# The Precipitation Imaging Package: Assessment of Microphysical and Bulk Characteristics of Snow

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## Abstract

**:**

## 1. Introduction

## 2. Data and Methods

#### 2.1. Location and Instrumentation

#### 2.1.1. Precipitation Imaging Package

#### 2.1.2. Snow Field Observations

^{2}with four 150 cm snow stakes evenly distributed. New accumulations of snow are obtained five times per day by NWS MQT meteorologists at 0000, 0459 (one minute prior to local midnight), 0600, 1200, and 1800 UTC during ongoing precipitation events. A plastic, white snow board is placed adjacent to the open field and cleared off between each measurement [32]. The liquid water equivalent (LWE) precipitation is also collected and determined using a 20.32 cm diameter standard rain gauge. Snow from the gauge is melted to obtain the LWE accumulation and calculate the snow-to-liquid ratios (SLRs) for the 6-hourly periods (combining accumulation from the 0459 and 0600 UTC measurements). Observations from the snow field will be compared to the PIP-derived products and the retrievals in this work.

#### 2.1.3. Accumulation Gauge

#### 2.1.4. MicroRain Radar

#### 2.1.5. Surface Meteorological Observations

#### 2.2. Methods for Estimating Snow Properties

_{e}) is the mass, V(D

_{e}) is the fall speed, N(D

_{e}) is the size distribution, and ${\rho}_{liq}$ is the density of water (note: all parameters discussed within this section are summarized in Table A1 in Appendix A). As part of the higher-order products created by the PIP processing software, the PIP method parameterizes particle density, herein referred to as equivalent density, to obtain the mass (see Section 2.2.1). The other two methods, von Lerber et al. [17] and Wood et al. [30], outlined in Section 2.2.2 and Section 2.2.3, respectively, retrieve mass directly. The von Lerber and Wood retrievals determine the parameters α and β of a power law, which describes particle mass as a function of the area-equivalent diameter (D

_{e}) of the particle:

_{m}) and bulk equivalent density, the equivalent density averaged over the PSD. With information about particle fall speed as a function of size (observed by the PIP and handled differently by the two retrievals as described below), snowfall rates and corresponding accumulations can also be calculated.

#### 2.2.1. PIP-Derived Data Products

_{e}the diameter of a circle with the same area as that projected by a particle in the observed plane of view). The concept is similar to the snow particle bulk densities derived by Brandes et al. [37] and Huang et al. [38] from 2D Video Disdrometer (2DVD) imagery. The ${\rho}_{e}$ formulation is a data-guided parameterization that is determined by the D

_{e}and size-resolved fall speed V(D

_{e}) values observed by the PIP and is constrained by empirically derived physical limitations of ${\rho}_{e}$ and V(D

_{e}). The ${\rho}_{e}$ parameterization includes assumptions about how density varies with particle size (D

_{e}), and a fall speed-based interpolation between limiting values for density. The formulation can be written as:

_{Ve}; as opposed to the PIP use of area-equivalent diameter) was well represented by the following power law:

_{e}is observed by the PIP, the gain (c) is based on empirical observations from a snow event (described below), and the exponent (x) is –0.86 following Huang et al. [38]. The boundary condition of the maximum density is simply the density of water, ${\rho}_{liq}$ (1 g cm

^{−3}).

_{e}that the observed fall speed is the terminal velocity, as the density increases the terminal velocity increases up to the limiting case of the terminal velocities of raindrops. When precipitation falls as rain, the fall speeds should approximate those determined by Atlas and Ulbrich [40] terminal velocity of rain as a function of D

_{e}. The Atlas and Ulbrich model is valid for raindrops up to 5 mm D

_{e}. Therefore, the maximum fall speed as a function of particle size, ${\mathrm{V}}_{max}\left({D}_{e}\right)$, is taken to be that of a raindrop of the same size and is estimated from expressions for raindrop fall speed by Atlas and Ulbrich [40]. The minimum boundary condition for the fall speed-based interpolation, V

_{ref}, is empirically derived from PIP snow observations (detailed below).

_{ref}were determined empirically from high-quality reference cases of snowfall event accumulations with data obtained from the PIP and snow field observations from the NWS MQT during the 2014–2015 winter. These events had SLRs ranging from low (10:1) to high (50:1) values, corresponding roughly to events with high and low snow particle densities, respectively. The snow event chosen to constrain the low-density end of the ${\rho}_{e}$ parameterization was a high SLR event with a mean ratio of 50:1, which had uniform snowfall and occurred under ideal meteorological conditions for accumulation accuracy (surface temperatures <−5 °C and wind speeds <5 m s

^{−1}) to obtain estimates of ${\rho}_{min}\left({D}_{e}\right)$. The event accumulation was determined using the following relationship:

_{e}, the size-resolved velocity distribution $V\left({D}_{e}\right)$, and the number concentration, $N\left({D}_{e}\right)$). The gain (c) was then adjusted so that the resulting accumulation from the 50:1 SLR event matched that of the NWS MQT snow field (represented as ${\sum}_{event}{\left(R\Delta t\right)}_{i}$ in Equation (6)). The PIP observations of particle fall speeds during this high SLR (50:1) event also informed the minimum boundary condition for fall speed in the ${\rho}_{e}$ parameterization, resulting in the constant value for V

_{ref}. The resulting ${\rho}_{e}$ parameterization was then tested and found to reproduce accumulations for both the low (10:1) and high (50:1) SLR NWS MQT observations. Additionally, the analyses in this work will further evaluate the performance of the ${\rho}_{e}$ parameterization more quantitatively.

_{e}and fall speed is illustrated in Figure 1.

_{e}and fall speeds ($V\left({D}_{e}\right)$) to create a data product of ${\rho}_{e}$ (in g cm

^{−3}) resolved by particle size and time. Additionally, a one-minute bulk equivalent density, hereafter $\overline{{\rho}_{e}}$, is produced, which is the volume-weighted average of the ${\rho}_{e}$ distribution as shown in Equation (8):

^{−3}, the inverse of the $\overline{{\rho}_{e}}$ represents an SLR. Note that the equivalence of the PIP $\overline{{\rho}_{e}}$-derived SLR to the NWS-measured SLR depends on the PIP acquired volume accumulation being consistent with the resulting volume of the snow as it lies on the ground [41]. It is important to note that the ${\rho}_{e}$ parameterization was developed and tested on only a few snow events with SLRs ranging from 10:1 to 50:1 (the limiting case). The presented work examines a larger sample size of snow events and includes a broader range of SLRs and will assess the ${\rho}_{e}$ parameterization for snow conditions outside of the initial training events. The snowfall events selected for comparison in this work have a range of NWS SLRs from 7:1 (wet, dense snow) to 70:1 (ultralow density) and therefore span $\overline{{\rho}_{e}}$ values of 0.14 to 0.014 g cm

^{−3}, respectively. These values are typical for precipitation events at MQT that are classified as snow, but do not approach the expected ${\rho}_{e}$ values for moderately melted snow, as would be found in mixed-phase precipitation, and for rain, which is an area for future study. In this work, we will compare the PIP-derived data products of the bulk density ($\overline{{\rho}_{e}}$) and LWE precipitation rate against results from two previously established snow mass retrievals: von Lerber et al. [17] and Wood et al. [30] described in the following sections, as well as compared to observations from the NWS MQT snow field 6-hourly accumulation measurement.

#### 2.2.2. von Lerber Mass Retrieval

^{−3}; second, by removing the isolated observations of large particles (excluding outliers if four smaller size bins are not containing any particles, i.e., Tiira et al. [15]); and third, by taking a 5 min mean. The coefficients of $m\left({\mathrm{D}}_{e}\right)$ in power-law are derived through a linear regression fit to the 5 min retrieved masses in log-scale, requiring at least 30 observed particles, and outliers are filtered utilizing Gaussian kernel density estimation (KDE; [46]) to find the most probable mass for each diameter bin, and considering only mass observations within half-width at half maximum from the bin peak KDE value [15]. The $\overline{{\rho}_{e}}$ is then determined every 5 min as a function of ${\mathrm{D}}_{e}$ with the coefficients of $m\left({\mathrm{D}}_{e}\right)$ and the averaged observed PSD.

#### 2.2.3. Wood Mass Retrieval

_{e}values of 2.75 ± 0.25 mm, 1.5 ± 0.125 mm, and 0.75 ± 0.125 mm. These ranges are intended to provide information about how fall speed varies with size without overemphasizing the importance of the fall speed information in the retrieval. If no fall speeds are observed in one or more of the size ranges, the retrieval is not performed for that time step. For this work, 1261 retrievals out of 4632 samples were not performed, leaving 3371 samples for retrieval. This was most frequently due to observing no particles in the largest size range. Radar reflectivities are taken from the fourth range bin above the surface, approximately 120 m above the surface, to avoid contamination by ground clutter. As in Wood et al. [13,30], observed, not fitted, PSDs are used for the retrieval.

#### 2.3. Snow Event Selection

^{−1}for the event duration. Additionally, we selected snow events that had continuous snowfall for at least six hours, so that we could compare the outputs to at least one snow field accumulation measurement. Finally, we partitioned the events into low versus high SLR snow categories by using the 6-hourly NWS MQT SLR observations. By using the NWS observed SLR values to categorize the snow events, we partition only on differences in the density of snow on the ground and not by information about the particle densities, in which number density, size, and riming will all have impacts [49]. The low SLR snow events are those where the SLR is 15:1 or less, and the high SLR snow events are where the SLR is greater than 15:1. Using these criteria, we acquired 11 low and 8 high SLR snow events from the NWS MQT site between January 2017 and April 2019.

## 3. Results and Discussion

#### 3.1. Low and High SLR Snow Event Characteristics

^{−1}. The observed event mean surface temperatures also have a large spread, ranging from −17 to −0.5 °C. There is a tendency for the warmer low SLR events (those with mean temperatures closer to 0 °C) to have higher mean snow rates. Generally speaking, the majority of these low SLR snow events are produced by synoptically forced, deep precipitation (figures not shown). However, two of the low SLR events would be categorized as shallow LeS: 4 January through 6 January 2018 and 20 January through 21 January 2019. Both of these low SLR LeS events have extremely cold temperatures (event means of −17 °C), which likely indicates that boundary layer temperatures were colder than the dendritic growth zone (DGZ) and would not be an environment conducive to large particle growth [52]. This is consistent with the characteristics of a secondary mode of LeS snow identified at MQT in previous work [19,20].

^{−1}. The event mean surface temperatures ranged from −10 to −5 °C, again a much smaller distribution than that of the low SLR snow events. All of the high SLR events were a product of surface and air interactions, namely LeS, orographic forcing, or both, as supported by the precipitation radar profiles (figures not shown).

#### 3.2. Snow Microphysical Characteristics

^{3}m

^{−3}mm

^{−1}) at small D

_{e}(<1 mm), while the high SLR snow events demonstrate a broader range of PSDs with an order of magnitude fewer small particles (most values <10

^{3}m

^{−3}mm

^{−1}). These PSD results are consistent with prior studies of snowfall regimes [19]. The composite fall speed distributions also indicate differences between the low and high SLR events (Figure 2b,d, respectively). The low SLR snow composite implies generally higher fall speeds as a function of D

_{e}compared to the high SLR snow composite, which has a flatter relationship and smaller particle fall speeds (<1 m s

^{−1}). The mean fall speeds for the low SLR snow events are 30–45% larger than those for the high SLR snow events as a function of D

_{e}for those D

_{e}values <5 mm.

_{e}. N

_{0}and Λ are the PSD intercept and the slope parameter, respectively [19,55,56,57,58]. Both the von Lerber and Wood retrieval methods applied the relation in Equation (9) to 5 min intervals of the PIP data and each obtained N

_{0}and Λ for the low and high SLR events. There are differences in the resulting N

_{0}and Λ derived by the von Lerber and Wood methods due to differences in fitting methods and preprocessing of the PIP PSD data (see Section 2.2.2 and Section 2.2.3 for details).

_{0}and Λ for the low SLR events (Figure 3a,b, respectively) and the high SLR events (Figure 3c,d, respectively). In general, the low SLR composites from the two methods show similar ranges, with N

_{0}ranging from 10

^{2}to 10

^{5}m

^{−3}mm

^{−1}and Λ values of 0.5 to 6.5 mm

^{−1}in a seemingly linear structure (see Figure 3a,b). The von Lerber shows fewer small values of both N

_{0}and Λ, which could be due to preprocessing that applies the threshold for total concentration and removes single occurring particle counts prior to the fitting routine (see Section 2.2.2). In both the von Lerber and Wood outputs, the high SLR events N

_{0}and Λ values are much smaller than that for the low SLR events, with N

_{0}ranging from 10 to 10

^{4}m

^{−3}mm

^{−1}and Λ ranging from 0.4 to 1.6 mm

^{−1}, and no apparent relationship between the intercept and slope parameter. These results clearly show there are different shapes to the PSDs as a function of events that are low versus high SLR, which align with the results illustrated in Figure 2a,c. The median von Lerber values of both N

_{0}and Λ are 66% smaller for the high versus the low SLR snow events, while the median Wood value of N

_{0}is 58% smaller and Λ is 49% smaller for the high versus low SLR snow events. The N

_{0}and Λ results from the low SLR composite imply that these snowfall events have narrow PSDs with large amounts of small particles, similar to what has been observed for previous synoptically forced snow [19,55,58,59,60]. While the high SLR composite indicates the opposite: that these snow events tend to have broad PSDs with an order of magnitude fewer small particles and a tendency towards containing more large particles. The N

_{0}and Λ are similar to values seen in previous studies of LeS [19,56,61].

_{m}) is:

_{m}(see Figure 4). The high SLR event composite of D

_{m}indicates a larger spread between the von Lerber and Wood values versus the low SLR, with the Wood D

_{m}values generally higher for both categories (biases of +13.7% and +10.1%, respectively). In the low SLR event composite, both methods indicate that the majority of D

_{m}values are smaller than 2 mm. However, in the case of the high SLR events, the range of values of D

_{m}is much larger, extending from 1 to 4 mm, with a concentration towards larger values of D

_{m}mostly between 1.5 and 3 mm. The median von Lerber value of D

_{m}is 51% larger and the median Wood value of D

_{m}is 56% larger for the high versus the low SLR snow events. The GPM Dual Precipitation Radar (DPR) algorithm has prescribed relationships for precipitation and D

_{m}for stratiform and convective rainfall [21,62], and it is important to also examine these relationships for snowfall. Figure 4 illustrates that there are clear D

_{m}differences for the low versus high SLR snowfall events. The SLR event types occur under different environmental conditions that should be therefore an additional factor that is considered when examining precipitation and D

_{m}relations.

^{−4}and exponent, β, between 2 and 2.5 as produced by the von Lerber retrieval, while the Wood retrieval has a lower range of α (between 10

^{−4.25}and 10

^{−4}) and similar β (2–2.5). The von Lerber high SLR event composite shows much lower values for α (between 10

^{−4.75}and 10

^{−4}) and β (between 1.75 and 2.25). Though there are few points, the Wood retrieval also indicates lower α values, whereas the β range is similar to the low SLR output. Similar to the N

_{0}and Λ comparisons, we see that the low and high SLR snow event composite relations for α and β exhibit a clear separation, as illustrated in the von Lerber retrievals (Figure 5a,c). The values of both α and β are larger for the snow particles observed by the PIP during the low SLR events, which indicates that the mass increases faster as the area-equivalent diameter of the particle increases compared to the high SLR particles. The median of the von Lerber α values for the low SLR snow events is twice that of the high SLR, while the medians of the von Lerber β values are approximately the same for the low and high SLR (difference of 6%). The differences seen between the low versus high SLR events imply that snowfall retrieval algorithms, which rely on a priori assumptions of α and β either explicitly [48] or implicitly (e.g., Kulie and Bennartz [63], Liu [4], and Table 1, Braham et al. [64]), might benefit by adjusting to variations in snow type.

^{−3}as determined by the Root Mean Square Error (RMSE). In general, low SLR snow events produce more IWC values below 0.6 g m

^{−3}for the von Lerber and 0.4 g m

^{−3}for the Wood retrievals, respectively. The high SLR event composite has far fewer values to compare and there is a wide spread in the retrieval comparison and reduced correlation (cc of 0.539). There is an indication that the Wood output retrieves larger values of IWC matched to that of the von Lerber output; however, with so few points we can only suggest this is a possibility. There is evidence that the low SLR events produce more integrated mass as the median von-Lerber-retrieved value of IWC is more than an order of magnitude larger for the low SLR versus the high SLR snow events.

_{0}and Λ are smaller (66% and ~50%, respectively) for the high versus low SLR snow events, which is consistent with findings from Pettersen et al. [19]. The D

_{m}values for the high SLR snow events are larger for von Lerber (51%) and Wood (56%) versus the low SLR events. The median von-Lerber-retrieved value of α was two times larger for the low SLR versus the high SLR snow events, while the β values were approximately the same. The von-Lerber-retrieved IWC was more than an order of magnitude larger for the low versus the high SLR snow events. In terms of comparisons between the retrievals, the Wood D

_{m}values were between 10% and 14% larger than the von Lerber D

_{m}values, regardless of snow event type, and the D

_{m}values for the retrievals were highly correlated (cc values of 0.88 and 0.95). The Wood-retrieved values of IWC were biased 50% lower than the von Lerber IWC values for the low SLR snow events; however, the retrieved values were highly correlated between the retrieval methods (cc of 0.86).

#### 3.3. Bulk Snowfall Characteristics

^{−1}with a very high correlation between the PIP-derived snow rates and the output from von Lerber (cc of 0.976), while less correlated with the snow rates retrieved from Wood (cc of 0.786). In general, the LWE precipitation rates are less than 2 mm h

^{−1}, but there are indications of repeated instances of higher rate values. The PIP LWE precipitation rates tend to be in good agreement with those of von Lerber, a bias of +1.56%, but biased high with respect to Wood (+7.41%) for the low SLR snow events. For high SLR snow events, the PIP and von Lerber retrievals compare well (cc of 0.940), with a linear relationship as LWE precipitation rates increase. There is again good agreement between the produced snow rates, with the PIP is biased slightly high (+3.1%) compared to the von Lerber values. Many of the high SLR snow event samples provided physically inconsistent inputs for the Wood method and were so excluded (see Section 2.2.3), so it is difficult to compare. However, we can compare the differences between the low and high SLR snow events by examining the PIP and von Lerber produced values of snow rate. Though the RMSE between the PIP and von Lerber values of snow rate is 0.115 mm h

^{−1}for the low SLR and 0.242 mm h

^{−1}for the high SLR snow events, the median values for the event regimes agree very well, with a 4% difference for the low SLR and a 9% difference for the high SLR snow events. Unsurprisingly, the low SLR snow events have much larger LWE precipitation rates, with median rates more than 20 times higher compared to the high SLR snow events for both the PIP and von Lerber outputs.

^{−3}) for the low and high SLR snow events (see Figure 8). As discussed in Section 2.2.1, the SLR output from the three methods is roughly the inverse of the ratio $\overline{{\rho}_{e}}$ to the density of water (1 g cm

^{−3}); however, it is important to note that this conversion does not account for compaction effects. Here, we compare the $\overline{{\rho}_{e}}$ values by inverting them to produce bulk SLR values for each time step. The low and high SLR events were defined using SLR observations from the NWS MQT snow field, and therefore we expect the comparisons in Figure 8 to have different ranges of PIP, von Lerber, and Wood produced SLRs as a function of event category, regardless of method. We see for the low SLR snow event composites (Figure 8a,b) that the vast majority of SLR values are less than 10:1 for the PIP, von Lerber, and Wood retrievals. The SLR output from the PIP and the von Lerber retrievals have a correlation of 0.756. There is a shift for SLR of >15 where von Lerber reports larger values compared to the PIP, which results in the PIP values biased 30% lower than output from von Lerber. However, the median values of the PIP and von-Lerber-derived SLR are within 6%. The low SLR composite for the PIP and Wood-derived SLR have a low correlation (cc of 0.382), and an inclination for the PIP SLR to be much lower than that of the Wood output (bias of –79.6%). The high SLR event composite between the PIP and von Lerber SLRs (Figure 8c) show a similar correlation to the low SLR composite (cc of 0.804); however, with more variability (RMSE of 4.843), and a low bias of almost 50%. Additionally, the median PIP-produced SLR value is 60% smaller than that of von Lerber for the high SLR snow events. There are too few values of the Wood method for the high SLR snow events to conclude similarities or differences with the PIP output (Figure 8d).

#### 3.4. Detailed Example of a Snow Transition Event

^{−1}; Figure 10b). We also see that the PIP PSDs are very narrow during this time period with particles smaller than 5 mm D

_{e}(Figure 10c). Additionally, the PIP ${\rho}_{e}$ distribution values are greater than 0.1 g cm

^{3}(10:1 SLR) during the early part of the snow event (Figure 10d). At 1300 UTC, we see an abrupt change in the observations with increasing reflectivity and Doppler velocity values with decreasing precipitation height (~1.5 km AGL). At this same time, the PIP PSDs respond with an immediate broadening (particles ranging up to 15 mm D

_{e}), while still maintaining a high concentration of small particles (>10

^{4}particles smaller than 1 mm D

_{e}). We also see that the ${\rho}_{e}$ distribution shifts to lower values, generally less than 0.1 g cm

^{−3}(Figure 10d). The accumulation (Figure 10e) is gradual during the low SLR period of the snow event, but the snow rate increases directly following the transition at 1300 UTC, with ~9 mm accumulation in 6 h (in agreement with the von Lerber accumulation). Overall, the von Lerber total accumulation exactly matched the NWS MQT snow field, while the PIP recorded a relatively higher amount (120%) and the Wood retrieval much less (67%). Unsurprisingly, we see an instantaneous response from the values of SLR and D

_{m}at 1300 UTC as well (Figure 10f,g, respectively), and both increase rapidly, with SLR values from 10:1 to greater than 20:1 and average D

_{m}growing from ~0.5 to more than 2 mm. During the transition period, winds shift to slightly higher speeds (Figure 10h) and more northerly direction.

## 4. Conclusions

_{0}and Λ were very different for the low versus high SLR and consistent with values found in previous studies of synoptically forced and lake-effect snowfall. In general, the D

_{m}values for the high SLR snow events are larger and more variable than those for the low SLR snow events. Similar to the N

_{0}and Λ comparisons, we see that the low and high SLR snow event composite relations for α and β exhibit a clear separation, with lower values of both for the high SLR snow events. There were too few IWC values for the high SLR snow events to compare the von Lerber and Wood methods, but low SLR IWC values are generally larger. In general, the PIP LWE snow rates compared well to those produced by the retrieval methods for the high and low (von Lerber only) density events. The PIP and von-Lerber-retrieved values of SLR were consistent for both low and high SLR snow events, with the von Lerber method producing consistently larger values. Finally, accumulation comparisons between all three methods and the six-hourly snow field were excellent for both the low and high SLR snow events.

## 5. Data Availability

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**This table described the parameters for the PIP-derived data products in Section 2.2.1.

Parameter Symbol | Parameter Description | Units |
---|---|---|

D_{e} | area-equivalent diameter | mm |

D_{Ve} | volume-equivalent diameter | mm |

D_{m} | mass-weighted mean diameter | mm |

${\rho}_{e}$ | particle distribution equivalent density | g cm^{−3} |

$\overline{{\rho}_{e}}$ | bulk equivalent density | g cm^{−3} |

${\rho}_{size}$ | size-averaged density | g cm^{−3} |

${\rho}_{liq}$ | water density | g cm^{−3} |

${\rho}_{min}$ | minimum density boundary condition | g cm^{−3} |

R | liquid water equivalent precipitation rate | mm h^{−1} |

m(D_{e}) | mass distribution | g |

V(D_{e}) | velocity distribution | m s^{−1} |

V_{max}(D_{e}) | maximum fall speed for rain drop of D_{e} | m s^{−1} |

V_{ref} | minimum fall speed boundary condition | m s^{−1} |

N(D_{e}) | size distribution | m^{−3} mm^{−1} |

## Appendix B

**Figure A1.**Example of a low SLR snow event on 15 April 2018. (

**a**) Shown is data from the MRR reflectivity, (

**b**) MRR Doppler velocity, (

**c**) PIP-produced PSDs, (

**d**) PIP-derived ${\rho}_{e}$ distribution as a function of D

_{e}, (

**e**) LWE accumulation for all three retrievals, the Pluvio, and the NWS 6-hourly snow field, (

**f**) calculated SLR from all three retrievals and the NWS 6-hourly snow field observations, (

**g**) the mass-weighted diameter (D

_{m}) from von Lerber and Wood, (

**h**) and the surface meteorological conditions. All variables are presented as a function of time from 1000 UTC to 2300 UTC.

**Figure A2.**Example of a high SLR snow event on 10 January 2019. (

**a**) Shown is data from the MRR reflectivity, (

**b**) MRR Doppler velocity, (

**c**) PIP-produced PSDs, (

**d**) PIP-derived ${\rho}_{e}$ distribution as a function of D

_{e}, (

**e**) LWE accumulation for all three retrievals, the Pluvio, and the NWS 6-hourly snow field, (

**f**) calculated SLR from all three retrievals and the NWS 6-hourly snow field observations, (

**g**) the mass-weighted diameter (D

_{m}) from von Lerber and Wood, (

**h**) and the surface meteorological conditions. All variables are presented as a function of time from 0000 UTC to 2300 UTC.

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**Figure 1.**Three-dimensional visualization of the relation of ${\rho}_{e}$ parameterization. The vertical axis illustrates the ${\rho}_{e}$ values, while horizontal plane axes represent the fall speed and D

_{e}.

**Figure 2.**Composite two-dimensional histograms of Precipitation Imaging Package (PIP) observations of PSD as a function of mean diameter of the particles for the low and high SLR snow events ((

**a**,

**c**), respectively), and composite two-dimensional histograms of PIP observations of fall speed as a function of mean diameter of the particles for the low and high SLR snow events ((

**b**,

**d**), respectively). Note: the discretization of the PIP measured values of PSD and mean diameter is due to the finite measurement volume of the PIP.

**Figure 3.**The N

_{0}and Λ relationships as calculated for the low SLR snow events are shown in (

**a**) (von Lerber) and (

**b**) (Wood). The N

_{0}and Λ relationships as calculated for the high SLR snow events are shown in (

**c**) (von Lerber) and (

**d**) (Wood). Note that both variables are shown as log

_{10}scaled.

**Figure 4.**Shown are comparisons of calculated mass-weighted diameter (D

_{m}) from the von Lerber and Wood retrievals for the low SLR (

**a**) and high SLR (

**b**) snow events. The von Lerber D

_{m}is plotted on the x-axes and the Wood D

_{m}on the y-axes. The black dashed line represents a 1:1 relationship, while the blue dotted line is the linear regression fit to the data.

**Figure 5.**The α and β output as calculated for the low SLR snow events are shown in (

**a**) (von Lerber) and (

**b**) (Wood). The α and β output as calculated for the high SLR snow events are shown in (

**c**) (von Lerber) and (

**d**) (Wood). Note that α values are shown as log

_{10}scaled. There are fewer points in the Wood-retrieved output due to the filtering of times when the Pluvio does not report any accumulation.

**Figure 6.**Shown are comparisons of five-minute values of IWC from the von Lerber and Wood retrievals for the low SLR (

**a**) and high SLR (

**b**) snow events. The von Lerber IWC is on the x-axes and the Wood IWC on the y-axes. There are fewer points in the Wood-retrieved output due to the filtering of times when the Pluvio does not report any accumulation, resulting in fewer comparisons of retrieved mass overall, but particularly in the high SLR events. The black dashed line represents a 1:1 relationship, while the blue dotted line is the linear regression fit to the data.

**Figure 7.**Shown are comparisons of the respective retrievals of snow rate (note: shown in log

_{10}). The PIP-derived snow rate product is plotted along the y-axes in each panel, where the von Lerber and Wood-retrieved snow rates are plotted along the x-axes ((

**a**,

**c**) and (

**b**,

**d**), respectively). (

**a**,

**b**) illustrate the results from the low SLR snow events and (

**c**,

**d**) illustrate the results from the high SLR snow events. The black dashed line represents a 1:1 relationship, while the blue dotted line is the linear regression fit to the data.

**Figure 8.**Shown are comparisons of the respective $\overline{{\rho}_{e}}$ inverted into SLR. The PIP-derived SLRs are plotted along the y-axes in each panel, whereas the von Lerber and Wood-retrieved SLRs are plotted along the x-axes ((

**a**,

**c**) and (

**b**,

**d**), respectively). (

**a**,

**b**) illustrate the results from the low SLR snow events and (

**c**,

**d**) illustrate the results from the high SLR snow events. The black dashed line represents a 1:1 relationship, while the blue dotted line is the linear regression fit to the data.

**Figure 9.**Displayed are comparisons of the 6-hourly accumulations from the PIP, von Lerber, and Wood output to corresponding times from the National Weather Service (NWS) Marquette, Michigan (MQT) snow field observations (x-axes). (

**a**) shows the PIP accumulations (46 6 h periods), (

**c**) shows the von Lerber accumulations (44 6 h periods), and (

**e**) shows the Wood accumulations (22 6 h periods). Shown also are the 6-hourly NWS MQT calculations of SLR (x-axes) matched to the median values for the same time periods for the three retrievals (right panels). (

**b**) shows the PIP median SLR, (

**d**) shows the von Lerber median SLR, and (

**f**) shows the Wood median SLR. The black dashed line represents a 1:1 relationship. Low SLR samples are in magenta, high SLR samples are in blue, and transition events are in green.

**Figure 10.**Example of a snow event that transitions from low to high SLR snowfall from 19 to 20 November 2018. (

**a**) Shown is data from the MRR reflectivity, (

**b**) MRR Doppler velocity, (

**c**) PIP-produced PSDs, (

**d**) PIP-derived ${\rho}_{e}$ distribution as a function of D

_{e}, liquid water equivalent (LWE) accumulation for all three retrievals, (

**e**) the Pluvio, and the NWS 6-hourly snow field, (

**f**) calculated SLR from all three retrievals and the NWS 6-hourly snow field observations, (

**g**) the mass-weighted diameter (D

_{m}) from von Lerber and Wood, (

**h**) and the surface meteorological conditions. All variables are presented as a function of time from 19 November at 0400 UTC to 20 November at 0200 UTC. The transition from low to high SLR occurs at approximately 1300 UTC.

**Table 1.**This is a table of the 11 low SLR snow events used in this work. Listed are the start and end times used for the analyses, as well as mean values of snow-to-liquid ratio (SLR), snow rate (here abbreviated as SR), wind speed (here abbreviated as WS), and temperature for the duration of each event.

Start (Date/Time) | End (Date/Time) | Mean SLR NWS | Mean SR PIP (mm h ^{−1}) | Mean WS (m s ^{−1}) | Mean Temp (°C) |
---|---|---|---|---|---|

11 November 2017 0600 UTC | 11 November 2017 1200 UTC | 12.14 | 0.899 | 3.33 | −5.25 |

11 December 2017 1300 UTC | 11 December 2017 1900 UTC | 15 | 0.095 | 3.28 | −8.95 |

13 December 2017 1000 UTC | 13 December 2017 1800 UTC | 13 | 0.278 | 1.55 | −11.49 |

4 January 2018 0000 UTC | 6 January 2018 1600 UTC | 15.03 | 0.137 | 3.42 | −17.16 |

22 January 2018 1800 UTC | 23 January 2018 0300 UTC | 7.5 | 3.751 | 3.96 | −3.53 |

3 February 2018 1800 UTC | 4 February 2018 0400 UTC | 12 | 0.316 | 1.83 | −12.88 |

12 April 2018 0800 UTC | 12 April 2018 1600 UTC | 10.45 | 1.672 | 0.88 | −0.46 |

15 April 2018 1000 UTC | 15 April 2018 2300 UTC | 7.34 | 3.134 | 6.00 | −6.41 |

2 December 2018 0600 UTC | 3 December 2018 0300 UTC | 9.11 | 2.455 | 4.73 | −1.74 |

7 January 2019 0700 UTC | 7 January 2019 2300 UTC | 12.65 | 1.035 | 3.47 | −2.22 |

20 January 2019 0600 UTC | 21 January 2019 0600 UTC | 14.89 | 0.274 | 2.87 | −16.89 |

**Table 2.**This is a table of the eight high SLR snow events used in this work. Organization follows that of Table 1.

Start (Date/Time) | End (Date/Time) | Mean SLR NWS | Mean SR PIP (mm h ^{−1}) | Mean WS (m s ^{−1}) | Mean Temp (°C) |
---|---|---|---|---|---|

14 December 2017 0000 UTC | 14 December 2017 0800 UTC | 32.75 | 0.259 | 2.59 | −10.21 |

15 January 2018 2200 UTC | 16 January 2018 2000 UTC | 36.39 | 0.351 | 1.00 | −9.76 |

28 January 2018 0800 UTC | 28 January 2018 2300 UTC | 70 | 0.054 | 2.48 | −8.86 |

6 March 2018 1800 UTC | 7 March 2018 2300 UTC | 27.58 | 0.511 | 3.24 | −7.26 |

13 March 2018 0400 UTC | 7 March 2018 2300 UTC | 30.33 | 0.132 | 3.94 | −7.78 |

17 November 2018 0000 UTC | 17 November 2018 2100 UTC | 29.62 | 0.148 | 3.14 | −6.04 |

25 November 2018 1200 UTC | 26 November 2018 2000 UTC | 30 | 0.079 | 3.49 | −5.43 |

10 January 2019 0000 UTC | 10 January 2019 2300 UTC | 59 | 0.053 | 3.39 | −10.50 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Pettersen, C.; Bliven, L.F.; von Lerber, A.; Wood, N.B.; Kulie, M.S.; Mateling, M.E.; Moisseev, D.N.; Munchak, S.J.; Petersen, W.A.; Wolff, D.B. The Precipitation Imaging Package: Assessment of Microphysical and Bulk Characteristics of Snow. *Atmosphere* **2020**, *11*, 785.
https://doi.org/10.3390/atmos11080785

**AMA Style**

Pettersen C, Bliven LF, von Lerber A, Wood NB, Kulie MS, Mateling ME, Moisseev DN, Munchak SJ, Petersen WA, Wolff DB. The Precipitation Imaging Package: Assessment of Microphysical and Bulk Characteristics of Snow. *Atmosphere*. 2020; 11(8):785.
https://doi.org/10.3390/atmos11080785

**Chicago/Turabian Style**

Pettersen, Claire, Larry F. Bliven, Annakaisa von Lerber, Norman B. Wood, Mark S. Kulie, Marian E. Mateling, Dmitri N. Moisseev, S. Joseph Munchak, Walter A. Petersen, and David B. Wolff. 2020. "The Precipitation Imaging Package: Assessment of Microphysical and Bulk Characteristics of Snow" *Atmosphere* 11, no. 8: 785.
https://doi.org/10.3390/atmos11080785