Small but Notable Influence of Numerical Diffusion on Super Coarse Dust Sedimentation: Insights from UNO3 vs. Upwind Schemes

Received: 25 July 2025 Revised: 10 September 2025 Accepted: 12 September 2025 Published: 15 September 2025 Citation: Drakaki, E.; Mallios, S.; García-Pando, C.P.; Katsafados, P.; Amiridis, V. Small but Notable Influence of Numerical Diffusion on Super Coarse Dust Sedimentation: Insights from UNO3 vs. Upwind Schemes. Atmosphere 2025,16, 1086. https://doi.org/10.3390/ atmos16091086 Copyright: © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/). Article Small but Notable Influence of Numerical Diffusion on Super Coarse Dust Sedimentation: Insights from UNO3 vs. Upwind Schemes Eleni Drakaki 1,2,* , Sotirios Mallios 1, Carlos Perez García-Pando 3,4, Petros Katsafados 2 and Vassilis Amiridis 1 1Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens, 152 36 Athens, Greece; [email protected] (S.M.); [email protected] (V.A.) 2Department of Geography, Harokopio University of Athens, 176 76 Athens, Greece; [email protected] 3Barcelona Supercomputing Center (BSC), 08034 Barcelona, Spain; [email protected] 4Catalan Institution for Research and Advanced Studies (ICREA), 08010 Barcelona, Spain *Correspondence: [email protected] Abstract Mineral dust plays a vital role in the Earth’s climate system, influencing radiation, cloud formation, biogeochemical cycles, and air quality. Accurately simulating dust transport in atmospheric models remains challenging, particularly for coarse and super-coarse particles, which are often underrepresented due to limitations in model physics and numerical treatment. Observations have shown that particles larger than 20 µ m can remain airborne longer than expected, suggesting that standard gravitational settling formulations may be insufficient. One potential contributor to this discrepancy is the numerical diffusion introduced by advection schemes used to model sedimentation processes. In this study, we compare the commonly used first-order upwind advection scheme, which is highly diffusive, to a third-order scheme (UNO3) that reduces numerical diffusion while maintaining computational efficiency. Using 2-D sensitivity tests, we show that UNO3 retains up to 50% more dust mass for the coarsest particles compared to the default scheme, although overall dust lifetime shows little change. In 3-D simulations of the ASKOS 2022 dust campaign, both schemes reproduced similar large-scale dust patterns, with UNO3 yielding slightly lower dust. Overall, domain-averaged dust load differences remain small (less than 2%), with minor decreases in fine dust ~3% and slight increases in coarse dust ~2%, indicating that reducing numerical diffusion modestly enhances the presence of larger particles. Near the surface, UNO3 produces a ~4% increase in dust concentration, with local differences up to 50 µ g/m 3 . These results highlight that while numerical diffusion does affect dust transport—especially for super-coarse fractions—its impact is relatively small compared to the larger underestimation of super-coarse dust commonly observed in models compared to measurements. Addressing the fundamental physics of super-coarse dust emission and lofting may therefore be a higher priority for improving dust model fidelity than further refining advection numerics. Future studies may also consider implementing more computationally intensive schemes, such as the Prather scheme, to further minimize numerical diffusion where highly accurate size-resolved transport is critical. Keywords: dust transport; dust settling; numerical diffusion; WRF-Chem Atmosphere 2025,16, 1086 https://doi.org/10.3390/atmos16091086 Atmosphere 2025,16, 1086 2 of 26 1. Introduction Mineral dust, predominantly derived from arid and semi-arid soils with minimal vegetation cover, constitutes one of the principal natural sources of the global atmospheric aerosol burden and exerts a significant influence on the Earth’s atmospheric processes. Dust mass burden is estimated at around 22–20 Tg [ 1 ] affecting human health, transportation, and various atmospheric processes such as weather patterns [ 2 – 4 ], solar radiation levels [ 5 ], biochemistry [ 6 , 7 ] and overall climate forcing [ 8 , 9 ]. On the one hand, mineral dust can both absorb and scatter radiation [ 3 , 10 , 11 ], leading to alternating effects of warming and cooling on the planet [ 8 ]. On the other hand, dust alternates cloud properties, acting as the nucleate for cloud and ice formation [12–14]. The atmospheric interactions of dust are sensitive to the total dust mass burden along with the particle size distribution (PSD) of dust. The dust particles can be divided into separate modes regarding the size of their volume equivalent diameter (D): fine dust particles with D < 2.5 µ m, coarse particles with 2.5 < D ≤ 10 µ m, super-coarse particles with 10 µ m < D ≤ 62.5 µ m, and giant dust particles with D > 62.5 µ m [ 15 ]. In the Short Wave radiation spectrum (SW), super coarse and giant dust particles with diameters above 10 µ m tend to have a warming effect, while finer particles tend to have an increasing cooling effect as the size diminishes. In the context of long-wave interactions, dust particles have a cooling effect which strongly depends on size, with coarse particles tending to cool the atmosphere more [15]. The size of dust particles influences the cloud characteristics, their abundance, and their spatial distribution, thereby shaping global precipitation patterns and climate conditions [ 16 , 17 ]. Although less abundant in the atmosphere, coarser dust is more hygroscopic than finer particles [ 18 ] and can act more effectively as cloud condensation nuclei (CCN) [ 18 ] and ice nuclei (IN) [ 19 ]. Moreover, when larger dust particles are activated as CCN, they produce larger cloud droplets. In turn, larger cloud droplets can accelerate the collision coalescence process and initiate rain faster, also affecting cloud lifetime [20,21]. Last but not least, larger dust particles increase the overall dust mass, which influences the extent to which dust affects the oceanic carbon cycle, as well as ocean and tropical rainforest ecosystems [22–24]. During the last decade, observations have shown that super-coarse and giant dust particles are transported over significant distances within the Saharan Air Layer (SAL) [ 24 – 28 ]. However, atmospheric dust models, a fundamental tool for studying dust interactions, either ignore particles with diameters larger than 20 µ m or struggle to realistically represent their contribution to the atmospheric dust load [ 29 – 31 ]. Dust PSDs measurements, during FENNEC and AER-D campaigns, showed a significant proportion of coarse and giant mode particles, both above the Sahara sources and within the Saharan Air Layer (SAL) [ 27 ]. By ignoring the particles with diameters greater than 20 µ m, mass concentration is underestimated by up to 60%, and scattering calculations showed that both shortwave and longwave extinction are underestimated by up to 18% and 26%, respectively [27]. The retention of mineral dust coarse and giant modes in the atmosphere exceeds initial expectations based solely on gravitational sedimentation [ 24 , 25 , 30 ]. In [ 30 ], the authors developed the WRF-L model, a modified version of the WRF-Chem v4.2.1 [ 32 , 33 ] model that extends the dust PSD up to 100 µ m, constraining the particle size distribution of the emitted dust to observations. By deploying the WRF-L model for the case of the AER-D campaign, they found that a reduction of 60–80% in the gravitational settling velocity is needed to compensate for potential underrepresented mechanisms opposing gravity in the model. Atmosphere 2025,16, 1086 3 of 26 Many studies have demonstrated that dust models remove the coarser dust particles too fast. The reasons behind this deficiency have not been clarified yet. Many physical mechanisms have been proposed that potentially counteract gravity. Among them are the numerical challenges that plague the numerical modeling of constituent transport [ 34 ], like dust aerosol. In the realm of numerical advection modeling, the most significant goal, after ensuring stability, is to make algorithms as accurate as possible. This means that the results they produce should be very close to the actual solution of the advection equation. Yet, the presence of numerical errors can compromise the accuracy of advection algorithms. In many cases, efforts to eliminate one type of error, like diffusion, can amplify other errors, like numerical dispersion, thereby rendering the achievement of a perfect advection scheme impractical in reality [ 34 ]. Ref. [ 34 ] provides a detailed explanation of the numerical errors found in the advective schemes. Uncertainty in modeling mineral dust transport stems not only from parameterizations of emission and deposition processes but also from the choice of numerical advection scheme. In a sensitivity study using the CHIMERE-DUST model, ref. [ 35 ] demonstrated that different horizontal transport schemes—such as UPWIND, Van Leer, and PPM—can lead to substantial variations in modeled dust concentration fields. Lower-order schemes tended to produce more spatially diffused dust plumes with reduced peak concentrations compared to higher-order methods like PPM, though the differences in total dust load were limited to about 1–2.5%. An earlier study by [ 36 ] evaluated the influence (i) of dustparticles’ asphericity in their settling velocities by assuming prolate ellipsoids and (ii) of the advection schemes on dust settling by replacing the UPWIND scheme with the less diffusive Prather scheme in the standalone GOCART model. The results indicated that asphericity effects are significant only for very elongated particles (aspect ratio greater than 5), while the less diffusive Prather scheme resulted in a doubling of the modeled dust load affecting coarser particles (diameters greater than 5 µ m), therefore highlighting the potential of less diffusive methods to better represent dust transport, particularly for super-coarse particles. The Prather scheme assumes a sub-grid polynomial distribution and conserves the second moments of tracer concentration, thereby addressing the limitations of uniform concentration assumptions within grid cells. Despite its advantages, its implementation is memory-intensive and presents difficulties for models that employ operator-splitting approaches, such as WRF-Chem [37]. Another advective scheme, which, from its implementation on 1-D and 2-D idealized tests, presents low self-constrained numerical diffusion, is the 3rd order Upstream Upstream non-oscillatory (UNO3) advection scheme [ 38 ]. UNO3 has been derived by optimizing existing classical advection schemes and combining them in different monotonic zones to avoid flux limiters for simplicity. It is also extended to irregular grids in the form of upstream mid-flux linear interpolation with symmetrical gradients and is adapted to multidimensions with an advective–conservative operator. UNO3 is given in finite-volume flux form and thus is consistent and conservative. In this study, we conduct both 2-D idealized experiments and 3-D real-case simulations to assess the performance of the new scheme in representing dust particle transport. The 3-D simulations are conducted for a 4-month period that coincides with the period of the ASKOS campaign 2022. ASKOS campaign was the ground-based component of the Joint Aeolus Tropical Atlantic Campaign (JATAC) organized by the European Space Agency (ESA) and the National Aeronautics and Space Administration (NASA). ASKOS took place at the Ocean Science Centre Mindelo (OSCM), on the island of São Vicente, Cabo Verde, during 2021–2022. The main objective of ASKOS was to collect synergistic measurements for the validation and enhancement of ESA’s satellite mission Aeolus. The collected dataset includes ground-based aerosol, cloud, wind, and radiation remote sensing measurements Atmosphere 2025,16, 1086 4 of 26 as well as UAV-based aerosol in situ particle size-distribution measurements, within the Saharan air layer, combined with sample collection for mineralogical analysis. More information about the ASKOS campaign can be found in [39]. In the current study, our analysis focuses on evaluating changes in simulated dust load, surface dust concentrations, and the vertical structure of dust distributions, with special attention to how these metrics are affected for the larger particle size classes. Our results highlight the modeling aspects of dust transport by using a computationally efficient and less diffusive scheme for the advection of gravitational settling losses. The paper is organized as follows. Section 2provides a description of the implemented advective schemes and an overview of the applied methodology to realize the objectives of the study. Section 3provides an analysis of the differences in the simulated dust distribution using the different numerical schemes. Section 4provides a discussion of the results, and Section 5provides a summary of the study along with the main concluding remarks. 2. Materials and Methods 2.1. Transport of Mineral Dust in WRF-L The continuity equations that govern mineral dust aerosols account for various external factors influencing their behavior. Mineral dust particles are introduced into the atmosphere through emission processes, while their removal occurs primarily through sedimentation and dry deposition onto water, soil, and other surfaces. Additionally, model equations often incorporate supplementary mechanisms such as particle washout, cloud and ice nucleation, and droplet evaporation, which serve as additional sources or sinks in the model. ∂C ∂t+ ∇ ·(vC) = K ∇ 2C+Rn, (1) where the first left-side term is the local time derivative of mineral dust concentration C, the second left-side term is the change due to transport, the first right-side term is the change in mineral dust concentration due to turbulent diffusion, with K the Eddy diffusivity, and Rn is the time rate of change of the mineral dust concentration due to the n th external sinks and sources (emission and sedimentation in this study). The concentration C can be related to the tracer mixing ratio τ and the density of atmospheric air ρair by Equation (2): C=τ·ρair, (2) Sedimentation occurs when particles fall through the atmosphere due to their mass (gravitational settling). The losses due to gravitational settling in WRF-L (and WRF-Chem in general), which are included in Rn , are calculated as the vertical advection of the mineral dust concentration due to the settling velocity, assuming that all particles within each transport size bin in a model grid cell share the same settling velocity. The corresponding advective equation in flux form is given below: ∂C ∂tsed =∂→ usC ∂zsed, (3) where → us is the settling velocity vector of the particles, calculated for the effective diameter of each model transport size bin, as described in [30]. By expressing Equation (3) in terms of the mixing ratio τ, we obtain: ∂ρair ·τ ∂tsed =∂→ u·ρair ·τ ∂zsed, (4) Atmosphere 2025,16, 1086 5 of 26 In the WRF-L (WRF-Chem) ARAKAWA-C grid, the mineral dust mixing ratio is computed at the mass grid points (Figure 1). Therefore, we can derive an equation using the discretization scheme of the interpolation approach to represent Equation (3) as follows: ρt+1 a,l·τt+1 l−ρt a,l·τt l ∆t= ut s,l−1 2 ·ρt a,l−1 2 ·τt l−1 2 −ut s,l+1 2 ·ρt a,l+1 2 ·τt l+1 2 ∆zt l , (5) or ρt+1 a,l·τt+1 l=(ρt a,l·τt l+(ut s,l−1 2 ·ρt a,l−1 2 ·τt l−1 2 −ut s,l+1 2 ·ρt a,l+1 2 ·τt l+1 2)·∆t ∆zt l ), (6) Figure 1. Description of the vertical levels based on the Arakawa C-Grid of WRF-L (and WRF-Chem). The “mass grid” where the dust concentration is solved is denoted with the “x” symbol and the defined “ghost” levels for the setting of the boundary conditions, in gray. Here, τt+1 l , ρt+1 a,l and τt l , ρt a,l represent the mixing ratio of mineral dust τ and the atmospheric air density ρa at the center of (l)th grid point and at time t+ 1 and t , respectively. ut l,s is the vector of settling velocity of the particle. The l+1 2 ( l−1 2 ) terms are evaluated at the grid cell faces between l and l+ 1 ( l and l− 1 ) cell faces. The grid cell width at grid point l and time t is denoted as ∆zt l , and ∆t represents the time step. Since the vertical coordinates of the WRF model are hybrid-pressure levels n , there is a temporal and spatial dependency on the ∆zvalue. Lastly, we must note that the solution of (6) is not affected by other transport processes in the model, such as transport due to wind components, turbulent diffusion, and vertical mixing. 2.1.1. The Default First Order UPWIND Advective Scheme of WRF-L The determination of the term τt l+1 2 (and ρt air,l+1 2 , ut s,l+1 2 ) can be accomplished using the following straightforward approach: τt l+1 2=τt l+1, (7) τt l−1 2=τt l, (8) Atmosphere 2025,16, 1086 6 of 26 The above approach, with the additional assumption that ρt+1 a,l=ρt a,l , leads to the following equations, which describe the default advective scheme of WRF-L (based on WRF-Chem v4.2.1) for the calculation of the changes in dust mixing ratio due to gravitational settling: τt+1 l=τt l·(1+ut s,l·∆t ∆zt l )−ut s,l+1·τt l+1·ρt a,l+1 ρt a,l ·∆t ∆zt l , (9) Or τt+1 l=τt l· 1−ut s,l·∆t ∆zt l!+ut s,l+1·τt l+1·ρt a,l+1 ρt a,l ·∆t ∆zt l (10) 2.1.2. The Upstream Non-Oscillating Scheme III (UNO3) in WRF-L Context The UNO3 scheme has been developed based on a combination of already existing interpolation numerical schemes to cure the problem of numerical oscillations, which are attributed to the evaluation of the Ct l+1/2 term in Equation (11). The cell notation in UNO3 follows that initially proposed by [40] and is presented here in Figure 1. Written in terms of concentration, the trace concentration Ct l in level l at integration time t is given by Equation (11): Ct+1 l=Ct l+(ut s,l−1 2 ·Ct l−1 2 −ut s,l+1 2 ·Ct l+1 2)·∆t ∆zt l , (11) The cell coordinate z represents the cell center, with a positive cell width ∆z that may vary for non-uniform grids. Consequently, a cell face is positioned at half the cell width from its respective cell center. Because of the sigma pressure vertical coordinates in the WRF model grid, a modification is needed in the definition of the grid cell width ∆z in the WRF model grid to align with the midpoint between the two bounding cells: ∆z=n2·zt l−zt f ull,l,f or l =1 ∆z=2zt l−2zt l−l−∆zt l−1,otherwise,(12) Other than the above modification, the implementation of UNO3 has been carried out as described in [ 38 ], with the settling velocities to be evaluated in the cell center (model “mass” grid) and the cell face velocities are interpolated from the settling velocity of the neighboring cell centers, weighting their relative distance from the cell face according to Equations (13) and (14). We should note that in our implementation, we assume that l= 1 refers to the bottom model level, thus settling velocity is negative ut l=−ut l. ut l+1 2=∆zt l+1 ∆zt l+1+∆zt l ut l+1+∆zt l ∆zt l+1+∆zt l ut l, (13) ut l−1 2=∆zt l−1 ∆zt l−1+∆zt l ut l−1+∆zt l ∆zt l−1+∆zt l ut l, (14) To set the boundary conditions, we add extra levels outside the bottom and top boundaries (ghost levels) with the same cell width and the same settling velocity as the first (bottom) and the last (top) model grid level, respectively. We assume that zero tracer concentration comes from the top and a zero-gradient boundary condition at the bottom. To implement this, the tracer concentration at the top ghost levels is set to zero, and the tracer concentration of the bottom ghost cells is equal to the concentration of the first model level. Atmosphere 2025,16, 1086 7 of 26 2.2. Model Experimental Set-Up In this work, we use the WRF-L [ 30 ] model in both 2-D and 3-D configurations. In the 2-D configuration, the model simulates the transport and the deposition of the dust particles, while in the 3-D configuration, the model additionally simulates the emission of dust based on the GOCART-AFWA modified scheme [30]. Before applying the new UNO3 scheme in real 3-D dust transport cases, we performed a set of 2-D idealized dust transport simulations to test the performance of the new advective scheme and provide a benchmark for its comparison with the default upwind scheme in WRF-L. Following the implementation of both schemes into WRF-L, we apply the model for simulations covering the period of the ASKOS 2022 experimental campaign. 2.2.1. WRF-L/2D Benchmark Sensitivity Tests To test the performance of the code, we performed 2-D idealized simulations with WRF-L coupled with the dust mode component. A list of the 2-D sensitivity tests is presented in Table 1. Table 1. 2-D Experimental runs that were performed in this study. 2-D Experiments Horizontal Resolution ∆x(km) Vertical Resolution ∆z±z′(km) Numerical Scheme for Gravitational Settling UPWIND_L30 50 km 1.058 ±0.187 UPWIND_WRF UPWIND_L60 50 km 0.516 ±0.086 UPWIND_WRF UPWIND_L120 50 km 0.258 ±0.046 UPWIND_WRF UPWIND_L240 50 km 0.129 ±0.023 UPWIND_WRF UNO3_L30 50 km 1.058 ±0.187 UNO3 UNO3_L60 50 km 0.516 ±0.086 UNO3 UNO3_L120 50 km 0.258 ±0.046 UNO3 UNO3_L240 50 km 0.129 ±0.023 UNO3 The model domain consists of 91 grid points with 50 km horizontal spacing. We performed several sensitivity tests by varying the number of vertical levels (30, 60, 120, and 240) to examine the sensitivity of the vertical spatial resolution on the dust transport. In the simulation, we reproduce the transport of a dust plume that travels approximately at 4–6 km altitudes from Cabo Verde Island toward Barbados. The dust plume is initialized in 2, 4, 8, or 15 vertical layers in the model with a total mass mixing ratio normalized to 1000 µ g/kg of dry air. The vertical resolution is approximately 1 km for the configuration with 30 vertical layers, and 500 m, 250 m, and 125 m for the configurations with 60, 120, and 240 levels, respectively. When applying both numerical schemes (UPWIND and UNO3), a constant timestep is applied. A more detailed description of the simulation setup is given in Table 2. Table 2. Domain resolution and size for the WRF-L/2D tests. The vertical resolution varies with height and surface pressure; therefore, the representative median value and the mean value, along with their standard deviation, are presented. # of Horizontal Grid Points in the x-Direction Lx * (km) ∆x(km) ∆z(km) Median ∆z±z′(km) Lz * (km) # of Vertical Levels 91 5050 50 1.005 1.058 ±0.187 30 30 91 5050 50 0.496 0.516 ±0.086 30 60 91 5050 50 0.246 0.258 ±0.046 30 120 91 5050 50 0.122 0.129 ±0.023 30 240 *Lx,Lz are the total horizontal and vertical dimensions of the domain in km. Atmosphere 2025,16, 1086 8 of 26 To initialize the meteorological conditions in the model, we used a radiosonde from Tenerife from the database of the University of Wyoming (Figure 2) with a modified wind profile. The wind profile has been replaced with the zonal wind speed profile, calculated based on the average wind speed and direction of the area of Cabo Verde provided by the Final Analysis (FNL) Operational Global Analysis data, at a 1 ◦× 1 ◦ grid and for the years 2014–2018. Simplified physics are used within the model, and the dust scheme linked to the dust simulation is that of WRF-L. Figure 2. SkewT − LogP diagram for the meteorological conditions used for the initialization of the 2-D WRF-L experiments. Only the zonal circulation is taken, based on the average wind speed and direction, of the area of Cabo Verde calculated from Final Analysis (FNL) Operational Global Analysis data, at a 1 ◦× 1 ◦ grid, for the years 2014–2018. The solid red and orange lines show the atmospheric temperature ( T ) and the dew point ( Td ). For the time integration, the RK3 scheme is activated. A fifth-order advection scheme is used for the horizontal advection of momentum and scalars, whereas a 3rd order scheme is utilized for the vertical advection [ 33 ]. Monotonic filters are applied to sustain monotonicity in the advection of turbulent kinetic energy, moisture, scalars, and chemical variables (e.g., mineral dust). Open lateral boundaries are assumed, and there is an implicit Rayleigh damping for the vertical velocity [33]. 2.2.2. WRF-L/3D: Real Cases Using the WRF-L code in a 3-D configuration, we first ran the CONTROL experiment using the default UPWIND scheme for the gravitational settling of dust, followed by identical experiments using the UNO3 scheme as described in Section 2.1.2. Our simulation period coincides with the ASKOS campaign of 2022. After we performed the control set of simulations activating the UPWIND scheme (UPWIND_ASKOS experiment), we performed an additional set of simulations applying the UNO3 scheme to calculate the gravitational losses of dust (UNO3_ASKOS). The two sets of runs differ only in the application of the advective scheme for sedimentation. We follow Atmosphere 2025,16, 1086 9 of 26 the same model configuration as in [ 30 ], regarding the selected physics and dynamics in the model and the simulation cycle structure. Moreover, we use the fifth-generation ECMWF (ERA5) reanalysis data to set the initial and boundary conditions every 6 h, in a spatial grid resolution of 0.25 × 0.25 ◦ . The domain is an equal-distance grid with a spatial grid spacing of 15 km × 15 km consisting of 620 × 320 points, and 33 vertical sigma pressure levels (automatically defined) of up to 50hPa. Approximate heights of the levels are provided in Table 3. As in 2-D simulations, when applying both numerical schemes (UPWIND and UNO3), we keep a constant timestep. Table 3. Approximate level heights of the 3-D WRF-L experiments. Model Levels Heights (km) ∆z(km) 1 0 - 2 0.05 0.05 3 0.1139 0.0639 4 0.1952 0.0813 5 0.298 0.1028 6 0.4272 0.1291 7 0.5878 0.1607 8 0.7855 0.1977 9 1.0256 0.24 10 1.3126 0.287 11 1.6496 0.337 12 2.0377 0.3882 13 2.4756 0.4379 14 2.9593 0.4837 15 3.4851 0.5258 16 4.0561 0.5709 17 4.675 0.6189 18 5.3449 0.6698 19 6.0684 0.7235 20 6.8482 0.7798 21 7.6865 0.8383 22 8.5850 0.8985 23 9.5449 0.9599 24 10.5662 1.0213 25 11.6479 1.0817 26 12.7033 1.0554 27 13.7271 1.0237 28 14.7508 1.0237 29 15.7746 1.0237 30 16.7983 1.0237 31 17.8221 1.0237 32 18.8458 1.0237 33 19.8696 1.0237 The simulation comprises nine 84 h forecast runs, with each run initialized at 12:00 UTC. The first cycle is a cold start for the dust field, while in the next cycles, the dust field is initialized based on the previous cycle. The 30 s Global Multi-Resolution Terrain Elevation Data 2010 [ 41 ] are used to represent model topography, while land use is determined using modified Moderate-resolution Imaging Spectroradiometer (MODIS) observational data from the University of Boston [ 42 ]. The initial 12 h of each 84 h cycle serve as a model spin-up and are neglected. Similarly, the first week of the simulation is designated as a spin-up period to accumulate background dust loading and is therefore omitted from the analysis. The simulation runs are performed in dust-only mode, Atmosphere 2025,16, 1086 16 of 26 (a) (b) (c) (d) Figure 7. The mean dust load ratio of the coarse dust particles (bins 3 and 4) and the finer dust particles (bins 1, 2, and 3) (C2F) for June, July, August, and September 2022 is presented for the experiments using the UPWIND (a) and UNO3 schemes (c). The absolute and relative differences, respectively, between the simulated dust load C2F ratio using the UNO3 scheme and that using the UPWIND scheme are presented (b,d). 4. Discussion Mineral dust, particularly coarse and super-coarse particles, plays a pivotal role in climate processes, yet remains difficult to simulate accurately. This study focused on quantifying the effect of numerical diffusion—arising from sedimentation advection schemes—on the transport of mineral dust particles of varying sizes. By comparing the standard first-order UPWIND scheme to the less diffusive third-order UNO3 scheme in both idealized 2D and realistic 3D setups, we assessed how reducing numerical diffusion influences dust mass retention, vertical and horizontal redistribution, and optical properties. In the 3D simulations of the ASKOS 2022 campaign, both advection schemes yielded similar large-scale dust load distributions, with domain-averaged total dust loads differing by less than 1%. However, this minimal global discrepancy conceals notable regional and size-dependent effects. The UNO3 scheme produced up to 2% lower dust load near Saharan sources and up to 5–10% lower loads over the tropical Atlantic and Caribbean—a redistribution pattern indicative of reduced numerical diffusion and reduced long-range transport capacity. The size-resolved behavior of dust under UNO3 shows an important distinction. For fine particles (D = 0.2–5.5 µ m; bins 1–2), UNO3 simulations yield small decreases in atmospheric and surface concentrations (~1–2% domain-averaged), reflecting a slightly more efficient deposition due to reduced vertical mixing. In contrast, coarse particles (D = 5.5–40 µ m; bins 3–4) are increased in both column and surface concentrations, Atmosphere 2025,16, 1086 17 of 26 reaching up to 2–3%, and local surface differences up to 50 µ g/m 3 . These trends affirm that numerical diffusion disproportionately affects larger particles, likely because their stronger gravitational settling is more sensitive to vertical smearing induced by low-order advection schemes. This differential behavior is further illustrated by the coarse-to-fine (C2F) dust load ratio, which consistently increases in UNO3 simulations—especially in long-range transport regions like the Atlantic outflow. The lower C2F ratio implies that the relative contribution of coarse particles increases, confirming that reduced diffusion helps retain these larger particles during westward transport. While absolute changes remain modest ~0.01–0.03, this has important implications for aerosol radiative forcing, sedimentation rates, and ocean fertilization studies that rely on accurate coarse dust representation. Our findings differ from previous studies on the role of numerical diffusion, with differences in the sign of impact and the impact magnitude. The authors of [ 36 ] showed that reducing numerical diffusion using a second-order moment scheme significantly increased simulated dust mass loading by up to a factor of two compared to a first-order upwind scheme. In contrast, our study finds modest negative differences between 2–10%, likely due to differences in model setup. The authors of [ 36 ] used a global standalone model with coarser resolution and shorter simulation periods, whereas we used a high-resolution, regional, online-coupled simulation over four months. Additionally, the two studies used different advective schemes. It should be noted that the UNO3 scheme performs higher numerical diffusion when it is applied on an irregular grid. This can explain the lower differences found in this study compared to the default UPWIND scheme. Despite these differences, both studies emphasize the importance of minimizing numerical diffusion to better represent the transport of coarse dust particles; however, the effects appear to be scaleand resolution-dependent, suggesting that the sensitivity to numerical diffusion may vary under different model configurations or grid structures. Similarly, ref. [ 35 ] evaluated the impact of different transport schemes on modeled dust concentrations using the CHIMERE-DUST model. They found that while numerical diffusion significantly affected dust plume spread and peak concentrations, the domainaveraged dust burden differences between highand low-diffusion schemes remained relatively modest (~1–2.5%). Their results are consistent with ours, showing that numerical diffusion has a measurable but moderate impact under realistic atmospheric conditions. Overall, our study shows that numerical diffusion has a measurable but moderate influence on the simulation of dust transport, particularly in terms of regional redistribution and the preservation of coarse particles. While it does not substantially alter domainaveraged dust budgets, it systematically affects the spatial distribution and size-resolved behavior of dust plumes. The magnitude and significance of these effects may depend on specific modeling conditions, such as the advective scheme, model configuration, or grid resolution. As such, further investigations involving additional numerical schemes and a broader range of test cases are warranted to better quantify the role of numerical diffusion and guide the selection of appropriate advection methods in dust modeling applications. 5. Summary and Conclusions This study assessed the impact of numerical diffusion in vertical sedimentation schemes on the simulation of mineral dust transport, using the WRF-Chem model with the ASKOS 2022 campaign as a reference. By comparing the commonly used first-order UPWIND scheme to the less diffusive third-order UNO3 scheme, we evaluated how reducing numerical diffusion affects dust mass retention, distribution, and optical properties, with a focus on particle size sensitivity. Atmosphere 2025,16, 1086 18 of 26 While domain-averaged differences in total dust load were small (~ − 0.8%), UNO3 produced notable regional and size-resolved effects. Specifically, it led to reduced dust near source regions (~ − 2%) and over the Atlantic and Caribbean (~5–10%). UNO3 reduced bin 1 and bin 2 dust loads each by ~2%, increased bin 3 dust load by 0.3%, and bin 4 and bin 5 dust loads, each by ~2% domain average. These effects were also reflected in the higher regions by ~1.5% coarse-to-fine (C2F) dust load ratio in UNO3 simulations, highlighting its ability to better preserve super-coarse dust during transport. Figure 8sums up the main differences in dust fields observed in this study between UPWIND and UNO3 schemes. Figure 8. Main differences observed in this study between UPWIND and UNO3 schemes. Despite these improvements, a large underestimation remains relative to broader model challenges, such as the persistent underrepresentation of super-coarse dust. This underscores the need to improve physical parameterizations related to emission and lofting processes in addition to refining numerical schemes. The results demonstrate that the sensitivity to numerical diffusion is highly dependent on model configuration, grid structure, and resolution. Therefore, further investigation involving additional advection schemes, different modeling frameworks, and a range of meteorological regimes is essential to better understand the scale-dependent behavior of numerical diffusion and to guide the development of robust dust transport modeling strategies. Author Contributions: Conceptualization, E.D., S.M. and V.A.; methodology, E.D. and S.M.; software, E.D.; investigation, E.D., S.M. and C.P.G.-P.; visualization, E.D.; resources, E.D. and V.A.; writing— original draft preparation, E.D.; writing—review and editing, E.D., C.P.G.-P., P.K., S.M. and V.A. All authors have read and agreed to the published version of the manuscript. Funding: E.D acknowledges support by the Hellenic Foundation for Research and Innovation (H.F.R.I.) under the “2nd Call for H.F.R.I. Research Projects to support Post-Doctoral Researchers” (Project Acronym: StratoFIRE, Project number: 3995). This paper has partially received funding from Horizon Europe programme under Grant Agreement No 101137680 via project CERTAINTY (Cloud-aERosol inTeractions & their impActs IN The earth sYstem); the HFRI Research Projects to support postdoctoral researchers (project acronym: REVEAL; Project number: 07222); the AIRSENSE (Aerosol and aerosol cloud Interaction from Remote SENSing Enhancement) project, funded from the European Space Agency under Contract number 4000142902/23/I-NS; and the CiROCCO project funded by the European Union under Grant Agreement number 101086497. CPG-P acknowledges Atmosphere 2025,16, 1086 19 of 26 support from the Spanish Ministerio de Economía y Competitividad (grant PID2022-140365OB-I funded by MICIU/AEI/10.13039/501100011033 and by ERDF, EU) and the AXA Research Fund. Data Availability Statement: Data are available upon request to [email protected]. Acknowledgments: This work is supported by computational time granted from the National Infrastructures for Research and Technology S.A. (GRNET S.A.) in the National HPC facility—ARIS— under project ID pr016030_thin-MIAMI. Conflicts of Interest: The authors declare no conflicts of interest. Abbreviations The following abbreviations are used in this manuscript: UNO3 Upstream Non-Oscillating III C2F Coarse to Fine dust load ratio Appendix A Figure A1. Transport of a square beam using the UPWIND and the UNO3 schemes for Courant number C = 0.2. We use constant transport velocity, while the timestep is adjusted to the levels’ width and the Courant number. (a) 60 (59), (b) 120 (119), (c) 240 (239), and (d) 480 (479) full (mid) levels during the transport of the beam at approximately the same height. Atmosphere 2025,16, 1086 20 of 26 (a) (b) (c) (d) Figure A2. The spatial distribution of the temporal mean dust load of June, July, August, and September 2022 for bin 1 is presented for the experiments using the UPWIND (a) and UNO3 (c) schemes. The absolute and relative differences, between the simulated dust load using the UNO3 scheme and those using the UPWIND scheme are presented in (b,d) respectively. (a) (b) Figure A3. Cont. Atmosphere 2025,16, 1086 21 of 26 (c) (d) Figure A3. The spatial distribution of the temporal mean dust load of June, July, August, and September 2022 for bin 2 is presented for the experiments using the UPWIND (a) and UNO3 (c) schemes. The absolute and relative differences, between the simulated dust load using the UNO3 scheme and those using the UPWIND scheme are presented in (b,d) respectively. (a) (b) (c) (d) Figure A4. The spatial distribution of the temporal mean dust load of June, July, August, and September 2022 for bin 3 is presented for the experiments using the UPWIND (a) and UNO3 (c) schemes. The absolute and relative differences, between the simulated dust load using the UNO3 scheme and those using the UPWIND scheme are presented in (b,d) respectively. Atmosphere 2025,16, 1086 22 of 26 (a) (b) (c) (d) Figure A5. The spatial distribution of the temporal mean dust load of June, July, August, and September 2022 for bin 4 is presented for the experiments using the UPWIND (a) and UNO3 (c) schemes. The absolute and relative differences, between the simulated dust load using the UNO3 scheme and those using the UPWIND scheme are presented in (b,d) respectively. (a) (b) Figure A6. Cont. Atmosphere 2025,16, 1086 23 of 26 (c) (d) Figure A6. The spatial distribution of the temporal mean dust load of June, July, August, and September 2022 for bin 5 is presented for the experiments using the UPWIND (a) and UNO3 (c) schemes. The absolute and relative differences, between the simulated dust load using the UNO3 scheme and those using the UPWIND scheme are presented in (b,d) respectively. Table A1. Temporal and spatial average, over the domain, dust load absolute and relative difference. Variable UNO3-UPWIND Absolute Difference [g/m2] UNO3-UPWIND Relative Difference [%] Total Dust load −0.009 −0.8 Dust load bin 1 −0.003 −2 Dust load bin 2 −0.007 −1.6 Dust load bin 3 0.007 0.3 Dust load bin 4 7×10−41.9 Dust load bin 5 9.2 ×10−52.3 References 1. Kok, J.F.; Adebiyi, A.A.; Albani, S.; Balkanski, Y.; Checa-Garcia, R.; Chin, M.; Colarco, P.R.; Hamilton, D.S.; Huang, Y.; Ito, A.; et al. Contribution of the World’s Main Dust Source Regions to the Global Cycle of Desert Dust. Atmos. Chem. Phys. 2021,21, 8169–8193. [CrossRef] 2. Chen, S.-H.; Liu, Y.-C.; Nathan, T.R.; Davis, C.; Torn, R.; Sowa, N.; Cheng, C.-T.; Chen, J.-P. Modeling the Effects of Dust-Radiative Forcing on the Movement of Hurricane Helene (2006): Effect of Dust-Radiative Forcing on Helene Movement. Q. J. R. Meteorol. Soc. 2015,141, 2563–2570. [CrossRef] 3. 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