the dust that influences mountain snow, we investigated the dust sources surrounding the Sierra Nevada and their typical transport patterns during the spring and early summer. Despite the strongest emissions from the Mojave Desert, dust is only transported northward to the mountain when the mesoscale weather pattern dominates the southwest United States (Fig. 14). During 64.25 % of our study period, dust from the Mojave Desert is transported away from the mountains. Dust emitted from the Great Basin is transported to the central Sierra Nevada during MSR transport and to the eastern part when the NPH builds in the eastern Pacific. It is blown eastward by air inflows from the ocean during SBJ or cross-Pacific transport. In contrast, dust produced by the Central Valley is persistently transported to the west mountain slope, playing an essential role in snow impurities there. Carried by intense air inflows, it can be transported to the lee side of the Sierra Nevada.
During April, Asian dust is transported zonally over the North Pacific through the straight zonal isobars at the middle level. The dust layer descends to 800 hPa when it reaches the California coast. In the presence of the NPH, dust emitted from Asia excurses north into Alaska and Canada and travels south along the US west coast. The dust travels at a higher altitude, and the concentrations are weaker than the zonal transport.
Large amounts of depositions are found on the west slope, which generally decrease with elevations. Dust particles transported to the higher altitude are small in size and difficult to deposit through gravitational effects. The SBJproduced AR collects dust in the rain and snow and deposits it on the high mountain. In addition, considerable depositions occur when the elevated dust layer from the Pacific collides with the mountain. We acknowledge that our characterization of dominant transport patterns might be limited by model uncertainties. Further, the coarse-resolution reanalyses data, MERRA-2, cannot accurately resolve the topography effects and tend to underestimate mesoscale regional transport. Furthermore, both WRF-Chem and MERRA-2 describe dust emissions from dryland by relating them to high wind speed, soil moisture, and soil type (Ginoux et al., 2001), while dust emission from agricultural lands is not specifically implemented. However, a comprehensive evaluation of airborne dust and PM 2.5 concentration between model simulation and site observations in our previous study shows a good agreement between both (Huang et al., 2022a). In addition, the dust transport pathways have well-defined patterns associated with the mesoscale and large-scale weather systems. The general consistency across different models (WRF-Chem and MERRA-2) and observations (satellite analysis) and across different years also gives us confidence that the results are valid despite model uncertainties.
The analyses of dust emissions and transport can be used to understand dust transport in a changing climate. Studies have shown that global warming continues to dry the soil, producing more dust emissions over the western United States. Nevertheless, the change in transport and deposition patterns has not been well recognized. Our study highlighted the connection between dust transport and dominant weather patterns across the Sierra Nevada; the latter might respond in a more predictable way to climate change. Future projections show that global warming may increase the frequency of the landfalling AR by 20 %-35 % by the end of the 21st century (Hagos et al., 2016;Rhoades et al., 2021). In addition, the widening of the Hadley Cell in response to global warm- Figure 14. Schematic diagram of typical dust transport patterns across the Sierra Nevada. "MSR" denotes mesoscale regional transport. "SBJ" and "NPH" denote dust transport dominated by Sierra barrier jets (SBJs) and the North Pacific High (NPH), respectively, while "CPZ" denotes cross-Pacific zonal transport.
ing might enhance the NPH and shift it poleward (Song et al., 2018;Choi et al., 2016). That said, the SBJ-and NPHrelated dust transport may occur more frequently, while MSR transport may become less common. In this regard, changes in dust emissions from the Central Valley might play a more critical role in mountain snow impurities than those from the Mojave Desert and the Great Basin, producing more depositions on the west slope of the Sierra Nevada.
Author contributions. HH performed the analysis and drafted the manuscript. The methodology was developed by HH and YL. JZ and AG provided the observational data used for model validation. YQ, CH, and ZZ helped with the analysis and offered valuable comments. All authors contributed to writing and editing the manuscript.
DOE by the Battelle Memorial Institute under contract DE-AC05-76RLO1830.