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  • View in gallery

    Model terrain height (filled contours) and the five north–south P-3 flight legs and the southwest–northeast Convair flight leg (white lines). The inset shows (bottom) the underlying model terrain and (top) the simulated vertical motion along the P-3 flight-leg 2 (second from the left).

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    Plot of as a function of (black line). The value of for is naught. The filled circles are collection efficiency data as a function of aspect ratio from Connolly et al. (2012) normalized such that the value at is unity.

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    The lowest-model-level radar reflectivity field at 0000 UTC 14 Dec 2001.The model domain is the color-filled region. The gray wind barbs are at 850 hPa from the simulation, and the red wind barbs are from the NCEP 850-hPa analysis. The black star marks the University of Washington sounding location, and the inset shows the 0000 UTC 14 Dec 2001 sounding temperature (red solid line), dewpoint temperature (red solid line), model-derived temperature (gray solid line), and the model-derived dewpoint temperature (gray dashed line). The sounding data and NCEP analysis winds are from Garvert et al. (2005a).

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    (a) Radar reflectivity from the WSR-88D at Portland at 0002 UTC 14 Dec 2001. Figure previously published in Milbrandt et al. (2008). (b) The lowest-model-level reflectivity field at 0000 UTC 14 Dec 2001 for the region shown in (a). The magenta arrows point to the mouth of the Columbia River for orientation.

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    The 18-h (1400 UTC 13 Dec–0800 UTC 14 Dec 2001) liquid-equivalent accumulated precipitation from ISHMAEL (filled contours) and from station observations (filled diamonds). The black contour lines are terrain height values of 0.25 and 1 km. The general locations of the Willamette valley and Umpqua River valley are shown. The inset is a scatterplot of the observed vs model precipitation with one observed data point greater than 120 mm removed.

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    (a)–(c) Ice mass mixing ratios (filled contours), (d)–(f) volume-weighted densities (filled contours) and number-weighted aspect ratios (contour lines; unitless), and (g)–(i) mass-weighted maximum diameters (filled contours) and mass-weighted terminal fall speeds (contour lines; m s−1) along the Convair flight track at 0000 UTC 14 Dec 2001. The dashed red lines in (a) indicate three of the Convair flight legs, the dashed black line in (a) is the melting level, and the thin and thick solid black contour lines in (a) show vertical motions of and , respectively. The thin and thick black contour lines in (b) show cloud water mixing ratios of 0.5 and 1 g kg−1, respectively. The magenta contour lines in (b) show rainwater mixing ratios of 0.5 g kg−1. Black asterisks in (d) indicate where broad-branched crystals and dendrites were observed. Black diamonds in (e) indicate where columns, capped columns, and needles were observed, and lime circles in (e) indicate where graupel was observed. Black stars in (f) indicate where aggregates were observed. Observations are from Garvert et al. (2005b) and Woods et al. (2005).

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    Ice size distributions for PN ice (gray), CN ice (red), and aggregates (blue) along leg 1 of the Convair flight track (topmost red dashed line in Fig. 6a) at 0030 UTC 14 Dec 2001. The black line shows the total (PN ice + CN ice + aggregates) average size distribution from ISHMAEL, and the black circles are observations from Garvert et al. (2005b).

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    (a) Model-derived 18-h accumulated precipitation from CTRL minus observed 18-h accumulated precipitation at all station locations. (b) Model-derived 18-h accumulated precipitation from CON-DEN minus CTRL at all station locations. Arrows indicate where CTRL improves precipitation prediction compared to CON-DEN in the Willamette and Umpqua River valleys. The stations circled in green in (b) are where CTRL improve precipitation prediction on the leeward side of the Cascades. The contour lines show terrain heights of 0.25, 0.5, 1, and 1.5 km, contoured from light gray to black. Accumulated precipitation is analyzed along two cross sections (solid red lines) in Fig. 9. The more northern cross section is the Convair flight track.

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    The 2-h (2300 UTC 13 Dec–0100 UTC 14 Dec 2001) accumulated precipitation for CTRL (black), MY2 (gray), THOMPSON (blue), CON-DEN (red), and CON-HAB (violet) along (a) the Convair flight track and (b) the southern red line in Fig. 8. The approximate locations of the Coast and Cascade Mountain Ranges are labeled in (b).

  • View in gallery

    (a) The 2-h (2300 UTC 13 Dec–0100 UTC 14 Dec 2001) average total ice (accounting for , , and ) mass-weighted fall speeds and standard deviations (plotted for every other point for visibility) for CTRL (black) and CON-DEN (red) along the first grid box above the melting level along the Convair flight track. (b) The 2-h average mass-weighted fall speeds and standard deviations for ice one (black), ice two (blue), and aggregates (salmon) from CTRL. The gray line indicates the 2-h-average w and standard deviations from CTRL. The green line shows the 2-h accumulated precipitation. (c) As in (b), but for the CON-DEN simulation.

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    The 18-h total accumulated precipitation from 1400 UTC 13 Dec to 0800 UTC 14 Dec 2001 along the Convair flight track for all simulations (see Table 1) and the 18-h ice-only (equivalent liquid) accumulated precipitation.

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    Correlation coefficients between terrain height and 18-h total accumulated precipitation as a function of longitudinal shift for CTRL (black), MY2 (gray), CON-DEN (red), CON-HAB (violet), and THOMPSON (blue). A positive longitudinal shift means that the terrain is shifted downwind (to the east) relative to the precipitation, and therefore, correlation at a positive longitudinal shift implies that local maxima in precipitation occur downwind of peaks in terrain.

  • View in gallery

    (a) The 2-h (from 2300 UTC 13 Dec to 0100 UTC 14 Dec 2001) vertically averaged bulk vapor growth rate divided by number mixing ratio for PN ice (black) and CN ice (red) for CTRL (solid) and COL (dashed). Averaging is done along the Convair cross section. (b) As in (a), but for number-weighted aspect ratio. The dotted gray line in both (a) and (b) indicates the −20°C height.

  • View in gallery

    Histograms of (a) mass-weighted fall speeds, (b) number-weighted aspect ratios, (c) mass-weighted maximum diameters, and (d) volume-weighted densities for CTRL (black), COL (red), CON-DEN (gray), and CON-HAB (blue). Values are shown for ice one (solid lines), ice two (dashed lines), and aggregates [dotted; shown in (a) and (c) only].

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Impacts of Ice Particle Shape and Density Evolution on the Distribution of Orographic Precipitation

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  • 1 National Center for Atmospheric Research, Boulder, Colorado
  • | 2 The Pennsylvania State University, University Park, Pennsylvania
  • | 3 National Center for Atmospheric Research, Boulder, Colorado
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Abstract

An IMPROVE-2 orographic precipitation case is simulated using the Ice-Spheroids Habit Model with Aspect-Ratio Evolution (ISHMAEL) microphysics. In ISHMAEL, the evolution of ice particle properties such as mass, shape, size, density, and fall speed are predicted. These ice particle properties along with the ice size distributions from ISHMAEL and model-derived spatial distribution of accumulated precipitation are compared to observations. ISHMAEL predicts planar and columnar particles at spatial locations that agree with observations. Sensitivity simulations are used to explore the impact of predicting ice particle shape evolution on orographic cloud properties and precipitation compared to the traditional approach of representing snow and graupel using separate categories with conversion from snow to graupel during riming. High biases in both IWCs aloft and surface precipitation accumulation occur in the Umpqua River valley using separate snow and graupel categories because snow that does not convert to graupel is advected over the Coast Range and precipitates out in the valley. Improvements in IWCs aloft and surface precipitation using ISHMAEL occur from both predicting various vapor-grown habits and predicting the impact of partial riming on ice particle properties. Compared to traditional microphysics schemes, ISHMAEL also produces less spatial variability in accumulated precipitation.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Anders A. Jensen, ajensen@ucar.edu

Abstract

An IMPROVE-2 orographic precipitation case is simulated using the Ice-Spheroids Habit Model with Aspect-Ratio Evolution (ISHMAEL) microphysics. In ISHMAEL, the evolution of ice particle properties such as mass, shape, size, density, and fall speed are predicted. These ice particle properties along with the ice size distributions from ISHMAEL and model-derived spatial distribution of accumulated precipitation are compared to observations. ISHMAEL predicts planar and columnar particles at spatial locations that agree with observations. Sensitivity simulations are used to explore the impact of predicting ice particle shape evolution on orographic cloud properties and precipitation compared to the traditional approach of representing snow and graupel using separate categories with conversion from snow to graupel during riming. High biases in both IWCs aloft and surface precipitation accumulation occur in the Umpqua River valley using separate snow and graupel categories because snow that does not convert to graupel is advected over the Coast Range and precipitates out in the valley. Improvements in IWCs aloft and surface precipitation using ISHMAEL occur from both predicting various vapor-grown habits and predicting the impact of partial riming on ice particle properties. Compared to traditional microphysics schemes, ISHMAEL also produces less spatial variability in accumulated precipitation.

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Corresponding author: Anders A. Jensen, ajensen@ucar.edu

1. Introduction

The Pacific Northwest Coast and Cascade Mountains are one of the wettest regions in the United States in January (Durre et al. 2013), and this wintertime rain and snow contributes significantly to yearly precipitation totals that on average exceed 2.5 m of equivalent liquid (Arguez et al. 2012). This considerable amount of precipitation in mountainous terrain necessitates forecasts for general hydrology, floods, and avalanches. Some of the largest uncertainties associated with predicting these hazards are related to precipitation forecasts. For example, uncertainties associated with predicting rain-on-snow flooding events include forecasts of precipitation totals and precipitation phase; those variables among other environmental factors determine the amount of snowmelt and runoff (McCabe et al. 2007). Avalanche risk assessment depends on predictions of new snow accumulation and spatial distribution, which partially control the stability of newly accumulated snow (Foehn et al. 2002). Thus, improvements to precipitation prediction would provide enhanced guidance for weather-hazard forecasts.

One way to improve precipitation forecasts is by advancing model representations of the rain and ice particles that produce precipitation. This can be achieved by constraining hydrometeor properties (i.e., for ice: size, habit type, density, fall speed) with observations. Microphysical observations in mountainous terrain have been targeted in field campaigns (e.g., Hobbs 1975; Bond et al. 1997; Houze et al. 2017), including in the first and second Improvement of Microphysical Parameterization through Observational Verification Experiments (IMPROVE-1 and IMPROVE-2; Stoelinga et al. 2003). Studies using observations from the IMPROVE campaigns have revealed that the spatial distribution of model-derived accumulated precipitation depends critically on the representation of ice particle fall speeds (Colle et al. 2005; Garvert et al. 2005b; Woods et al. 2007; Milbrandt et al. 2008, 2010; Morrison et al. 2015). Many traditional bulk microphysics schemes (e.g., Ferrier 1994; Milbrandt and Yau 2005a,b; Morrison et al. 2005; Hong and Lim 2006; Thompson et al. 2008; Mansell et al. 2010) parameterize ice using predefined categories, such as cloud ice, unrimed precipitating ice (snow), and rimed precipitating ice (graupel, hail, or both). Rimed ice particles are parameterized as being more compact for a given mass (having a smaller maximum diameter and a larger density) and have greater fall speeds for a given size than unrimed ice, in agreement with observations of snow and graupel (e.g., Locatelli and Hobbs 1974). However, this traditional approach cannot represent the wide range of different particle types associated with partial riming and transitional particle types between snow and graupel. Schemes with separate snow and graupel categories also require a method to convert snow to graupel as it collects rime, which is done by transferring mass directly and instantaneously between these categories. This abrupt conversion is unphysical since it does not account for partially rimed ice and the gradual transition from snow to graupel, yet model-derived spatial precipitation distributions are sensitive to this conversion because it determines the relative concentrations of faster-falling graupel and slower-falling snow (Garvert et al. 2005b; Colle et al. 2005; Morrison and Grabowski 2008). Simulations of orographic precipitation cases, where windward vertical motions reached 2–3 m s−1 (Garvert et al. 2005b), revealed that the amount of leeward precipitation depends on the amount of snow left unconverted to graupel. Simulations using the Reisner-2 scheme (Reisner et al. 1998) with modification by Thompson et al. (2004) of an IMPROVE-2 case showed that tuning the riming threshold needed to convert snow to graupel had a greater benefit to the precipitation forecast than changing physical snow properties such as the snow size distribution assumptions and fall speed (Colle et al. 2005).

Microphysics schemes that separate snow and graupel also generally parameterize the size, fall speed, and density of unrimed precipitating ice using observations of one habit type, usually dendrites or aggregates. These schemes exclude the various unrimed ice particle types that exist in nature and their wide range of fall speeds that depend on their particle properties (Kajikawa 1972). The choice of unrimed ice habit type and fall speed impacts model-derived spatial precipitation distribution in orographic environments (Woods et al. 2007). Model assumptions for unrimed snow particle shape and density have been shown to be unrepresentative of the variety of particle types observed during IMPROVE-2, which included assemblages of planar ice, aggregates, dendrites, broad-branched crystals, and columns. This misrepresentation of unrimed ice has been linked to model overestimates of in-cloud ice water contents and leeward precipitation rates (Garvert et al. 2005b; Woods et al. 2005). Various unrimed habits could be included in traditional microphysics schemes (e.g., Straka and Mansell 2005), but each habit type would require a separate category, and therefore adds considerable complexity and computational cost. Other schemes, such as the Regional Atmospheric Modeling System (RAMS; Walko et al. 1995; Meyers et al. 1997), have options to change habit based on temperature, but these methods also suffer from abrupt shifts in size and fall speed when particles are converted between habit types.

Efforts to improve the representation of ice particle properties within traditional categories have included diagnosing snow density as a function of size (Milbrandt et al. 2008; Thompson et al. 2008), predicting rime density based on liquid and ice properties (Mansell et al. 2010; Milbrandt and Morrison 2013), and including an ad hoc increase in snowfall speed due to rimed snow not converted to graupel (Thompson et al. 2008). Such improvements can lead to better ice property representation for a given ice category, but they do not remove sensitivities to the snow–graupel conversion process. Moreover, these improvements cannot account for the variety of vapor-grown habits observed during IMPROVE-2. Lin and Colle (2011) developed a parameterization with one precipitating ice category and diagnosed riming intensity and its impact on fall speed. This approach removes the need for conversion from rimed snow to graupel. By predicting the impact of partial riming on snow fall speeds, snow water contents aloft were reduced compared to other bulk microphysics schemes because of an increase in snow fallout and a reduction in vapor growth aloft, in better agreement with observations from IMPROVE-2 (Lin and Colle 2011). Their riming intensity is diagnosed from the ice and liquid water contents, and thus, it depends minimally on ice particle properties. Another limitation is that this approach cannot address the horizontal advection of rimed ice that is often important for orographic precipitation cases (Colle and Zeng 2004) because riming intensity is diagnosed.

Recently developed microphysics schemes (Chen and Lamb 1994, 1999; Hashino and Tripoli 2007; Harrington et al. 2013a; Morrison and Milbrandt 2015; Jensen et al. 2017) have attempted to better represent ice particle properties by adding prognostic ice variables, allowing for the smooth evolution of particle properties. Schemes that include a parameterization for the increase in ice particle fall speed due to riming, either in an ad hoc way (Thompson et al. 2008), diagnostically (Lin and Colle 2011), or based on prognostic quantities (Morrison and Milbrandt 2015), reduce the high bias in leeward model-derived accumulated precipitation (Morrison et al. 2015). However, the above studies did not address how the evolution of ice particle properties that depend on habit (shape) impact orographic precipitation. Ice particle vapor growth and riming rates strongly depend on ice particle shape (Magono and Lee 1966; Takahashi and Fukuta 1988; Takahashi et al. 1991; Fukuta and Takahashi 1999), through the capacitance for vapor growth and the collection kernel for riming. Snow particles gradually change their shape, density, and fall speed as mass is added during riming. The resulting transition to graupel particles, therefore, causes changes in particle properties that feed back with microphysical growth rates. This indicates that ice particle shape and density evolution may have important impacts on orographic cloud characteristics and precipitation distributions, yet these impacts are presently unknown.

The predicted particle property method developed by Jensen et al. (2017, 2018), called the Ice-Spheroids Habit Model with Aspect-Ratio Evolution (ISHMAEL), differs from traditional bulk microphysics schemes in that it evolves bulk ice properties (mass, shape, maximum diameter, density, and fall speed) freely in time due to microphysical processes (vapor growth, sublimation, riming, and melting). Predicting ice particle shape evolution allows for the representation of various habits with different shapes, sizes, densities, and fall speeds and for the representation of partially rimed ice without needing to convert ice between categories. Fall speeds in ISHMAEL are calculated from ice particle properties, directly impacting the spatial distribution of model-derived accumulated precipitation as will be shown. Hence, ISHMAEL provides an appropriate way to study the impacts of ice particle property evolution on orographic precipitation. In this study, ISHMAEL is used to test the hypothesis that predicting ice particle properties in a microphysics scheme will affect the spatial distribution of accumulated precipitation compared to traditional microphysics schemes. We also test whether the ISHMAEL simulations are more representative of the orographic system, because the ice particle properties that evolve in ISHMAEL because of vapor growth and riming will be more representative of those observed.

In this study, a well-observed IMPROVE-2 case is simulated and analyzed, providing a test of ISHMAEL for an orographic precipitation case. Sensitivity tests are used to highlight the impacts of model assumptions made in both traditional microphysics schemes and in ISHMAEL. Differences in the spatial distribution of ice particle properties aloft and their influence on the surface precipitation distribution are explored for simulations using traditional ice categories with conversion between snow and graupel and for simulations where ice particle shape evolves during riming. In sections 2 and 3, the IMPROVE-2 case, the simulation setup, and ISHMAEL microphysics are briefly described. In section 4, a baseline simulation of the case using ISHMAEL is analyzed and compared to observations, and in section 5, sensitivity studies are described.

2. The IMPROVE-2 13–14 December 2001 case

a. Case description

The synoptic setup for the 13–14 December 2001 orographic precipitation event has been described in detail by Garvert et al. (2005a). The National Centers for Environmental Prediction (NCEP) reanalysis data (not shown) revealed that at 0000 UTC 14 December 2001 a 500-hPa trough was located just off the coast of Oregon, a 984-hPa surface low was centered on Vancouver Island, and an occluded front extended from the surface low southwestward to just off the coast of Oregon (Garvert et al. 2005a). Significant stratiform precipitation was produced from both synoptic forcing and the southwesterly cross-barrier flow across the Coast and Cascade Mountain Ranges that generated orographic lift.

b. Observations

Data obtained during the case study included microphysical measurements from the University of Washington Convair-580 aircraft and a National Oceanic and Atmospheric Administration (NOAA) WP-3D Orion (P-3) aircraft, including ice particle habits, ice size distributions, ice water contents (IWCs), and cloud liquid water contents (LWCs). These data were taken on both north–south and southwest–northeast flight tracks (Fig. 1), the latter of which were roughly parallel to the 850-hPa winds at 0000 UTC 14 December 2001. The Convair had a Particle Measuring Systems (PMS) two-dimensional cloud (2D-C) probe (Knollenberg 1976) and a Stratton Park Engineering Company (SPEC) high-volume precipitation spectrometer (HVPS; Lawson et al. 1993). These instruments were used to determine ice particle habit types and size spectra. Woods et al. (2005) used these data along with assumed mass–dimensional (mD) relationships to estimate average IWCs along the Convair flight legs. Thus, errors in the IWCs arise from instrumentation errors, particle classification errors, and the degree to which the observed particles can be characterized using mD relationships. Precipitation accumulation measurements were made at several locations spanning the Coast and Cascade Ranges. The undercatchment of snow was likely an issue at higher elevations in the Cascade Range because of both high winds and possible riming on the instruments, which would cause a low bias of 20%–50% in observed precipitation accumulation (Rasmussen et al. 2012).

Fig. 1.
Fig. 1.

Model terrain height (filled contours) and the five north–south P-3 flight legs and the southwest–northeast Convair flight leg (white lines). The inset shows (bottom) the underlying model terrain and (top) the simulated vertical motion along the P-3 flight-leg 2 (second from the left).

Citation: Journal of the Atmospheric Sciences 75, 9; 10.1175/JAS-D-17-0400.1

3. The IMPROVE-2 simulation

a. Simulation setup

This study uses the Advanced Research version of WRF, version 3.8.1 (Skamarock et al. 2008). The WRF Model employs fully compressible and nonhydrostatic dynamics. The governing equations are solved using a third-order Runge–Kutta method. The horizontal domain is 1200 km × 830 km with 3-km grid spacing. This horizontal grid spacing is currently used by high-resolution operational models [e.g., the High-Resolution Rapid Refresh (HRRR) model], and it is therefore useful to study model sensitivities of the spatial precipitation distribution at this resolution. The 3-km grid spacing is sufficient to produce orographically induced vertical motions of magnitude 2–3 m s−1 along the P-3 flight legs (Fig. 1) and across the Coast and Cascade Mountains (shown later); 4-km grid spacing has also been shown to produce similar quantitative precipitation forecasts (QPFs) compared to a 1.33-km grid using the Global Environmental Multiscale (GEM) model (Milbrandt et al. 2008). Seventy-two vertical levels are used, and the vertical grid spacing is stretched with a higher density of vertical levels near the surface. The top and bottom domain boundaries are rigid, and a Rayleigh damping layer is applied to the top 5 km. The model is run using a 5-s time step for 36 h starting at 0000 UTC 13 December 2001, allowing for adequate spinup before the analysis period, which begins at 1400 UTC 13 December 2001. Meteorological fields in the model are initialized from NCEP North American Regional Reanalysis (NARR) data (NCEP 2005; Mesinger et al. 2006). NARR data are provided at 29 pressure levels and 32-km horizontal grid spacing. Both the lateral and lower boundary conditions were updated every 6-h during the simulations. A sensitivity simulation (not shown) using the Global Forecast System (GFS) final (FNL) analysis as initial and boundary conditions, used by Morrison et al. (2015), reveal that both the NARR and FNL initial conditions produce comparable precipitation statistics and distribution.

Model parameterizations used in this study include a 1.5-order turbulence closure scheme, the Noah land surface model, the Rapid Radiative Transfer Model for GCMs (RRTMG; Iacono et al. 2008), and ISHMAEL microphysics. Sea surface temperatures are updated every 6 h. Both shortwave and longwave radiation are coupled to ISHMAEL microphysics. A brief description of ISHMAEL microphysics is provided below.

b. ISHMAEL microphysics

The ISHMAEL (Melville 1851) is described in detail by Jensen et al. (2017). Ice in ISHMAEL is modeled using spheroids as a general shape; both a major and minor axis length can evolve for all ice particles, and therefore, implicit assumptions regarding the minor axis that are embodied in mD relationships are avoided. Spheroids are characterized by two dimensions, the c- and a-axis lengths ( and , respectively), where the maximum diameter of an oblate (prolate) spheroid is and the aspect ratio, , of an oblate (prolate) spheroid is <1 (>1).

In ISHMAEL, changes in spheroidal ice particle mass ,
e1
from growth processes (e.g., vapor growth and riming) must be linked to changes in , , and the effective particle density (Chen and Lamb 1994; Jensen et al. 2017). This methodology differs from the traditional approach of using mD relationships to link changes in mass and particle maximum diameter for a specific ice category. Linking changes in mass to changes in particle shape allows, for example, planar habits at −15°C to grow by vapor deposition preferentially along the major axis and to collect rime along the minor axis. Planar habits thicken as they collect rime, which causes to increase and fall speed to increase faster than for ice growth along because of aerodynamics (Heymsfield 1982; Takahashi and Fukuta 1988). This fall speed increase is captured in both single ice particle (Jensen and Harrington 2015) and bulk (Jensen et al. 2017) models.
In bulk microphysics schemes, growth equations are integrated over a size distribution. In ISHMAEL, this integration is simplified by formulating a relationship between and so that bulk integration occurs over a single axis length. A relationship between and results from differentiating [Chen and Lamb 1994, their Eq. (36)], using the mass-distribution hypotheses that relate changes in to changes in during growth [e.g., Chen and Lamb 1994, their Eq. (26a)], and integrating in time. This yields
e2
where the power exponent is related to the growth history of the particle, and is dependent on the initial size and shape (Harrington et al. 2013a). As long as the relationship between and , where t is time, is tracked during growth (through mass-distribution hypotheses), we can relate and to one another. The benefit of this relationship can be seen by writing mass as a function of the a axis only:
e3
where and . This equation for mass has a similar form to an mD relationship, and it can be integrated over the size distribution to compute the ice mass mixing ratio . The difference between the traditional formulation and ours is that (and therefore ) evolves in time as ice particle shape evolves.
Ice particle size distributions are assumed to follow a gamma function, where
e4
Here, is the ice number concentration, ν is the shape parameter, is the slope parameter for the distribution as a function of , and is the Euler gamma function. A value of is chosen for ISHMAEL based on comparisons to wind-tunnel data for vapor growth and riming growth rates (Harrington et al. 2013b; Jensen et al. 2017). Bulk ice properties such as number-weighted aspect ratio are computed by integrating those properties over the size distribution. For example,
e5
where is written as a function of using Eq. (2).

Similar to other two-moment microphysics schemes, mass and number mixing ratios (, with the air density) are predicted. Additionally, volume and volume times aspect ratio mixing ratios are predicted in ISHMAEL, allowing the two axis lengths and the effective density to evolve independently. Currently, three separate ice species are used in ISHMAEL. During nucleation, ice is initiated as either ice one or ice two (with mass mixing ratios and , respectively) depending on nucleation temperature: ice is initiated as ice one at planar vapor growth temperatures (e.g., −15°C) and as ice two at columnar vapor growth temperatures (e.g., −7°C). Two species are used to allow both oblate and prolate ice to exist in the same model grid volume at the same time without diluting the properties of those ice species if only a single species were used (Milbrandt and Morrison 2016). For clarity, ice one is referred to as planar-nucleated (PN) ice and ice two is referred to as columnar-nucleated (CN) ice, although after nucleation, the shapes of both ice species evolve based on process rates, and either species can become oblate or prolate.

The third ice species is aggregates , which is parameterized separately because aggregation causes abrupt changes to ice shape and density, in contrast to vapor growth and riming, which cause relatively gradual changes in particle properties. Aggregates are parameterized as oblate spheroids using a constant shape and density (Jensen et al. 2017). The aggregation efficiencies for PN ice and CN ice are modified so that processes such as the self-collection of graupel do not produce abundant aggregates. This is accomplished using weighting factors that depend on the shape and density (for details, see Jensen et al. 2017). A new parameterization for the shape dependence of aggregation is employed in ISHMAEL for all of these simulations. Values of aggregation efficiencies for ice particles in a cloud chamber with various aspect ratios were estimated by Connolly et al. (2012). Ice particle aspect ratios were also estimated from a cloud particle imager (CPI). These data are used to determine the relative decrease in aggregation efficiency that occurs for increasingly isometric particles. Aggregation efficiencies are formulated to decrease for oblate particles with (the approximate aspect ratio of individual particles at −15°C in the cloud chamber) because of particle shape being more isometric (either less branched or filled in with rime), and this is parameterized by decreasing with increasing (Fig. 2). As shown in this figure, the value of the aggregation efficiency itself (not including the collection kernel) for a thick, partially rimed particle with would be approximately 15% of the value for a dendrite with . The same parameterization is used for prolate ice particles by formulating the decrease in as a function of increasing inverse aspect ratio .

Fig. 2.
Fig. 2.

Plot of as a function of (black line). The value of for is naught. The filled circles are collection efficiency data as a function of aspect ratio from Connolly et al. (2012) normalized such that the value at is unity.

Citation: Journal of the Atmospheric Sciences 75, 9; 10.1175/JAS-D-17-0400.1

4. Baseline simulation results

The lowest model-level reflectivity field at 0000 UTC 14 December 2001 from the baseline simulation (CTRL) reveals a comma-shaped precipitation structure (Fig. 3). Both the cross-barrier flow and vertical profiles of the temperature and dewpoint temperature (Fig. 3) are well-simulated compared to sounding data and the NCEP analysis from Garvert et al. (2005a). Compared to radar observations, the model captures the broad region of precipitation east of Portland, Oregon, where reflectivity values are generally 30–35 dBZ, with pockets of reflectivity greater than 35 dBZ (Fig. 4). The liquid-equivalent 18-h (from 1400 UTC 13 to 0800 UTC 14 December 2001) accumulated precipitation1 predicted by ISHMAEL (Fig. 5) captures the lower precipitation totals from the station observations in the Willamette and Umpqua River valleys. Model-derived precipitation is higher than was observed along the ridge of the Cascades, but blowing snow may have produced undercatchment of frozen particles and a low bias in observed precipitation at higher elevations (Rasmussen et al. 2012). Model-derived precipitation is also biased high at a few locations directly on the leeward side of the Cascades. The total averaged precipitation from ISHMAEL at all of the observation locations is biased high by approximately 7 mm (Table 2), though all eight bulk microphysics schemes tested in Morrison et al. (2015) produced a high bias in averaged precipitation for this case.

Fig. 3.
Fig. 3.

The lowest-model-level radar reflectivity field at 0000 UTC 14 Dec 2001.The model domain is the color-filled region. The gray wind barbs are at 850 hPa from the simulation, and the red wind barbs are from the NCEP 850-hPa analysis. The black star marks the University of Washington sounding location, and the inset shows the 0000 UTC 14 Dec 2001 sounding temperature (red solid line), dewpoint temperature (red solid line), model-derived temperature (gray solid line), and the model-derived dewpoint temperature (gray dashed line). The sounding data and NCEP analysis winds are from Garvert et al. (2005a).

Citation: Journal of the Atmospheric Sciences 75, 9; 10.1175/JAS-D-17-0400.1

Fig. 4.
Fig. 4.

(a) Radar reflectivity from the WSR-88D at Portland at 0002 UTC 14 Dec 2001. Figure previously published in Milbrandt et al. (2008). (b) The lowest-model-level reflectivity field at 0000 UTC 14 Dec 2001 for the region shown in (a). The magenta arrows point to the mouth of the Columbia River for orientation.

Citation: Journal of the Atmospheric Sciences 75, 9; 10.1175/JAS-D-17-0400.1

Fig. 5.
Fig. 5.

The 18-h (1400 UTC 13 Dec–0800 UTC 14 Dec 2001) liquid-equivalent accumulated precipitation from ISHMAEL (filled contours) and from station observations (filled diamonds). The black contour lines are terrain height values of 0.25 and 1 km. The general locations of the Willamette valley and Umpqua River valley are shown. The inset is a scatterplot of the observed vs model precipitation with one observed data point greater than 120 mm removed.

Citation: Journal of the Atmospheric Sciences 75, 9; 10.1175/JAS-D-17-0400.1

ISHMAEL predicts large variations in the properties of PN and CN ice along the Convair flight track in agreement with observations (Fig. 6). At upper levels (400–200 hPa), PN ice evolves to be what would be considered cloud ice, with volume-weighted density values of (Fig. 6d), mass-weighted maximum diameter values of (Fig. 6g), and mass-weighted fall speed values of (Fig. 6g). At lower levels (below 400 hPa), PN ice mass mixing ratios become as large as 2 g kg−1 (Fig. 6a). This lower-level ice evolves to mass-weighted maximum diameters of 2–3 mm (Fig. 6g) and volume-weighted densities of 200–400 kg m−3 (Fig. 6d). Dendrites and broad-branched crystals were observed aloft near the crest of the Cascades and on the leeward side (Fig. 6d, black asterisks), and here, PN ice attains number-weighted aspect ratios of 0.05–0.1 (Fig. 6d), volume-weighted densities of 400–700 kg m−3 (Fig. 6d), and mass-weighted maximum diameters of 1–2 mm (Fig. 6g). PN ice evolves to become lower-density planar ice (similar to branched particles; Harrington et al. 2013b) in agreement with observations at this location. Significant riming occurs where cloud water mixing ratios exceed 0.5 g kg−1 (Fig. 6b, thick black contours near 122.2°W), and here, PN ice evolves to become similar to partially rimed ice and graupel: the particles are more isometric and of moderate density (ρ1 = 400–500 kg m−3), and they have fall speeds above 1 m s−1. Riming can reduce the density of particles provided that the predicted rime density is less than the density of the particle collecting rime. Aspect ratio sorting of PN ice occurs from the crest of the Cascades rearward, where more eccentric particles (lower aspect ratios) advect farther downwind than heavily rimed and more isometric particles (Fig. 6d, contour lines). This sorting (Jensen et al. 2017) is arguably physically realistic because fall speeds increase commensurately with the degree of riming and therefore control how far ice particles advect horizontally before reaching the surface.

Fig. 6.
Fig. 6.

(a)–(c) Ice mass mixing ratios (filled contours), (d)–(f) volume-weighted densities (filled contours) and number-weighted aspect ratios (contour lines; unitless), and (g)–(i) mass-weighted maximum diameters (filled contours) and mass-weighted terminal fall speeds (contour lines; m s−1) along the Convair flight track at 0000 UTC 14 Dec 2001. The dashed red lines in (a) indicate three of the Convair flight legs, the dashed black line in (a) is the melting level, and the thin and thick solid black contour lines in (a) show vertical motions of and , respectively. The thin and thick black contour lines in (b) show cloud water mixing ratios of 0.5 and 1 g kg−1, respectively. The magenta contour lines in (b) show rainwater mixing ratios of 0.5 g kg−1. Black asterisks in (d) indicate where broad-branched crystals and dendrites were observed. Black diamonds in (e) indicate where columns, capped columns, and needles were observed, and lime circles in (e) indicate where graupel was observed. Black stars in (f) indicate where aggregates were observed. Observations are from Garvert et al. (2005b) and Woods et al. (2005).

Citation: Journal of the Atmospheric Sciences 75, 9; 10.1175/JAS-D-17-0400.1

Ice is initiated as CN ice between approximately −5° and −9°C. The properties of CN ice, when unrimed, evolve differently than PN ice aloft near the crest of the Cascades. The most eccentric CN ice particles, where (Fig. 6e), ρ2 = 400–500 kg m−3 (Fig. 6e), and (Fig. 6h), advect over the Cascades along with the planar particles of PN ice. On the leeward side of the Cascades along this cross section, CN ice particles are confined to heights below 500 hPa (Fig. 6b). Locations where both columns and capped columns were observed (Fig. 6e, black diamonds) coincide with where (Fig. 6e). The reason that at these locations, similar to PN ice, is because CN ice grows by vapor deposition in regions of planar growth for long enough to evolve into oblate spheroids. Capped columns were observed along this cross section (Garvert et al. 2005b), suggesting that columnar ice spent a significant amount of time growing by vapor deposition at temperatures conducive to planar growth. Where significant riming occurs, CN ice becomes more isometric, similar to PN ice. Observations of graupel (Fig. 6e, green circles) advecting over the Cascade Range coincide with locations where , whereas PN ice number-weighted aspect ratios at these locations are approximately 0.1. There is no way to tell from the aircraft observations if this graupel originated as planar or columnar ice, although results from ISHMAEL suggest that this graupel may have originated as columns or capped columns.

Along the Convair flight track, aggregate mass mixing ratios become as large as 1 g kg−1 (Fig. 6c). The locations where PN ice, CN ice, and aggregate mass mixing ratios are largest are all between 123.4° and 122.8°W longitude, upwind of where significant orographic lift causes substantial riming. Thus, this region is more conducive to aggregation than riming. Aggregate mass-weighted maximum diameters become larger than 5 mm (Fig. 6i), and mass-weighted fall speeds become slightly larger than 1 m s−1 (Fig. 6i). Aggregates were observed on the windward side of the Cascades (Fig. 6, black stars), and in ISHMAEL, aggregates advect over to the leeward side where the mass mixing ratios decrease to <0.1 g kg−1.

The baseline simulation produces a high bias in IWC aloft compared with observations (Table 3), like other bulk microphysics schemes (Morrison et al. 2015). PN ice dominates the hydrometeor mass budget at upper levels along this cross section because ice is initiated as PN ice at temperatures less than −9°C. The size distributions of all ice species along leg 1 of the Convair flight track, plotted when IWC between 2300 UTC 13 December and 0100 UTC 14 December 2001 is lowest and in better agreement with observations, show that the high bias in ice mass for ice with maximum diameters less than 3 mm is from PN ice (Fig. 7). Along the Convair flight leg 1 at this time, the total IWC predicted from ISHMAEL is 0.31 g m−3, with 94.4% being PN ice, 3.1% being CN ice, and 2.4% being aggregates. The total averaged ice size distribution follows a similar shape as observations, but the concentrations are biased high in the model (Fig. 7, black line vs black circles). Overall, using three ice species with variable particle properties and distribution shape parameters of captures the general shape of the observed ice size distribution along with some of the general features of those observed habits.

Fig. 7.
Fig. 7.

Ice size distributions for PN ice (gray), CN ice (red), and aggregates (blue) along leg 1 of the Convair flight track (topmost red dashed line in Fig. 6a) at 0030 UTC 14 Dec 2001. The black line shows the total (PN ice + CN ice + aggregates) average size distribution from ISHMAEL, and the black circles are observations from Garvert et al. (2005b).

Citation: Journal of the Atmospheric Sciences 75, 9; 10.1175/JAS-D-17-0400.1

5. Sensitivity simulations

a. Overview

The sensitivity simulations (described in Table 1) are designed to highlight the impacts that predicting ice particle shape and density evolution have on orographic systems and some of the model sensitivities to assumptions made in ISHMAEL. Thus, various model assumptions that impact the spatial precipitation distribution can be compared. First, changes to the spatial precipitation distribution that arise from predicting ice shape evolution versus the traditional approach are explored. This is tested by employing two different traditional microphysics schemes and by also modifying ISHMAEL to include an unrimed-to-rimed ice conversion (CON) parameterization rather than smoothly evolving particle properties during riming as is done in CTRL. Traditional microphysics schemes are used to confirm that differences seen in the CON simulations compared to CTRL, which are due to the snow–graupel conversion, are consistent with differences between the traditional schemes and CTRL. An unrimed-to-rimed ice conversion parameterization is added to ISHMAEL so that the impact of predicting ice particle shape evolution on spatial precipitation distribution can be explored in a consistent framework. Then changes to the spatial precipitation distribution that arise from other sensitivities such as ice particle habit choice and ice particle size distribution shape are studied to determine some of the main controls of spatial precipitation distribution for this case.

Table 1.

List of simulations.

Table 1.

b. Impacts of snow–graupel conversion on orographic systems

1) Simulation descriptions

The two traditional microphysics schemes used are the Milbrandt and Yau two-moment microphysics with hail turned off (MY2; Milbrandt and Yau 2005a,b) and Thompson microphysics (THOMPSON; Thompson et al. 2008). In MY2, if the riming rate is greater than the vapor growth rate for snow, then snow (including the rime mass) is converted to graupel at a rate that depends on the riming rate and the snow mass mixing ratio. In THOMPSON, if the riming rate is greater than twice the vapor growth rate, then some rime mass becomes graupel at a rate that depends on the ratio of the riming to vapor growth rate. In THOMPSON, rime mass that does not become graupel becomes snow, and this snow source is accompanied by an ad hoc increase in snow fall speed that depends on the ratio of the riming to vapor growth rate and can increase snow fall speed by up to 1.5-fold.

The modification to ISHMAEL to include an unrimed-to-rimed ice conversion is performed as follows: when small-ice nucleation occurs (e.g., frozen cloud droplets), ice is initiated to ice one, and when large-ice nucleation occurs (e.g., frozen raindrops), ice is initiated to ice two. In these simulations, frozen raindrops likely represent a tiny fraction of the total nucleated ice because the orographic forcing is generally too weak to loft significant numbers of raindrops to heights where they can freeze. Ice one is grown by vapor deposition the same way as in CTRL, and various habits (HAB) can develop depending on the vapor growth temperature. When ice one collects rime, ice one is converted to ice two following the approach used in MY2. Ice two is assumed to be spherical in this simulation, as is often assumed for graupel, though ice two density and fall speed are still predicted like in CTRL. The aggregation parameterization is left unchanged, although as aggregates rime, they too are converted to ice two following the same method as conversion for ice one. In this simulation, ice one, ice two, and ice three correspond to cloud ice/snow, graupel, and aggregates, respectively. This is in contrast to CTRL in which ice one (PN ice) and ice two (CN ice) can freely evolve to any type of ice. This simulation is referred to as CON-HAB. Another test is the same as CON-HAB except with a fixed vapor-grown habit for ice one, assumed to be dendrites (DEN). This simulation (CON-DEN) is similar to the approach used in traditional microphysics schemes.

2) Simulation results

The total averaged 18-h precipitation at all observation stations (Table 2) are biased high in all of the simulations. Both CON-DEN and CON-HAB have higher average precipitation root-mean-square errors (RMSEs) than CTRL; these simulations produce on average higher deviations from the observations compared to CTRL. The CON-DEN, CON-HAB, MY2, and THOMPSON simulations produce significantly more IWC aloft compared to CTRL along the Convair flight legs, though the averaged IWCs aloft are biased high in all of the simulations (Table 3). Even when predicting vapor-grown habit (as done in CON-HAB), representing snow and graupel using separate categories leads to IWCs that are larger than when ice particle shape and fall speed evolve during riming (as done in CTRL), in agreement with results from Lin and Colle (2011).

Table 2.

The 18-h (1400 UTC 13 Dec–0800 UTC 14 Dec 2001) precipitation accumulation (mm) averaged for all observation stations. Model-derived values are calculated by linearly interpolating to the station locations, and the RMSE is also calculated for each simulation.

Table 2.
Table 3.

Observed and modeled IWC (g m−3) along three legs of the Convair flight track (Fig. 6a, red dashed lines). The modeled values are averaged for 2 h (2300 UTC 13 Dec–0100 UTC 14 Dec 2001) and include all ice-phase species for simulations using ISHMAEL and all ice-phase categories for simulations using MY2 and THOMPSON.

Table 3.

The region where CON-DEN has a high bias in precipitation occurs in the Umpqua River valley and the southern Willamette valley (Fig. 8, arrows). There are six stations in this region where 18-h precipitation from CTRL is within 5 mm of the observations (Fig. 8a) while CON-DEN is high biased compared to CTRL by 5–30 mm (Fig. 8b). The CTRL simulation has the largest high bias along the ridge of the Cascades, where CON-DEN produces a low bias compared to CTRL in better agreement with observations. Along the ridge of the Cascades, the observations may be suspect because of measurement uncertainty associated with snow (e.g., blowing snow and riming on instruments). There are several stations on the leeward side of the Cascades where 18-h precipitation from CTRL is biased high compared to observations and CON-DEN is biased high compared to CTRL (Fig. 8b, stations circled in green). In general, there is a pattern that emerges when comparing CTRL and CON-DEN: CON-DEN is biased high on the leeward side of the Coast and Cascade Mountain Ranges and biased low along the ridge of the Cascades (Fig. 8b).

Fig. 8.
Fig. 8.

(a) Model-derived 18-h accumulated precipitation from CTRL minus observed 18-h accumulated precipitation at all station locations. (b) Model-derived 18-h accumulated precipitation from CON-DEN minus CTRL at all station locations. Arrows indicate where CTRL improves precipitation prediction compared to CON-DEN in the Willamette and Umpqua River valleys. The stations circled in green in (b) are where CTRL improve precipitation prediction on the leeward side of the Cascades. The contour lines show terrain heights of 0.25, 0.5, 1, and 1.5 km, contoured from light gray to black. Accumulated precipitation is analyzed along two cross sections (solid red lines) in Fig. 9. The more northern cross section is the Convair flight track.

Citation: Journal of the Atmospheric Sciences 75, 9; 10.1175/JAS-D-17-0400.1

The cause of the CON-DEN high bias in precipitation in the Umpqua and southern Willamette valleys can be determined by studying the precipitation and the interaction between ice particle fall speeds and vertical air motion during the 2 h from 2300 UTC 13 December to 0100 UTC 14 December 2001, during which high reflectivity values encompassed the region (Fig. 3). Along the Convair flight track (Fig. 8, northern red lines) just south of where CTRL improves precipitation prediction compared to CON-DEN (122.5°W), CON-DEN produces a higher variability in the spatial distribution of precipitation compared to CTRL (Fig. 9a, red vs black line). This spatial variability in 2-h precipitation is also seen in MY2 (Fig. 9a, gray line), which is nearly identical to the CON-DEN variability in precipitation distribution (though MY2 produces larger peaks in accumulation) along this cross section.

Fig. 9.
Fig. 9.

The 2-h (2300 UTC 13 Dec–0100 UTC 14 Dec 2001) accumulated precipitation for CTRL (black), MY2 (gray), THOMPSON (blue), CON-DEN (red), and CON-HAB (violet) along (a) the Convair flight track and (b) the southern red line in Fig. 8. The approximate locations of the Coast and Cascade Mountain Ranges are labeled in (b).

Citation: Journal of the Atmospheric Sciences 75, 9; 10.1175/JAS-D-17-0400.1

The increased precipitation in the Umpqua River valley is more apparent along the southern cross section where the Coast Mountains are higher (Fig. 9b). Large spatial variability in 2-h precipitation occurs in CON-HAB, CON-DEN, MY2, and THOMPSON in the region encompassing 123.5°–122.5°W (Fig. 9b), whereas in CTRL, a more steady decrease in precipitation occurs across the valley. CTRL also produces less precipitation on the leeward side of the Cascades compared to the other simulations along both cross sections (Fig. 9).

One of the main differences between CTRL and CON-DEN is the ice-to-graupel conversion in CON-DEN that produces a large jump in fall speed (Fig. 10c) that might ultimately be responsible for the larger variability in precipitation. The local maximum in CON-DEN precipitation along the Convair flight track near 122.5°W (Fig. 10c, green line) is just downwind of a region with a 2-h average (at the first model layer above the melting level) downdraft (Fig. 10c, gray line). The time-averaged total ice mass-weighted fall speeds (mass weighting considering all ice categories) for CON-DEN in this downdraft region are approximately 1 m s−1 (Fig. 10a, red line), consistent with a large fraction of this ice being aggregates (Fig. 10c, salmon line). Thus, the local maximum in CON-DEN precipitation near 122.5°W longitude is attributed to significant fallout of aggregates. Just upwind of this region (near 123.5°W), the temporal standard deviation of the total ice mass-weighted fall speeds is larger for CON-DEN than CTRL (Fig. 10a). This occurs in CON-DEN when the precipitation is from a mix of snow and graupel over the 2-h period. In CTRL, the ice particle properties evolve freely between those of snow and graupel, which produces less fall speed variability in time.

Fig. 10.
Fig. 10.

(a) The 2-h (2300 UTC 13 Dec–0100 UTC 14 Dec 2001) average total ice (accounting for , , and ) mass-weighted fall speeds and standard deviations (plotted for every other point for visibility) for CTRL (black) and CON-DEN (red) along the first grid box above the melting level along the Convair flight track. (b) The 2-h average mass-weighted fall speeds and standard deviations for ice one (black), ice two (blue), and aggregates (salmon) from CTRL. The gray line indicates the 2-h-average w and standard deviations from CTRL. The green line shows the 2-h accumulated precipitation. (c) As in (b), but for the CON-DEN simulation.

Citation: Journal of the Atmospheric Sciences 75, 9; 10.1175/JAS-D-17-0400.1

Between 122.5° and 122.3°W, CON-DEN and MY2 show a decrease in precipitation just downwind of an updraft, which reaches approximately (Fig. 10c, gray line) and exceeds the mass-weighted fall speed of snow and aggregates. In this region in CTRL, the peak in w also reaches 2 m s−1 (Figs. 10b,c, gray line), but the particles are partially (or fully) rimed, so their fall speeds exceed w, leading to increased precipitation accumulation (Fig. 10b, green line). There is also significantly more variability in precipitation downwind of the Cascades in CON-DEN compared to CTRL in response to the increased variability in w in this region (between 122° and 121°W).

In the CTRL simulation, the mass-weighted fall speeds of both ice one (PN ice) and ice two (CN ice) are approximately the same just above the melting level (Fig. 10b), and additional sensitivity tests (not shown) reveal that using one ice species instead of two at nucleation predicts 18-h averaged precipitation accumulation reasonably well compared to CTRL. This occurs because one of the main precipitation formation processes is riming, and riming is similar for both planar and columnar ice above the melting level. The main effect of riming on planar and columnar particles is to increase ice particle fall speeds. Using two ice species at nucleation has the advantage of allowing two separate habit types (i.e., planar and columnar) to evolve in the same grid volume while only adding four extra prognostic variables. Both planar and columnar habit types were observed in this case, and thus, predicting two different habit types likely leads to a better comparison with observations of particle types than if only one habit type were to be predicted. For quantitative precipitation forecasts, using one ice species at nucleation (and also parameterizing aggregates) or combining aggregates with the one free ice species, as is done in the one-category configuration of the P-3 microphysics scheme (Morrison and Milbrandt 2015), may yield results comparable to the CTRL simulation with the added computational benefit of needing fewer prognostic variables. If the goal is to represent detailed microphysical characteristics of the observed system, it then makes sense to use two species, which allows for the separate evolution of planar and columnar ice. However, if the goal is to capture the overall precipitation rates, then one species works well, at least in this orographic case. This may not be true for other cloud systems. For instance, if a real cloud system has a large number of small columnar particles (perhaps formed by rime splintering), and also has large dendrites, then riming may show a strong habit dependence.

The gradual riming of PN and CN ice in CTRL also leads to lower overall aggregation, whereas in CON-DEN, riming of dendrites requires a threshold growth rate, so unrimed ice easily produces copious aggregates. From the perspective of cloud system evolution, whether or not dendrites aggregate in CON-DEN may have little impact on the simulated results since dendrites and aggregates have similar mass-weighted fall speeds (Fig. 10c, black and salmon lines). However, the overall concentration of simulated ice will be impacted.

Along the Convair flight track (Fig. 8, northern red lines), both MY2 and CON-DEN show a noticeable spatial shift in 18-h total precipitation compared with other simulations with local maxima in precipitation near 123.8°, 123.3°, and 122.5°W (Fig. 11, gray and red lines at the arrows). These shifts in precipitation occur downwind of the Coast Range, in the southern Willamette valley, and in the foothills of the Cascades and are consistent with previous studies showing that traditional microphysics schemes tend to produce excessive leeward-side precipitation because of snow advecting downwind (Garvert et al. 2005b; Milbrandt et al. 2008). The local maximum in the 18-h precipitation at 122.5°W in MY2 and CON-DEN occurs in the 2-h precipitation as well (Fig. 9a). The spatial distribution of precipitation from THOMPSON (Fig. 11, light blue line) has similar features to CON-DEN, including increased ice precipitation at the crest of the Cascades and increased leeward-side precipitation at 121.5°W compared to CTRL (Fig. 11, black line). All simulations that include a snow-to-graupel conversion produce increased ice precipitation at the crest of the Cascades and increased precipitation on the leeward side of the Cascades (at 121.5°W) compared to CTRL, where precipitation more steadily decreases on the leeward side of the Cascades.

Fig. 11.
Fig. 11.

The 18-h total accumulated precipitation from 1400 UTC 13 Dec to 0800 UTC 14 Dec 2001 along the Convair flight track for all simulations (see Table 1) and the 18-h ice-only (equivalent liquid) accumulated precipitation.

Citation: Journal of the Atmospheric Sciences 75, 9; 10.1175/JAS-D-17-0400.1

The net effect of predicting ice particle shape evolution on the spatial distribution of precipitation is apparent when analyzing the correlation coefficients between terrain height and 18-h precipitation. Snow-to-graupel conversion in CON-HAB and especially CON-DEN and MY2 leads to somewhat higher correlation between accumulation and terrain height than when ice particle shape evolution is predicted, as is done in CTRL (Fig. 12). An analysis of lag correlation shows that the 18-h precipitation from the CON-HAB, CON-DEN, and MY2 simulations is most correlated with terrain height for a shift of about 0.1° longitude; peaks in terrain are associated with peaks in precipitation 0.1° longitude downwind in these simulations. In THOMPSON, the increase in the fall speed of rimed snow produces peaks in precipitation that are shifted upwind compared to the other simulations with snow-to-graupel conversion. Accumulated precipitation from MY2 and CON-DEN are most correlated with the terrain height, whereas precipitation accumulation from CON-HAB shows a weaker correlation with terrain height than CON-DEN. Note that a second correlation peak exists at −0.2° longitude in the CON and MY2 simulations, which is the approximate width of the major terrain peaks along the cross section (see Fig. 11). The results imply that CON-HAB, CON-DEN, MY2, and THOMPSON precipitation responds more strongly to the terrain, and this is due in part to the interactions between orography, winds, and ice particle fall speeds. Microphysics schemes that have bifurcations in ice particle fall speeds caused by separating ice categories can produce rapid changes in precipitation rate from a shift in vertical motion.

Fig. 12.
Fig. 12.

Correlation coefficients between terrain height and 18-h total accumulated precipitation as a function of longitudinal shift for CTRL (black), MY2 (gray), CON-DEN (red), CON-HAB (violet), and THOMPSON (blue). A positive longitudinal shift means that the terrain is shifted downwind (to the east) relative to the precipitation, and therefore, correlation at a positive longitudinal shift implies that local maxima in precipitation occur downwind of peaks in terrain.

Citation: Journal of the Atmospheric Sciences 75, 9; 10.1175/JAS-D-17-0400.1

One of the main conclusions that can be drawn from the above comparison between CTRL and the CON-HAB and CON-DEN simulations is that predicting ice particle shape evolution during riming leads to a steady decrease in precipitation across the Umpqua valley in better agreement with observations than when snow is converted to graupel. Moreover, representing snow and graupel using separate categories in both the CON-HAB and CON-DEN simulations leads to large spatial variability in precipitation accumulation that coincides with local fallout of snow or graupel, depending on vertical and horizontal air velocities.

c. Impacts of vapor-grown habit on orographic systems

The impact of vapor-grown habit on orographic systems is also explored to determine the extent to which IWC aloft and precipitation depend on habit. First, CTRL is modified such that vapor growth produces dendrites instead of various habits. In this simulation (DEN), ice nucleation occurs the same way as in CTRL. However, the habit evolution of both PN ice and CN ice is fixed such that they grow as dendrites. In this simulation, the shapes of vapor-grown habits still evolve during riming, and thus, this simulation is used to determine the relative impact of predicting unrimed habit on orographic systems. Another habit sensitivity simulation is run where vapor-grown habits at temperatures below −20°C are assumed to be columnar (COL). Ice habits growing at temperatures below −20°C are generally polycrystalline and platelike from −20° to −40°C and columnar at temperatures below −40°C (Bailey and Hallett 2009). For simplicity, the model sensitivity to vapor growth at temperatures below −20°C is explored by parameterizing columnar instead of planar growth at these temperatures.

When the vapor-grown habit in ISHMAEL is assumed to be DEN, both the IWC aloft and spatial distribution of precipitation accumulation are strongly affected. Dendrites have lower collection efficiencies for a given cloud droplet size than other habit types because of the airflow around them (Wang and Ji 2000). Dendrites also grow by vapor deposition to larger masses in a given time, fall slower, and aggregate more easily than other habit types. The reduced riming rates in DEN lead to an increase in cloud LWCs (Table 4) on the windward side of the Cascades and to less precipitation accumulation over the Cascades compared to CTRL (Fig. 11, brown vs black lines). The increase in vapor growth rate for dendrites produces higher IWCs aloft (Table 3) compared to CTRL, and these dendrites aggregate and advect downwind, producing an increase in precipitation accumulation on the leeward side of the Cascades (Fig. 11). The DEN simulation produces the largest 18-h station-averaged precipitation RMSE of all simulations using ISHMAEL as the modeling framework. Thus, correct estimate of habit is important. Even though shape evolution is still predicted during vapor growth and riming in this simulation, the unrimed ice particle properties are not properly represented in DEN, leading to larger vapor growth rates, which leads to larger errors in both IWC aloft and the spatial distribution of precipitation compared to CTRL.

Table 4.

Observed and modeled cloud LWC (g m−3) along five legs of the P-3 flight track (Fig. 1). The modeled values are averaged for 2 h (2300 UTC 13 Dec–0100 UTC 14 Dec 2001).

Table 4.

Columns and capped columns were observed in this case, which suggests that columns were either nucleated above and fell through the −15°C layer or that columns were nucleated in orographically forced updrafts and lofted into the planar growth regime. In the simulation that nucleates columns at temperatures below −20°C (COL), there is a reduction in IWC aloft compared to CTRL, in better agreement with observations (Table 3). The COL simulation produces similar precipitation statistics (Table 2) and similar cloud LWCs (Table 4) compared to CTRL. Ice nucleated and grown as columns at temperatures below −20°C in COL falls into the region of planar growth (at temperatures above −20°C), causing the columnar ice to become more isometric in time (Fig. 13b). This behavior roughly resembles the production of capped columns. For the same volume, spherical particles have a lower growth rate than eccentric particles. Consequently, as particles become more isometric, there is a decline in the vapor growth rate (Fig. 13a). This reduction in vapor growth rate aloft produces better agreement with observed IWCs but has limited impact on surface precipitation. This suggests that the production of precipitation depends less on vapor growth aloft and more on the growth of ice at lower altitudes in orographic systems. Ice nucleation and growth at lower altitudes could result from orographically forced updrafts or through the seeder–feeder process.

Fig. 13.
Fig. 13.

(a) The 2-h (from 2300 UTC 13 Dec to 0100 UTC 14 Dec 2001) vertically averaged bulk vapor growth rate divided by number mixing ratio for PN ice (black) and CN ice (red) for CTRL (solid) and COL (dashed). Averaging is done along the Convair cross section. (b) As in (a), but for number-weighted aspect ratio. The dotted gray line in both (a) and (b) indicates the −20°C height.

Citation: Journal of the Atmospheric Sciences 75, 9; 10.1175/JAS-D-17-0400.1

Along the Convair cross section, the CTRL and COL simulations have wider distributions of number-weighted aspect ratios than CON-HAB and CON-DEN, spanning from to for CTRL (Fig. 14b, solid and dashed black lines). The columnar particles that grow at temperatures below −20°C in COL have number-weighted aspect ratios as large as (Fig. 14b, salmon lines), and these particles do not exist in CTRL. The CON-HAB and CON-DEN simulations have relatively narrow aspect ratio distributions for ice one, and ice two particles are spherical since ice two is used as the rimed category in this sensitivity test (Fig. 14b, blue and gray lines). As expected, CON-DEN produces the largest ice one particles (Fig. 14a, gray solid line) with the lowest densities (Fig. 14d, gray solid line) and the smallest aspect ratios (Fig. 14b, gray solid line). Ice one particle volume-weighted densities and mass-weighted maximum diameters from CON-HAB are similar to CTRL because unrimed habits evolve similarly in the two simulations, though ice particle shape evolution during riming produces ice one particles in CTRL that are more isometric and faster falling than in CON-HAB.

Fig. 14.
Fig. 14.

Histograms of (a) mass-weighted fall speeds, (b) number-weighted aspect ratios, (c) mass-weighted maximum diameters, and (d) volume-weighted densities for CTRL (black), COL (red), CON-DEN (gray), and CON-HAB (blue). Values are shown for ice one (solid lines), ice two (dashed lines), and aggregates [dotted; shown in (a) and (c) only].

Citation: Journal of the Atmospheric Sciences 75, 9; 10.1175/JAS-D-17-0400.1

d. Impacts of ice size distribution shape and riming rate on orographic systems

Ice size distribution shape impacts microphysical processes such as vapor growth and riming, thereby altering the processes that create precipitation. Ice size distribution shape also impacts size sorting, which occurs when mass-weighted fall speeds are larger than number-weighted fall speeds and can increase the precipitation rate by increasing the downward mass flux of ice. Size sorting increases with decreasing ice distribution shape parameter (Milbrandt and Yau 2005a). Traditional models generally assume that ice size distributions are inverse exponential , in agreement with some observations. Therefore, we change the distribution shape parameter to for PN ice and CN ice (NU1) while leaving for aggregates. Tests using for aggregates (not shown) produce significantly more aggregates than when , which increases precipitation accumulation on the leeward side of the Cascades. This increase in aggregation when is likely due to the tail of larger aggregates that more easily collect PN ice, CN ice, and the significant number of small aggregates that exist when . For this simulation, the focus is on the impact of size sorting of PN ice and CN ice on precipitation; hence, is used for aggregates for the NU1 simulation.

Inverse exponential PN and CN ice size distributions (NU1) lead to a reduction in IWCs aloft (Table 3) compared to CTRL. This is expected because of smaller vapor growth rates (Harrington et al. 2013b) and an increase in size sorting that occur from reducing the value of ν. When size sorting is increased, total precipitation increase on the windward side of the Cascades compared to CTRL, and ice precipitation approximately triples in better agreement with both MY2 and THOMPSON where and both CON-DEN and CON-HAB where (Fig. 11). Thus, the increases in ice precipitation from increased size sorting compared to CTRL is of similar magnitude to the increase in ice precipitation resulting from rimed snow producing graupel production along the ridge of the Cascades.

Finally, to study the impact of cloud droplet number concentration on orographic systems, a simulation is run with a constant cloud number concentration of 20 cm−3 (20CC), which is one-tenth the value used in CTRL. Cloud droplet concentrations at heights from 600–450 hPa were measured on the Convair by a PMS Forward Scattering Spectrometer Probe (FSSP) to be 10–30 cm−3 (Woods et al. 2005). All else equal, the decrease in assumed cloud droplet number concentration in 20CC compared to CTRL will cause an increase in riming rate because cloud droplets will be larger, resulting in higher collection efficiencies.

An increase in the riming rate by setting the cloud droplet number concentration to 20CC produces an expected reduction in cloud LWCs compared to CTRL on the windward side of the Cascades (Table 4, legs 1–3), and 18-h station-averaged precipitation and RMSE are slightly improved compared to CTRL. The peak in 18-h precipitation along the Convair track seen in all other simulations near 121.8°W does not appear in 20CC (Fig. 11, dashed blue line). A more even distribution of precipitation falls across the Cascades in this simulation, while less precipitation accumulates on the leeward side of the tallest peak (Fig. 11, blue dashed line near 121.75°W). A similar increase in windward-side and decrease in leeward-side precipitation accumulation when reducing cloud droplet number concentrations in an orographic environment was seen in simulations by Colle and Zeng (2004).

6. Conclusions

Predicting the evolution of ice particle properties for various vapor-grown habits and degrees of riming using the ISHMAEL microphysics scheme allows ice particle fall speeds to evolve more naturally compared to the traditional approach of representing unrimed (snow) and rimed (graupel) ice in separate categories. WRF simulations using ISHMAEL for the 13–14 December 2001 IMPROVE-2 case produce a range of ice particle properties broadly consistent with aircraft observations of ice particle types over the Willamette valley and Cascade Range.

The more natural evolution of ice particle fall speeds in ISHMAEL improves the spatial distribution of accumulated precipitation for this case compared to observations, especially in the Umpqua River valley, relative to simulations using the traditional approach of separate categories for snow and graupel, which tend to substantially overpredict precipitation downwind of the Coast Range. This is caused by snow that does not convert to graupel over the Coast Range and advects downwind into the valley. Simulations using the traditional approach also produce large high-frequency variability in the spatial distribution of precipitation in this region. One cause of this large variability is the bifurcation of snow and graupel fall speeds when ice is represented using separate unrimed and rimed ice categories. In contrast, ISHMAEL produces a range of particle fall speeds associated with evolving particle shape and degree of riming. Interactions between the orography, winds, and ice particle fall speeds produce a spatial distribution of precipitation that is more correlated to terrain features than when predicting ice particle properties using ISHMAEL. The separation of snow and graupel, producing a substantial fraction of the ice mass aloft as unrimed ice (snow) with relatively low fall speeds and large vapor growth rates, also leads to a larger bias in IWC aloft than when ice particle properties evolve during riming, compared to aircraft observations.

Sensitivity studies show that when columnar habits are parameterized to grow at temperatures below −20°C, predicted IWCs aloft improve compared to observations, while the precipitation statistics remain similar. Habit choice at temperatures below −20°C produces a reduction in IWC aloft of similar magnitude compared to when size sorting is increased. Columns and capped columns were observed in this case, and therefore, this type of ice growth and the growth of other particles (e.g., bullet rosettes; Sheridan et al. 2009) that grow by vapor deposition slower than dendrites may be critical, especially when simulating relatively deep cold cloud systems, yet these habit types remain generally absent from microphysics schemes.

ISHMAEL provides a useful framework to compare ice particle properties to observations because ice particle aspect ratios are predicted. Ice properties from ISHMAEL can be directly compared to in situ observations and to dual-polarization radar retrievals. Predicting ice properties, including shape, density, size, and fall speed, provides additional model constraints for making such comparisons. Understanding of microphysical processes such as nucleation, vapor growth, aggregation, and riming needs to be improved with laboratory measurements and field-campaign observations to fully realize the impact that these processes and their interactions have on cloud systems and precipitation.

Acknowledgments

This research was supported by an NSF AGS Postdoctoral Research Fellowship (AGS-1524267), the U.S. Department of Energy’s Atmospheric Science Program Atmospheric System Research, an Office of Science, Office of Biological and Environmental Research program, under DE-SC0012827, and the National Science Foundation, Grant AGS-1433201. We would like to acknowledge high-performance computing support from Cheyenne (https://doi.org/10.5065/D6RX99HX) provided by NCAR’s Computational and Information Systems Laboratory, sponsored by the National Science Foundation.

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