1. Introduction
The frequent inland and orographic enhancement of lake-, sea-, and ocean-effect (hereinafter lake effect) precipitation results in climatological precipitation maxima over downstream hills, mountains, and upland regions. As summarized by Niziol et al. (1995, p. 62) for the Laurentian Great Lakes, “the greatest snowfall occurs where the prevailing winds blow [along] the longest fetch of the lake, particularly where orographic features enhance precipitation processes.” Veals and Steenburgh (2015) show that a prominent maximum in mean cool-season lake-effect liquid precipitation equivalent (LPE) exists over the Tug Hill Plateau (hereinafter Tug Hill), a broad upland region east of Lake Ontario that rises 500 m above lake level. Similarly, downstream of the Great Salt Lake of northern Utah, mean cool-season LPE during lake-effect periods increases fourfold from the lake shore to the Wasatch Mountains (Yeager et al. 2013). Additionally, high elevation sites along the west coast of Japan, where the Sea of Japan produces heavy snowfalls during the Asian winter monsoon, observe seasonal snowpacks of immense depth, with snow-water equivalent frequently exceeding 300 cm (Yamaguchi et al. 2011).
During individual lake-effect storms, however, the inland and orographic enhancement of LPE can vary widely. In some cases, the ratio of upland to lowland LPE can greatly exceed that expected from climatology, with a dramatic increase in LPE with elevation, whereas in others it may be <1, with lowland snowfall exceeding that at upper elevations (e.g., Magono et al. 1966; Ishihara et al. 1989; Nakai and Endoh 1995; Eito et al. 2005; Nakai et al. 2008; Campbell et al. 2016).
In this paper, we examine the factors affecting such inland and orographic variations in lake-effect precipitation east of Lake Ontario and over Tug Hill. This represents a unique problem, requiring a synthesis of knowledge of lake-effect precipitation, coastal and inland effects, and orographic processes. To provide a foundation for our analysis, we begin with a synthesis of prior literature in these areas.
2. Literature synthesis
a. Environmental conditions and lake-effect mode
Lake-effect precipitation occurs when a cold air mass flows over a relatively warm body of water, initiating moist convection (e.g., Peace and Sykes 1966; Hjelmfelt and Braham 1983; Niziol et al. 1995). Sensible and latent heat fluxes over the water body generate a convective boundary layer that deepens with downwind extent, is frequently surmounted by a capping inversion or stable layer (hereafter cap), and contains precipitating clouds. The depth of the lake-effect boundary layer is modulated by the characteristics of the upstream air mass, the strength of the sensible and latent heat fluxes, and the fetch, with a larger lake–air temperature difference, stronger winds, and longer fetch producing a deeper boundary layer and higher cap (Hill 1971; Kristovich et al. 1999; Laird and Kristovich 2002). The strength of the fluxes and height of the cap in turn affect the behavior and intensity of the lake-effect convection. Larger fluxes and a higher cap enable deeper, stronger convection and greater LPE downwind of the lake (e.g., Braham 1983; Niziol 1987; Hjelmfelt 1990; Byrd et al. 1991; Smith and Boris 2017).
For operational forecasting, the potential for boundary layer growth and lake-effect convection is often assessed using estimates of the lake-induced instability such as the lake–850-hPa temperature difference, 
Lake-effect convection frequently assumes the mode of disorganized open cells or horizontal roll convection, referred to collectively as broad coverage in some studies (Hjelmfelt 1990; Steenburgh et al. 2000; Veals and Steenburgh 2015; Campbell et al. 2016). The likelihood of roll convection increases with wind speed and vertical wind shear (Kristovich et al. 1999). The resulting cloud and precipitation bands can align either parallel to or normal to the mean boundary layer wind and are sometimes referred to as longitudinal (“L” mode) and transversal (“T” mode) bands, respectively (Nakai et al. 2005). The band orientation is determined by the orientation of the wind shear vector relative to the mean wind vector, with longitudinal (transversal) bands favored when the two are approximately parallel (normal) (Asai 1972; Kelly 1984; Kristovich 1993; Kristovich et al. 1999; Cooper et al. 2000; Eito et al. 2010).
In addition to boundary layer circulations, convergence generated by thermally driven flows can influence lake-effect mode. Areas where the upstream shore features a large bay or channel favor thermally driven convergence and lake-effect initiation, with the resulting bands often broader and more intense than neighboring bands produced by horizontal roll convection (e.g., Andersson and Gustafsson 1994; Norris et al. 2013; Mazon et al. 2015). When the wind blows along the major axis of an elongated lake (e.g., Lakes Michigan, Erie, and Ontario) land-breeze convergence can generate an intense, mesoscale band that produces especially large snowfall rates and accumulations. Although called midlake or type-I bands by some authors (e.g., Braham 1983; Kelly 1986; Niziol et al. 1995; Steenburgh et al. 2000), following more recent studies (Steiger et al. 2013; Veals and Steenburgh 2015; Steenburgh and Campbell 2017), we refer to these as long-lake-axis parallel (LLAP) bands. LLAP bands are favored during periods of large lake–land temperature differences, 
b. Coastal and inland effects
Lake-effect systems undergo significant changes as they approach the downstream coast and penetrate inland, in some cases interacting with a land breeze or land-breeze front. Campbell and Steenburgh (2017) showed that a key contributor to the enhancement of LPE during a lake-effect event over Tug Hill was a land-breeze front that formed along the southeast shore and cut obliquely across the lake-effect system. Along the west coast of Japan, offshore katabatic flow from the coastal topography can oppose the large-scale flow, reinforcing convergence along the land-breeze front and producing a coast-parallel precipitation band (e.g., Ishihara et al. 1989; Eito et al. 2005).
As the lake-effect system penetrates inland, there is a transition in the character of lake-effect convection. Downstream of Lake Ontario, Minder et al. (2015) and Welsh et al. (2016) showed that lake-effect systems become less turbulent, more spatially continuous, and shallower with inland extent, consistent with a convective to stratiform transition. The inland penetration of lake-effect precipitation varies, with Villani et al. (2017) concluding that higher boundary layer wind speed, a connection of the lake-effect system to upstream lakes, and a lower 
c. Orographic precipitation processes
The flow regime has a profound influence on the distribution of LPE upstream and over a barrier, with higher (lower) values of 
The effects of 
The orographic enhancement can also be affected by the presence of nonorographic ascent. Steenburgh (2003) examined a storm cycle over the Wasatch Range and found that the lowest ratio of upland to lowland precipitation occurred during the passage of a cold-frontal precipitation band, when strong mesoscale ascent produced similar LPE in both the lowlands and uplands. Similarly, Mass et al. (2015) found that periods of precipitation forced by strong synoptic scale ascent were associated with little orographic enhancement over the Cascade Mountains.
d. Summary
Advancing knowledge of the inland and orographic enhancement of lake-effect storms requires the synthesis of concepts from the preceding sections. The cap height likely has some control over the depth and intensity of the convection, while also influencing the characteristics of the flow over the downstream barrier (e.g., a cap near or below crest level might induce blocking). High wind speeds may be associated with more intense lake-effect precipitation (Smith and Boris 2017), while simultaneously increasing the cross-barrier moisture flux and inland hydrometeor transport (Sinclair et al. 1997; Neiman et al. 2002). Similar to the effects of mesoscale and synoptic-scale forcing on orographic precipitation, the mesoscale organization of lake-effect precipitation systems may affect the ratio of upland to lowland LPE. Single, organized bands (LLAP and shoreline) generally feature the most intense LPE rates and ascent, and the location of their associated LPE/ascent maxima may supersede any orographically induced ascent to produce a lowland LPE maximum or a nearly equal distribution between upland and lowland sites (e.g., Ishihara et al. 1989; Eito et al. 2005; Campbell et al. 2016).
The remainder of this paper examines the inland and orographic enhancement of lake-effect precipitation east of Lake Ontario and over Tug Hill. In section 3, we describe the datasets and methods used in the analysis, which is based on a multicool-season radar climatology and observations from the Ontario Winter Lake-effect Systems (OWLeS) project, conducted from December 2013 to January 2014 [see Kristovich et al. (2017) for a full description]. The radar climatology is used to examine the factors affecting the inland and orographic enhancement of lake-effect precipitation in section 4, while the OWLeS observations are used to examine a smaller subset of lake-effect periods in section 5. A summary and conclusions are presented in section 6.
3. Data and methods
a. Radar climatology
Development of the radar climatology for this study began with the lake-effect periods identified east of Lake Ontario by Veals and Steenburgh (2015) using lowest-level reflectivity data from the Montague/Ft. Drum, New York (KTYX), WSR-88D during the 13 cool seasons during 2001–14. Lake-effect periods during the subsequent cool seasons (2014–15, 2015–16, and 2016–17) were then identified following Veals and Steenburgh (2015) and added to the analysis. We then focused on the period of continuous level-II radar data, which spans nine cool seasons during 2008–17, because the level-II format includes full-volume scans, allowing for the plotting and analysis of higher-quality vertical cross sections. We also focused on periods from 16 November to 15 April to minimize the inclusion of lake-effect rain events that could include a radar bright band.
To simplify the analysis, we concentrated on times during these periods when lake-effect features extend along a transect that runs across the center of Tug Hill, through the climatological lake-effect precipitation maximum identified by Veals and Steenburgh (2015), and approximately over two OWLeS snow measurement sites, North Redfield (NR) and Sandy Creek (SC; Fig. 1). Following Campbell et al. (2016), we classified the lake-effect mode along the transect during these periods as banded, weakly banded, nonbanded, or other based on visual inspection of lowest-level radar reflectivity data. Thus, our analysis concentrates on 311 periods (683 h) with either banded, weakly banded, or nonbanded lake-effect features along the transect.
(a) The Lake Ontario region, with the outline of the NARR averaging area depicted by the dashed red box. The solid black box indicates the location of the inset. (b) The Tug Hill region with the OWLeS observing sites at Sandy Creek (SC) and North Redfield (NR), and the KTYX WSR-88D annotated. The dashed line indicates the transect, with the bracketed magenta portion indicating the domain over which quantitative variables are calculated. Elevation (m MSL) depicted in the scale.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
(a) The Lake Ontario region, with the outline of the NARR averaging area depicted by the dashed red box. The solid black box indicates the location of the inset. (b) The Tug Hill region with the OWLeS observing sites at Sandy Creek (SC) and North Redfield (NR), and the KTYX WSR-88D annotated. The dashed line indicates the transect, with the bracketed magenta portion indicating the domain over which quantitative variables are calculated. Elevation (m MSL) depicted in the scale.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
(a) The Lake Ontario region, with the outline of the NARR averaging area depicted by the dashed red box. The solid black box indicates the location of the inset. (b) The Tug Hill region with the OWLeS observing sites at Sandy Creek (SC) and North Redfield (NR), and the KTYX WSR-88D annotated. The dashed line indicates the transect, with the bracketed magenta portion indicating the domain over which quantitative variables are calculated. Elevation (m MSL) depicted in the scale.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
b. Environmental conditions
To examine the relationship between inland/orographic enhancement and environmental conditions during lake-effect periods, we focused on three parameters that were selected based on a review of the lake-effect and orographic precipitation literature. These parameters are as follows: 1) the lake-effect mode along the transect, 2) the mean 950–850-hPa zonal wind speed 
During lake-effect events, mesoscale circulations induced by Lake Ontario result in low-level flow convergence over eastern Lake Ontario and Tug Hill (e.g., Steenburgh and Campbell 2017; Campbell and Steenburgh 2017). As a result, no single location serves as the source region for air impinging on Tug Hill. Therefore, all variables are averaged across all grid points within a rectangle spanning the study area (Fig. 1). Results obtained using a grid point immediately upstream of the eastern shore of Lake Ontario were generally similar and are not presented here.
The zonal wind speed 
We also evaluated the influence of the 
c. OWLeS data
To augment the radar-based climatological analysis, we also examined events during OWLeS, when LPE observations at SC and NR were available. These two sites measured (among other variables) LPE with an automated gauge, automated snow depth, 6-hourly manual LPE, and 6-hourly manual snowfall (Campbell et al. 2016).
d. Quantification of inland and orographic enhancement
To objectively compare the relationship of the three parameters to the LPE distribution downstream of Lake Ontario and over Tug Hill, we define six variables, all calculated along a portion of the transect stretching from the Lake Ontario shoreline through Tug Hill to the base of the Adirondack Mountains (hereafter Adirondacks; Fig. 1). 
4. Radar-based climatology
a. Univariate statistics
To examine the influence of 
(a),(c),(e) Mean radar-derived LPE rate from KTYX in the plan view for all periods occurring along the transect during 2008–17, with the dashed line indicating the transect. (b),(d),(f) Frequency of occurrence of echoes >10 dBZ in the X–Z plane along the transect, with the graph indicating mean KTYX LPE rate along the transect. The panels are for (a),(b) low; (c),(d) moderate; and (e),(f) high 
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
(a),(c),(e) Mean radar-derived LPE rate from KTYX in the plan view for all periods occurring along the transect during 2008–17, with the dashed line indicating the transect. (b),(d),(f) Frequency of occurrence of echoes >10 dBZ in the X–Z plane along the transect, with the graph indicating mean KTYX LPE rate along the transect. The panels are for (a),(b) low; (c),(d) moderate; and (e),(f) high
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
(a),(c),(e) Mean radar-derived LPE rate from KTYX in the plan view for all periods occurring along the transect during 2008–17, with the dashed line indicating the transect. (b),(d),(f) Frequency of occurrence of echoes >10 dBZ in the X–Z plane along the transect, with the graph indicating mean KTYX LPE rate along the transect. The panels are for (a),(b) low; (c),(d) moderate; and (e),(f) high
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
Box-and-whisker plot of (a) 
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
Box-and-whisker plot of (a)
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
Box-and-whisker plot of (a)
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
LCAPE was similarly divided into lower (≤802 J kg−1; hereinafter low), middle (1066–1454 J kg−1; hereinafter moderate), and upper quintile (
As in Fig. 2, but for (a),(b) low; (c),(d) moderate; and (e),(f) high LCAPE. There were 1509, 1481, and 1497 scans in the low, moderate, and high LCAPE periods, respectively.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
As in Fig. 2, but for (a),(b) low; (c),(d) moderate; and (e),(f) high LCAPE. There were 1509, 1481, and 1497 scans in the low, moderate, and high LCAPE periods, respectively.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
As in Fig. 2, but for (a),(b) low; (c),(d) moderate; and (e),(f) high LCAPE. There were 1509, 1481, and 1497 scans in the low, moderate, and high LCAPE periods, respectively.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
Box-and-whisker plot of (a) 
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
Box-and-whisker plot of (a)
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
Box-and-whisker plot of (a)
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
The lake-effect mode (nonbanded, weakly banded, and banded) along the transect is the third variable presented. Nonbanded periods feature relatively low LPE rates throughout the domain, with precipitation confined mainly to Tug Hill (Figs. 6a,b). LPE rates increase throughout the transect for weakly banded periods (Figs. 6c,d) and further still for banded periods, especially in the lowlands near the shoreline (Figs. 6e,f). Radar echoes tend to be shallow and confined to the plateau for nonbanded periods, but the transition to weakly banded and especially banded periods brings deep echoes over the shoreline, with depth gradually increasing with inland extent (cf. Figs. 6b,d,f). Quantifying these results, 
As in Fig. 2, but for (a),(b) nonbanded; (c),(d) weakly banded; and (e),(f) banded periods. There were 5578, 1071, and 817 scans in the nonbanded, weakly banded, and banded periods, respectively.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
As in Fig. 2, but for (a),(b) nonbanded; (c),(d) weakly banded; and (e),(f) banded periods. There were 5578, 1071, and 817 scans in the nonbanded, weakly banded, and banded periods, respectively.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
As in Fig. 2, but for (a),(b) nonbanded; (c),(d) weakly banded; and (e),(f) banded periods. There were 5578, 1071, and 817 scans in the nonbanded, weakly banded, and banded periods, respectively.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
Box-and-whisker plot of (a) 
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
Box-and-whisker plot of (a)
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
Box-and-whisker plot of (a)
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
b. Multivariate statistics
To examine the interactions between 
nonbanded/low LCAPE/low
nonbanded/high LCAPE/low
nonbanded/low LCAPE/high
nonbanded/high LCAPE/high
banded/low LCAPE/low
banded/high LCAPE/low
banded/low LCAPE/high
banded/high LCAPE/high
The NB/HL/L
Frequency of occurrence of echoes >10 dBZ in the X–Z plane along the transect, with the graph indicating mean KTYX LPE rate along the transect for periods that are (a) nonbanded/high LCAPE/low 
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
Frequency of occurrence of echoes >10 dBZ in the X–Z plane along the transect, with the graph indicating mean KTYX LPE rate along the transect for periods that are (a) nonbanded/high LCAPE/low
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
Frequency of occurrence of echoes >10 dBZ in the X–Z plane along the transect, with the graph indicating mean KTYX LPE rate along the transect for periods that are (a) nonbanded/high LCAPE/low
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
Box-and-whisker plot of (a) 
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
Box-and-whisker plot of (a)
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
Box-and-whisker plot of (a)
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
In contrast, the NB/LL/H
Across the eight regimes, nonbanded periods generally feature lower LPE rates, but a maximum that is displaced farther inland, with a larger ratio of upland to lowland LPE compared to banded periods. The absolute enhancement, however, is larger for banded periods than nonbanded periods, with the exception of nonbanded periods with high LCAPE and high 
5. OWLeS period
The analysis above highlights the influence of 
The effect of 
Frequency of occurrence of echoes >10 dBZ in the X–Z plane along the transect for the 2013–14 OWLeS period, with the graph indicating mean KTYX LPE rate along the transect, for (a) low, (b) moderate, and (c) high 
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
Frequency of occurrence of echoes >10 dBZ in the X–Z plane along the transect for the 2013–14 OWLeS period, with the graph indicating mean KTYX LPE rate along the transect, for (a) low, (b) moderate, and (c) high
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
Frequency of occurrence of echoes >10 dBZ in the X–Z plane along the transect for the 2013–14 OWLeS period, with the graph indicating mean KTYX LPE rate along the transect, for (a) low, (b) moderate, and (c) high
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
As in Fig. 10, but for LCAPE. There were 157, 149, and 157 scans in the low, moderate, and high LCAPE periods, respectively.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
As in Fig. 10, but for LCAPE. There were 157, 149, and 157 scans in the low, moderate, and high LCAPE periods, respectively.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
As in Fig. 10, but for LCAPE. There were 157, 149, and 157 scans in the low, moderate, and high LCAPE periods, respectively.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
As in Fig. 10, but for mode. There were 397, 101, and 152 scans in the nonbanded, weakly banded, and banded periods, respectively.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
As in Fig. 10, but for mode. There were 397, 101, and 152 scans in the nonbanded, weakly banded, and banded periods, respectively.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
As in Fig. 10, but for mode. There were 397, 101, and 152 scans in the nonbanded, weakly banded, and banded periods, respectively.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0385.1
It should be noted that ERSC/NR and AENR–SC are calculated using data from NR and SC, sites located at the middle and lower slopes of Tug Hill, respectively. In contrast, ER and AE are calculated using data at the shoreline and the maximum, wherever that may be located. Therefore, AENR–SC and ERSC/NR may not capture the full magnitude of the inland and orographic enhancement, but rather only the difference between the lower and middle slopes of Tug Hill. The LPE in each of these methods is also not analogous, as ERSC/NR and AENR–SC are calculated using disaggregated manual LPE observations, and ER and AE are calculated using radar-derived LPE. As can be seen in Figs. 10–12, the mean manual LPE rates at NR and SC (depicted with red dots) sometimes differ from the mean radar-derived LPE rates along the transect (depicted with the blue line). Nevertheless, the KTYX LPE rates are generally fairly close to the observations at NR and SC, and their values relative to one another generally agree with the shape of the KTYX LPE plot. Therefore, despite these caveats, the OWLeS manual LPE observations provide further evidence of the effects of 
6. Summary and conclusions
This study has examined the environmental variables affecting the inland and orographic enhancement of lake-effect LPE east of Lake Ontario and over the Tug Hill Plateau. Lake-effect events occurring along the transect were identified for cool season (November–March) periods from November 2008 to March 2017, with the lake-effect mode along the transect also recorded. The effect of 
High (low) 
When considered in a multivariate sense, the effects of each variable can be more complex than those observed in a univariate approach. For periods with low 
The effects 
The effects of LCAPE are multifaceted. LCAPE represents the theoretical buoyancy of surface parcels over the lake, and higher values likely result in convection that is deeper and/or more intense, has higher LPE rates, and initiates farther upstream over the lake. On the other hand, LCAPE is also strongly correlated with the strength of the forcing for the land breeze. For periods with low 
Lake-effect mode has effects generally consistent with those documented in Campbell et al. (2016) during OWLeS IOP2b. Consistent with their findings, the strong mesoscale ascent within bands produces intense LPE in both the lowlands and uplands, superseding the effects of ascent over Tug Hill, which has a greater effect during nonbanded periods. This reasoning also likely explains the effects upon LPE rates throughout the transect, and the inland displacement of the LPE maximum.
Our results indicate that 
Acknowledgments
This research was supported by National Science Foundation Grants AGS-1635654 and AGS-1262090. Comments and input from Justin Minder, Tyler West, and Tom Gowan greatly improved this manuscript. We thank NCEI, NCAR, MathWorks, Unidata, and the University of Utah Center for High Performance Computing for the provision of datasets and/or software. We thank Mike Dixon at NCAR for developing the Radx software package and providing invaluable help running it. The OWLeS data were gathered and made possible by a number of PIs and students working on the program. The instrumentation was also graciously hosted on the property of Jim, Cindy, John, and Cheryl Cheney and Diane and Gerhardt Brosch. Finally, we thank two anonymous reviewers, whose suggestions greatly improved the quality of this manuscript. Any opinions or findings do not necessarily represent those of the National Science Foundation or the University of Utah.
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