1. Introduction
Accurately simulating aerosol and cloud microphysical processes is becoming increasingly important in process-scale, mesoscale, and climate-scale models. Much of our understanding of aerosol and microphysical effects on the water cycle and global climate rely on the use of such models (Solomon et al. 2007). The indirect effects of cloud and ice nucleating aerosols (Twomey 1974; Albrecht 1989), including cloud albedo, cloud lifetime, and precipitation efficiency, remain relatively poorly understood (Solomon et al. 2007). As such, improvements in the representation of aerosols and related cloud processes in models is necessary to improve confidence regarding aerosol impacts on climate. One such model being used for aerosol and microphysical research across multiple cloud scales is the Colorado State University (CSU) Regional Atmospheric Modeling System (RAMS), version 6.0 (Cotton et al. 2003).
The RAMS model has proven to be versatile across atmospheric scales as a large-eddy-simulation model (e.g., Jiang et al. 2001; Jiang and Feingold 2006), cloud-resolving model (e.g., Saleeby et al. 2009; van den Heever et al. 2006), and regional climate model (e.g., Lu and Shuttleworth 2002; Castro et al. 2007). It has demonstrated success in simulating a range of atmospheric phenomena, such as supercell thunderstorms (e.g., van den Heever and Cotton 2004), mesoscale convective systems (e.g., Olsson and Cotton 1997; Bernardet and Cotton 1998), mixed-phase orographic precipitation (Saleeby et al. 2009, 2011, 2013), monsoon systems (e.g., Saleeby and Cotton 2004b), sea breeze circulations (e.g., Darby et al. 2002), extratropical cyclones (e.g., Igel et al. 2013), and hurricanes (e.g., Zhang et al. 2007; Carrio and Cotton 2011).
List of equation variables and symbols.
Saleeby and Cotton (2004a) implemented a cloud nucleation scheme in RAMS, version 4.3, for two-moment prediction of cloud and drizzle droplets. Lagrangian parcel-bin simulations were performed offline with a single-column model (Heymsfield and Sabin 1989; Feingold and Heymsfield 1992) to generate lookup tables that contain the percentage of aerosols that activate over a range of vertical velocity, temperature, aerosol concentration, and aerosol size. Studies using this aerosol parameterization have examined the cloud droplet nucleating effects of aerosols over a wide variety of cloud systems, including orographic snowfall (Saleeby et al. 2009, 2011, 2013), shallow clouds (Cheng et al. 2009; Lee et al. 2009), deep convection (Lee 2012; van den Heever et al. 2006, 2011; Storer and van den Heever 2013), hurricanes (Zhang et al. 2007; Carrio and Cotton 2011), and extratropical cyclones (Igel et al. 2013). Stokowski (2005) expanded the model capability by implementing an aerosol–radiation interaction scheme, and he presented an investigation of noncloudy aerosol layer radiative effects. Smith (2007) and Seigel and van den Heever (2012) discuss the development of a mineral dust source model and removal by dry and wet deposition for investigating dust transport in various systems. Carrio and Cotton (2011) discuss an implemented sea salt source model and a wet scavenging scheme for use in examining the impact of sea salt on tropical cyclones. While much has been learned about aerosol effects from these studies above, the RAMS aerosol modules used in these past studies lacked one or more of the following areas of aerosol representation: multiple aerosol modes, variable solubility, nucleation scavenging, regeneration, scavenging by dry and wet deposition, aerosol–radiation interactions, and/or the ability to track the temporal and spatial variability in activated, scavenged, and in situ aerosols by type. As such, even more could potentially have been gained from a more comprehensive treatment of aerosols.
With use of a cloud parcel model, Flossmann et al. (1985, 1987) demonstrated the importance of representing aerosol nucleation scavenging, impaction or precipitation scavenging, and aerosol regeneration upon evaporation of hydrometeors. They showed that nucleation scavenging accounts for the majority of aerosol removal, but that precipitation scavenging of aerosol can be of importance in many situations. Further, representing the regeneration of aerosols can be quite important in evaporative regions, and it can lead to a significant change in the aerosol distribution size, chemistry, and hygroscopicity or solubility due to aerosol mixing within drops grown by collision–coalescence. More recent work has been done to include these aerosol sources and sinks into more complex aerosol–cloud microphysics models (Ekman et al. 2004, 2006) and to interface these with limited cloud dynamics models (Wang and Chang 1993) so as to provide a more complete representation of aerosols and their impacts on complex cloud systems. Such models are then capable of representing aerosol life cycles and thus more realistically simulate their impacts on clouds. Improvements in the understanding of ice nucleation mechanisms and their representation in numerical models are also of great importance in prediction of ice concentrations, radiation budgets, and frozen precipitation (Fridlind et al. 2007). As such, we have implemented a new scheme for heterogeneous ice nucleation that is based on data from numerous of field studies (DeMott et al. 2010).
The goal of the research presented in this paper is twofold. The first is to present the details of development completed within the RAMS aerosol module with a view to improving the representation of the key sources and sinks of the aerosol life cycle, how they relate to cloud condensation nuclei and ice nuclei (IN), and their links to other microphysical and dynamical processes. The second is to demonstrate the relative importance of the aerosol source and sink mechanisms across cloud scales via an examination of simulated precipitation within raining stratocumulus clouds, deep convection, and orographic snowfall. This manuscript documents the individual modules governing the treatment of aerosols from emissions to activation, scavenging, and regeneration and the radiative impacts of aerosols, as well as the importance of such changes on the surface precipitation of stratiform and convective precipitation. The inclusion of these individual aerosol representations will allow for more robust studies of aerosol effects over a range of cloud systems. The aerosol modules in RAMS 6.0 are discussed in the following sections.
2. Developments in the treatment of aerosols
a. Aerosol activation and cloud droplet nucleation
Given the newly added aerosol species and the potential for large variability in aerosol solubility, we have extended the dimension of the lookup tables to include soluble fraction ɛ. Ward et al. (2010) and Reutter et al. (2009) represented aerosol solubility with the kappa parameter κ (Petters and Kreidenweis 2007). These studies demonstrated the sensitivity of aerosol activation to the solubility. Rather than using a single ɛ for all aerosol species, it is most reasonable to allow sea salt aerosols to be nearly fully soluble, while mineral dust may be nearly insoluble; meanwhile, sulfate-based particles could vary over a range of solubility depending on the aerosol source and degree of sulfate coating. The user assigns the aerosol solubility for each species at the time of model initialization, and the solubility remains constant in time for each aerosol category. Figure 1 displays a plot of the percentage of activated aerosols that lead to new droplet nucleation over a range of solubility ɛ from 5% to 100% and for several values of vertical velocity and aerosol median radius. The solubility has a minimal impact for a situation with 1) strong updrafts and large aerosol median radii (dotted black line) and 2) weak updrafts and small aerosol median radii (solid red line), which represent the upper and lower bounds of the nucleation percentage in the plot. Intermediate combinations of size and updraft lead to larger variations in nucleation with a change in solubility. Permitting variability with ɛ provides a more accurate representation of aerosols with known chemistry and allows for differentiation among aerosol species.
During the simulated cloud nucleation process, the 4D lookup tables are accessed each time step with the fraction of aerosol number to activate being determined from the five parameters of the lookup tables. For each aerosol species, if the median radius of the distribution is less (greater) than 1 μm at the time of activation, newly nucleated droplets enter the cloud water (drizzle) category. From parcel model results, larger particles tend to result in larger initial droplets that exceed the upper bound on model cloud droplet diameter (2–50 μm) and fit more closely within the drizzle range (50–100 μm).
b. Nucleation scavenging and aerosol regeneration
Upon nucleation of new cloud droplets, the aerosol mass that is removed from the aerosol population is transferred to a 3D scalar variable that is used to track the amount of total aerosol mass contained within cloud droplets, called aerosol in cloud. This mass is a conglomerate of all aerosol types consumed during nucleation. There is a different 3D scalar tracking variable associated with each hydrometeor type so as to allow transfers of aerosol mass in hydrometeors among hydrometeor categories whenever transfers of condensate mass occur from one hydrometeor category to another. During the condensate mass transfers that would occur during collision–coalescence, freezing, or melting, the aerosol mass in hydrometeors is transferred in proportion to the amount of transferred hydrometeor mass. So, for example, if 50% of the hail mass melts in a given grid cell and becomes rain, then 50% of the aerosol mass contained within hail particles, referred to as aerosol mass in hail, will be transferred to the aerosol mass in rain category. This method of tracking aerosol mass contained within hydrometeors is similar to the aerosol mass ratio transfer scheme of Rutledge et al. (1986) and Hegg et al. (1986).
When grid cells containing hydrometeors undergo evaporation, a number of precipitation particles may fully evaporate and restore aerosols back to the environment. The amount of restored aerosol mass is in proportion to the amount of mass of fully evaporated hydrometeors relative to the total hydrometeor mixing ratio. If the mass of the fully evaporated hydrometeors in a given hydrometeor category is 10% of the total hydrometeor mass in that category, then 10% of the tracked aerosol mass within that hydrometeor species is restored to one of the regenerated aerosol categories. The number of restored aerosols equals the number of fully evaporated hydrometeors. From the restored aerosol mass and number, Eq. (5) is used to compute the median radius of the regenerated aerosols. If the median radius is less than (greater than) 1 μm, then the aerosols are returned to the submicrometer (supermicrometer) regenerated aerosol category. By not restoring aerosols back to a parent category, we can examine the spatial and temporal changes in the initial aerosol categories. It should be noted that the regenerated aerosols must be given a constant solubility fraction. A reasonable approximation could be computed as the mass-weighted solubility of the total initial aerosol distributions.
Figure 2 displays a cross section of the number concentration of submicrometer sulfate aerosols and regenerated aerosols through the main updraft of an idealized deep convective storm at 2 h into the test simulation (similar to Saleeby and Cotton 2004a). The model was initialized with 3D homogenous aerosol number concentrations of 1000 cm−3 and a median radius of 0.04 μm in the submicrometer sulfate category only. Other aerosol species were initialized with zero concentration. There is a distinct area of aerosol nucleation scavenging (reduced aerosol concentration) where the center of the updraft resides. Regenerated aerosols are concentrated near and below cloud base (2–3 km) and along the edges of the updraft (up to 11 km). It is likely that the modest amount of aerosol regeneration along the region where cloud edges would exist at mid to upper levels is a result of turbulent mixing and entrainment. Engström et al. (2008) found similar regions of aerosol regeneration along cloud boundaries because of mixing with dry air. The greatest zone of aerosol regeneration is to the rear of the storm (left side), where the convective downdraft resides and enhanced subsidence increases evaporation of hydrometeors.
c. Heterogeneous ice nucleation
It should be noted that the DeMott formula provides the maximum number of activated IN for a given temperature. Once the formula is applied at a certain model grid point it cannot be directly reapplied at this location in the subsequent model time step unless conditions are colder or more saturated so as to support additional nucleation; otherwise, overnucleation of IN occurs. To prevent overnucleation, the number of activated IN are tracked within the model. The IN tracking variable is treated as a new 3D scalar variable with predictive tendencies computed accordingly throughout the model. By knowing the number of activated and unactivated IN at a given location, we can determine if additional ice nucleation should occur for the given ambient conditions.
It should be noted here that, while the DeMott formula is not active in water subsaturated conditions, the microphysics model simulates contact nucleation, homogeneous freezing of cloud droplets, and homogeneous freezing of deliquesced, but unactivated, haze particles (Walko et al. 1995). Furthermore, the user retains the option to use the Meyers et al. (1992) formula, which allows water subsaturated activation of IN.
d. Sea salt model
O’Dowd et al. (1999) compiled these relationships for wind speeds from 2 to 17 m s−1, Fan and Toon (2011) presented sea salt emissions for wind speeds up to 20 m s−1, and Smith et al. (1993) provided spume emissions for winds speeds up to 32 m s−1. As such, we apply an upper wind speed limit of 20 m s−l for the film and jet modes and 32 m s−l for the spume mode so as to prevent overproduction of sea salt in high wind conditions. When implementing Eq. (7) for sea salt number concentration, we apply these values to the lowest model level above ground. If mixing or deposition reduces the salt concentrations at the surface, we apply a time weighted tendency function, acting on a time scale of
Figure 4 displays a vertical cross section of the number concentration of particles in the film sea salt mode resulting from emissions due to strong surface winds associated with convective downdraft outflow over an ocean surface (the same test simulation as used in Fig. 2, but here with an ocean surface). These results occurred during the mature phase of the convection when near-surface horizontal winds were strong. The top (bottom) panel displays the concentrations that result without (with) the maximum wind speed limit of 20 m s−1. There is a maximum source region of sea salt particles near the peak in the surface wind speed, and some of the emitted particles are drawn into the updraft. Without the wind speed limit, number concentrations become twice as large.
e. Dust aerosol source model
RAMS soil type and characteristics for soil dust particle lofting.
RAMS vegetation type and roughness length used for dust lofting suppression (based on TAI for summer season).
f. Aerosol wet deposition (precipitation scavenging)
This equation set [Eq. (16)] computes a collection efficiency value based on single aerosol and raindrop sizes; however, in the absence of a bin model, the RAMS bulk microphysics model uses hydrometeor gamma distributions and aerosol lognormal distributions. To apply the collection efficiency and scavenging coefficient equations to RAMS, we must use the mean raindrop diameter for
For verification, Fig. 6 displays scavenging rates for aerosol particle collection at a rainfall rate of 1 mm h−l. These are in good agreement with Wang et al. (2010) and Seinfeld and Pandis (2006). A demonstration of scavenging is shown in Fig. 7 for the collection of 3-μm diameter dust aerosols by precipitation hydrometeors along a transect through the main updraft within our deep convection simulation. We have isolated the precipitation scavenging process by not allowing dust to be removed by nucleation scavenging. Figure 7a (Fig. 7b) reveals dust number concentrations near the main updraft of the storm without (with) scavenging. The initial dust concentration vertical profile can be seen in the lower levels of the undisturbed region to the right of the updraft. Without scavenging, these large dust particles are transported from the boundary layer into the updraft and diverge into the anvil region. With active scavenging, precipitation in the updraft removes the dust, thereby preventing dust from reaching high concentrations at upper levels. Though not shown, plots of the scavenging of smaller particles with lower scavenging rates showed less aerosol removal and more transport to the anvil. It is important to also note that aerosols subject to precipitation scavenging are tracked within hydrometeor species and can be regenerated by hydrometeor evaporation.
g. Aerosol dry deposition (gravitational settling)
Figure 8 displays the aerosol dry deposition velocities from gravitational settling and deposition onto water and vegetation for a range of aerosol sizes. This plot agrees well with the results from Slinn and Slinn (1980) for deposition onto water, and from Slinn (1982) and Zhang et al. (2000) for deposition onto vegetation. Note that the gravitational settling velocity of submicrometer-diameter particles in the free atmospheric is substantially lower than surface deposition. The increase in surface dry deposition of particles >~1 μm in diameter is from the increased effects of inertial impaction.
h. Aerosol direct radiation effects
An aerosol radiative transfer scheme, implemented by Stokowski (2005) into RAMS 4.3, has been applied to the nine aerosol species in RAMS 6.0. This scheme runs interactively with the hydrometeor-sensitive two-stream radiation model of Harrington (1997) that computes the absorption and scattering of primary atmospheric gases (Ritter and Geleyn 1992) and hydrometeors (Mie 1908) across eight radiation bands. Mie theory is also applied to the aerosol distributions to compute their impact on the optical depth (
An idealized simulation was run to assess the aerosol radiation scheme in a controlled environment. Dust layer concentrations for the submicrometer and supermicrometer modes (Fig. 9a) were approximated from the vertical profiles of aerosols shown in DeMott et al. (2003). The previously used thermodynamic sounding was applied, though initial winds were set to zero to minimize short-term mixing of the aerosol layer. The solar angle was set at 65°, and incoming solar radiation at the top of the aerosol layer (4 km) is ~1100 W m−2. Figure 9b displays the radiative impact of dust particles in a noncloudy atmosphere after 1 h. The radiative impacts of dust lead to an increase in the heating rate in the dust layer of ~0.2 K h−1. This falls within the range of heating rates shown by Carlson and Benjamin (1980) when integrated over a full solar day.
3. Testing of new modules
Recent developments described herein have been tested in simulated cases of precipitating stratocumulus clouds, deep convection, and winter orographic precipitation. In these cases, we examined the aerosol sensitivity with regard to 1) aerosol solubility, 2) aerosol regeneration, 3) precipitation scavenging, 4) nucleation scavenging, and 5) the DeMott ice nucleation scheme.
The stratocumulus simulations (referred to as ATEX) were initialized horizontally homogeneous with a sounding from the Atlantic Trade Wind Experiment (ATEX) experiment (Stevens et al. 2001). Simulations were run in 2D for 24 h with periodic boundary conditions, 200-m horizontal grid spacing, 50-m vertical grid spacing, and an ocean surface with SST of 298 K. A sample cross section of the precipitating stratocumulus field is shown in Fig. 10a. Simulations of deep convection (referred to as STORM) were initialized horizontally homogeneous with a high CAPE sounding suitable for producing a supercell thunderstorm; this is the same set of initial conditions from Saleeby and Cotton (2004a). The storm was simulated for 2 h with 1-km horizontal grid spacing, 100-m vertical grid spacing at the surface stretched to 1000 m aloft, and convection was initiated with a 2-K warm bubble. A sample cross section through the developed supercell is shown in Fig. 10b. Last, we ran the winter orographic snowfall experiments (referred to as TOPO) for 42 h over the central mountains of Colorado for a snowfall event occurring 12–13 February 2010, following Saleeby et al. (2013). For these simulations, we initialized and boundary nudged with the Global Forecast System reanalysis, triple nested our model domain down to 3-km horizontal grid spacing, used 75-m vertical grid spacing at the surface stretched to 800 m aloft, and focused the fine mesh grid on the Park Range of Colorado. A cross section through a representative orographic cloud is displayed in Fig. 10c; cross-barrier flow is left to right. All simulations were run with the two-moment RAMS microphysics described herein.
For each simulation, aerosols were initialized with a vertically decreasing profile of ammonium sulfate aerosols with 0.04 micrometers median radius [similar to Saleeby et al. (2013)]. Initial maximum aerosol concentrations were 1000 cm−3 for the ATEX and STORM simulations and 1500 cm−3 for TOPO. The higher concentration for the TOPO simulations was set to that used in the simulations by Saleeby et al. (2013). For direct comparison between the Meyers and DeMott IN schemes, a common IN concentration profile was initialized that scales with the decrease in density with height with a maximum concentration of 10 L−l. In the control simulations aerosols are 90% soluble, removed via nucleation and precipitation scavenging, and regenerated via hydrometeor evaporation. Heterogeneous ice nucleation is represented by the Meyers scheme.
For each event type (ATEX, STORM, and TOPO), five sensitivity tests were performed in which a single aerosol effect was modified relative to the control simulation: 1) aerosol solubility was reduced from 90% to 5%, 2) aerosol regeneration was turned off, 3) aerosol precipitation scavenging was turned off, 4) aerosol nucleation scavenging was turned off (aerosol nucleation was supersaturation limited such that droplet number concentration cannot exceed aerosol number concentration), and 5) the IN scheme was changed from Meyers to DeMott. For these five sensitivity experiments, we will focus the discussion on their impact on precipitation rates. Figure 11 reveals histograms of the spatial and temporal summation of the counts of grid cells that fall within bins of light, moderate, and heavy precipitation rate (mm h−1). Note from the panel labels that cases vary by row and precipitation rate varies by column; further, the scales of gridcell count vary in each panel for visualization purposes. The percentage change relative to the control simulation is displayed above each sensitivity test histogram.
One of the most noticeable characteristics drawn from these histograms is that the various aerosol schemes are of differing importance among simulated cloud systems. In the ATEX simulations, both the low solubility and no-regeneration simulations lead to substantial percentage increases in all precipitate rate bins. Both of these experiments lead to production of fewer but larger nucleated cloud droplets, relative to the control, that produce an efficient warm rain process and greater precipitation production. In the test with no precipitation scavenging, more aerosols remain available for nucleation. This leads to more numerous cloud droplets and slight precipitation suppression, though the suppression is small. It should be noted that the median radius of the initial aerosol distribution is in the size range where precipitation scavenging is limited. Had we initialized with supermicrometer-sized aerosols or much smaller aerosols, this scavenging effect would likely have been larger, but the impact of solubility and nucleation scavenging would be substantially altered. In the test with no nucleation scavenging, there is a large increase in lightly precipitating grid cells and a decrease in heavy precipitation. Without nucleation scavenging, the model tends to have higher cloud droplet concentration over a greater area, thus leading to suppression of heavier precipitation and an increase in the frequency of light precipitation. The DeMott IN scheme is not tested in the ATEX case since all clouds are below the freezing level.
In the STORM simulations, only the regeneration and nucleation scavenging tests produce precipitation rate changes greater than a few percent. Without aerosol regeneration, the environment remains cleaner and leads to a more efficient warm rain process. This results in fewer lightly and moderately precipitating grid cells and a greater number of heavily precipitating grid cells. Without nucleation scavenging, there is the potential for enhanced cloud droplet production, which leads to droplets of smaller size. This response leads to suppression of precipitation, with the greatest impact on heavy precipitation. The DeMott IN test shows very little change in this case since heterogeneous ice nucleation produces few ice crystals in comparison with homogeneous freezing of cloud droplets lofted above the −40°C level by the updraft. The impact of these aerosol parameterizations in the STORM case is small relative to the percentage impact in the ATEX case. The STORM case is strongly dynamically forced, thus making these particular aerosol parameterizations of secondary importance.
In the TOPO simulations, the model responds most noticeably to the choice of IN parameterization compared to the other aerosol tests. In a winter orographic precipitation environment, cloud nucleating aerosols primarily affect precipitation by modifying the riming efficiency of snow falling through clouds of supercooled water. This may have a substantial localized effect and potentially induce changes in the spatial distribution of precipitation (Saleeby et al. 2009, 2013). When switching from the Meyers to the DeMott IN scheme, there is a substantial decrease in heavy precipitation. Figure 12 displays plan views of the total accumulated precipitation across the domain as well as the difference in total precipitation. Along the ridgeline and windward slope of the Park Range in the center of the domain, the accumulated precipitation is reduced upward of 20%. A comparison between these tests and those from Saleeby et al. (2013) suggests that total precipitation resulting from the DeMott IN parameterization may fall more inline with Snowpack Telemetry (SNOTEL) observations within the region of maximum snowfall.
4. Summary and conclusions
Recent developments in the CSU-RAMS model, version 6.0, provide for a more comprehensive aerosol model that extends beyond the capabilities of previous aerosol–microphysics–related research (e.g., Saleeby et al. 2009, 2013; van den Heever et al. 2006, 2011). This work has sought to develop and describe a more unified version of the aerosol model embedded within RAMS and builds upon the prior work by various authors and colleagues. The aerosol model represents nine aerosol species: submicrometer and supermicrometer modes of ammonium sulfate, mineral dust, and regenerated aerosols and three modes of sea salt. Aerosol concentrations can be prescribed and/or the user can make use of the dust and sea salt source models for emissions of these species. Each of these aerosol species may compete for activation and subsequent nucleation of new cloud droplets. All particles >0.5 μm, except sea salt, may potentially act as heterogeneous IN. Further, each aerosol species may have a distinct solubility, contribute to the radiation budget, and undergo dry deposition (gravitational settling), wet deposition (precipitation scavenging) and evaporative regeneration. Figure 13 offers a schematic depicting the aerosol-related sources, sinks, transfer mechanisms, and radiation effects.
Sensitivity tests of the influence of aerosol solubility, nucleation scavenging, precipitation scavenging, and regeneration were performed for simulations of stratocumulus clouds, deep convection, and winter orographic precipitation. The Meyers and DeMott heterogeneous ice nucleation schemes were also compared. Results indicate that in cloud systems with active warm rain processes, the representations of aerosol nucleation scavenging and regeneration are most influential among these five tested aerosol parameterizations, though, in weakly forced clouds, aerosol solubility can be important. In deep convection, the dynamical influence overwhelms these secondary aerosol effects and the degree of impact is less than in shallow clouds. The impact of the DeMott ice nucleation scheme is limited in deep convection since other ice nucleation processes are dominant. However, in winter orographic precipitation, the DeMott scheme reduces orographic precipitation and appears to bring snowfall accumulations more in line with observations. In future work, we will continue to refine the treatment of aerosols and work to improve the simulation of their physical impacts on cloud and climate systems.
Acknowledgments
This work was supported by the National Science Foundation Division of Atmospheric Sciences Grants 1005316 and 1005020. We thank Robert B. Seigel for his work with the dust source model and Fig. 5 and Leah Grant for testing the aerosol radiation model and for Fig. 9. We also thank Dr. Paul DeMott for his insightful guidance in implementing the heterogeneous ice nucleation parameterization. (All three contributors are affiliated with the Department of Atmospheric Science at Colorado State University.)
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