Differentiating Freezing Drizzle and Freezing Rain in HRRR Model Forecasts

Sarah A. Tessendorf aNational Center for Atmospheric Research, Boulder, Colorado

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Allyson Rugg aNational Center for Atmospheric Research, Boulder, Colorado

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Alexei Korolev bEnvironment and Climate Change Canada, Toronto, Ontario, Canada

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Ivan Heckman bEnvironment and Climate Change Canada, Toronto, Ontario, Canada

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Courtney Weeks aNational Center for Atmospheric Research, Boulder, Colorado

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Gregory Thompson aNational Center for Atmospheric Research, Boulder, Colorado

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Darcy Jacobson aNational Center for Atmospheric Research, Boulder, Colorado

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Dan Adriaansen aNational Center for Atmospheric Research, Boulder, Colorado

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Julie Haggerty aNational Center for Atmospheric Research, Boulder, Colorado

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Abstract

Supercooled large drop (SLD) icing poses a unique hazard for aircraft and has resulted in new regulations regarding aircraft certification to fly in regions of known or forecast SLD icing conditions. The new regulations define two SLD icing categories based upon the maximum supercooled liquid water drop diameter (Dmax): freezing drizzle (100–500 μm) and freezing rain (>500 μm). Recent upgrades to U.S. operational numerical weather prediction models lay a foundation to provide more relevant aircraft icing guidance including the potential to predict explicit drop size. The primary focus of this paper is to evaluate a proposed method for estimating the maximum drop size from model forecast data to differentiate freezing drizzle from freezing rain conditions. Using in situ cloud microphysical measurements collected in icing conditions during two field campaigns between January and March 2017, this study shows that the High-Resolution Rapid Refresh model is capable of distinguishing SLD icing categories of freezing drizzle and freezing rain using a Dmax extracted from the rain category of the microphysics output. It is shown that the extracted Dmax from the model correctly predicted the observed SLD icing category as much as 99% of the time when the HRRR accurately forecast SLD conditions; however, performance varied by the method to define Dmax and by the field campaign dataset used for verification.

Significance Statement

Aircraft icing is a hazardous condition that can lead to aviation accidents. We are working to improve forecasts of when aircraft icing conditions occur, especially with respect to a special type of icing condition that occurs from larger supercooled liquid drops that can more detrimentally impact some aircraft than icing from small drops. We investigated a method to distinguish two types of large drop icing in operational forecast models: freezing drizzle and freezing rain. These findings suggest that forecast models are capable of distinguishing these two types of icing, which can provide valuable information to aviation weather forecasters. However, there are improvements that still need to be made to improve how often models accurately predict supercooled large drop icing.

© 2021 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: Sarah A. Tessendorf, saraht@ucar.edu

Abstract

Supercooled large drop (SLD) icing poses a unique hazard for aircraft and has resulted in new regulations regarding aircraft certification to fly in regions of known or forecast SLD icing conditions. The new regulations define two SLD icing categories based upon the maximum supercooled liquid water drop diameter (Dmax): freezing drizzle (100–500 μm) and freezing rain (>500 μm). Recent upgrades to U.S. operational numerical weather prediction models lay a foundation to provide more relevant aircraft icing guidance including the potential to predict explicit drop size. The primary focus of this paper is to evaluate a proposed method for estimating the maximum drop size from model forecast data to differentiate freezing drizzle from freezing rain conditions. Using in situ cloud microphysical measurements collected in icing conditions during two field campaigns between January and March 2017, this study shows that the High-Resolution Rapid Refresh model is capable of distinguishing SLD icing categories of freezing drizzle and freezing rain using a Dmax extracted from the rain category of the microphysics output. It is shown that the extracted Dmax from the model correctly predicted the observed SLD icing category as much as 99% of the time when the HRRR accurately forecast SLD conditions; however, performance varied by the method to define Dmax and by the field campaign dataset used for verification.

Significance Statement

Aircraft icing is a hazardous condition that can lead to aviation accidents. We are working to improve forecasts of when aircraft icing conditions occur, especially with respect to a special type of icing condition that occurs from larger supercooled liquid drops that can more detrimentally impact some aircraft than icing from small drops. We investigated a method to distinguish two types of large drop icing in operational forecast models: freezing drizzle and freezing rain. These findings suggest that forecast models are capable of distinguishing these two types of icing, which can provide valuable information to aviation weather forecasters. However, there are improvements that still need to be made to improve how often models accurately predict supercooled large drop icing.

© 2021 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: Sarah A. Tessendorf, saraht@ucar.edu

1. Introduction

It is well established that some clouds contain supercooled liquid water (SLW), which poses an icing hazard for the aviation industry (Sand et al. 1984). Under favorable conditions, supercooled large drop (SLD) icing can occur, such as from freezing drizzle and freezing rain (Pobanz et al. 1994; Cober et al. 1996, 2001a; Cober and Isaac 2012; Bernstein et al. 2019). SLD icing is particularly hazardous to aircraft as current deicing techniques do not in general protect against this type of icing (Sand et al. 1984; Cooper et al. 1984; Politovich 1989; Marwitz et al. 1997; Ashenden and Marwitz 1998). A consequence of SLD icing was starkly illustrated by the fatal crash of a commercial ATR-72 aircraft on 31 October 1994 (Roselawn, Indiana; Marwitz et al. 1997). The presence of SLD during this accident spurred the aviation industry and scientists to examine the role of SLD icing (e.g., Rasmussen et al. 1992; Politovich and Bernstein 1995; Rasmussen et al. 1995; Isaac et al. 2001; Bernstein et al. 2005; Cober and Isaac 2012) and eventually led to new regulatory actions to certify new aircraft to fly into known or forecast SLD icing conditions. Prior to this, regulations known as appendix C1 covered all known atmospheric icing conditions. The new regulations, known as appendix O,2 were added to cover aircraft certification to fly in regions of SLD icing conditions. Accidents (and incidents) similar to Roselawn, Indiana, prompted the Federal Aviation Administration (FAA) to support the development and improvement of icing guidance products, particularly with respect to SLD icing conditions.

Appendix O covers icing environments with SLD in which the maximum drop size (Dmax) is 100 μm or greater (Cober and Isaac 2012). Unlike for appendix C, there is no minimum threshold of LWC to fall under appendix O. Appendix O is further categorized into freezing drizzle (FZDZ) or freezing rain (FZRA) where FZDZ is defined by a Dmax at or below 500 μm while FZRA is defined by Dmax greater than 500 μm. The median volume diameter (MVD; divides the mass distribution of droplets into two halves where half of the total water content has droplet diameters smaller, and the other half larger, than the MVD) is a common measure of how condensed water is distributed across the droplet size distribution and has often been used as part of defining droplet size for aircraft icing (e.g., appendix C, Finstad et al. 1988). However, the reason the FAA regulations use Dmax to define these two categories of SLD was because it was shown to be most useful in distinguishing FZDZ from FZRA (Cober et al. 2009; Cober and Isaac 2013). In this paper, we focus on a method to estimate Dmax from model output.

In the literature, there are typically two atmospheric scenarios that lead to SLD icing (Cortinas et al. 2004): one characterized by a “classical” ice-melting process, and the other based on a “nonclassical” collision–coalescence, or a warm-rain, process. Classical SLD environments often lead to FZRA conditions (Bocchieri 1980; Martner et al. 1992; Rauber et al. 1994) and are typically characterized by an inversion in the thermodynamic structure that includes a warm layer (or “warm nose”) of temperatures greater than 0°C. As ice and snow particles fall through a warm inversion, they melt to form rain-sized liquid drops that fall through a subfreezing layer before reaching the surface. In contrast, nonclassical SLD environments leading to freezing drizzle are typically characterized by the entire profile being subfreezing, but with relatively warm cloud-top temperature (typically >−12°C), such that ice formation within the cloud is weak or inactive. This may occur in a relatively clean atmosphere devoid of ice nucleating particles (INP) that also has conditions supporting collision–coalescence, such as low concentrations of cloud condensation nuclei (CCN) or relatively high SLW content (Ohtake 1963; Huffman and Norman 1988; Cober et al. 1996; Bernstein 2000; Rauber et al. 2000; Kajikawa et al. 2000; Rasmussen et al. 2002; Bernstein et al. 2019). It is possible that under the right conditions, FZRA-sized drops may also grow in these “nonclassical” environments, but this phenomenon has seldom been observed.

To forecast SLD icing hazards, numerical weather prediction (NWP) models need to accurately predict a variety of atmospheric processes conducive to the formation of these SLD environments. Such processes include atmospheric dynamics that lead to vertical motions supporting cloud formation, thermodynamic cloud structure that supports either the classical or nonclassical environments for SLD, and microphysical cloud processes that explicitly predict ice formation, droplet and ice crystal growth, depletion of SLW by ice crystals, and drop size distribution (DSD) evolution that directly impacts Dmax. This study focuses on evaluating the microphysical processes related to the production of SLD and how it is categorized as FZDZ or FZRA. It is beyond the scope of this paper to address the ability of the model to capture the dynamic and thermodynamic aspects of SLD-producing environments. As a result, this analysis focuses on points in which the model correctly predicted the presence of SLD, so its ability to distinguish FZDZ and FZRA can be examined.

Historically, early NWP models did not explicitly predict SLD and thus atmospheric variables, such as temperature, humidity, and vertical profiles of these, were used as proxies for icing using simple correlation studies (Schultz and Politovich 1992; Thompson et al. 1997; Bernstein et al. 2005). More recently, explicit NWP model predictions of hydrometeor phase and amount of SLW has shown improved skill compared to older icing forecast methods (Thompson et al. 2017; Xu et al. 2019). Most recently, Xu et al. (2019) compared pilot reports (PIREPs) of icing conditions aloft to forecasts of supercooled cloud and rainwater in the High-Resolution Rapid Refresh (HRRR) model and found probability of detection (POD) > 60% (increasing to ~80% when using the time-lagged ensemble approach). This result was quite improved when compared to previous generations of NWP icing forecasts that had a POD of ~40%. To investigate appendix O icing forecast performance, they also compared surface METAR observations—of FZDZ and FZRA combined to represent SLD observations as a whole—to supercooled rainwater at the surface in the HRRR and found POD 45%–50%3 (which increased to 55%–65% when using the time-lagged ensemble approach). These results focused on forecasting the presence of icing as appendix C or appendix O and not based more specifically on drop size due to the lack of requisite observations. In addition, direct prediction of drop size metrics (i.e., Dmax or MVD) has not been a standard forecast model output. This was mostly due to operational computational constraints requiring lower sophistication in the microphysics parameterizations to accommodate computer memory and time requirements.

In version 2 (v2) of the HRRR model (Benjamin et al. 2016b), running operationally at the National Centers for Environmental Prediction (NCEP) since August 2016, the updated Thompson–Eidhammer bulk microphysics scheme (Thompson and Eidhammer 2014, hereafter TE14) predicts both the number concentration and mixing ratio of the cloud drop and rain categories due to its addition of a prognostic variable for CCN. This allows the DSDs of cloud and rain to vary in space and time and allows the MVD or Dmax to vary for a given water content. NWP models that separately predict water content and number concentration potentially provide valuable information about the DSD needed to forecast SLD icing conditions.

In this study, a method to estimate Dmax from these model size distributions is presented with the goal of using this technique to discriminate between the FZDZ and FZRA icing categories defined by appendix O using the HRRR model. Section 2 outlines the observational datasets used in this analysis. Section 3 describes the NWP model and methods for drop size metrics being evaluated. Section 4 presents two brief case studies to illustrate the two SLD formation mechanisms. Section 5 presents statistical results and evaluates the method for calculating the model Dmax compared to in situ observations, and section 6 provides a summary and the conclusions.

2. Observational data

Direct measurements of supercooled drop size are required to verify the presence of SLD icing conditions. However, these types of measurements are not routinely collected, nor is this information often included in PIREPs, the primary source of observed icing conditions above the surface. To overcome this limitation, we utilize data from two recent field campaigns that took place between January and March 2017: 1) The Seeded and Natural Orographic Wintertime clouds: the Idaho Experiment (SNOWIE; Tessendorf et al. 2019); and 2) the Buffalo Area Icing Research Study (BAIRS), part II (BAIRS II; Williams et al. 2020) in the Buffalo, New York area. Both field programs collected in situ, cloud microphysical measurements within SLW clouds during a time when the operational HRRR model ran with the TE14 microphysics.

a. SNOWIE overview

The SNOWIE field campaign focused on collecting measurements in orographic clouds in the mountains north of Boise, Idaho, and was conducted for 10 weeks between 7 January and 17 March 2017. In total, 23 research flights were conducted by the University of Wyoming King Air, equipped with a suite of cloud microphysical probes and a profiling W-band cloud radar. Although it was not the intent of the program to focus on collecting data in icing conditions, clouds targeted for research flights typically contained SLW and SLD, making this dataset valuable for the present study. Frequent rawinsondes were launched nearby before and during each flight to capture thermodynamic profile data for each case. For more details on the types of data collected during SNOWIE, see Tessendorf et al. (2019). Of the 23 research flights, 17 flights had good quality cloud drop size measurements from both the Cloud Droplet Probe (CDP) and 2D-Stereo (2D-S) optical array probes (OAPs). The 2D-S is the primary probe that can be used for detecting drop sizes in SLD conditions by its ability to measure particle sizes > 100 μm. All 17 flights included in this analysis encountered SLD icing conditions at some point in the flight.

b. BAIRS II overview

BAIRS II was conducted out of Ottawa, Canada, focusing on collecting measurements in icing clouds in the Buffalo, New York, area. The campaign utilized the National Research Council of Canada (NRC) Convair-580 aircraft equipped with a suite of cloud microphysical instruments and a profiling X- and W-band cloud radar (Williams et al. 2020; Korolev et al. 2020). There were five research flights conducted between January and March 2017, each targeting SLD icing conditions. Of note, BAIRS II collected measurements in the warm layer of a classical FZRA environment, in addition to nonclassical environments. Of the instruments flown on the Convair-580, those comparable to the SNOWIE measurements that provide data relevant for this study include a Forward Scattering Spectrometer Probe (FSSP), which provides similar information as the CDP, and a 2D-S optical array probe.

c. Data processing and methods

Data from all particle instruments operated during the two flight campaigns were processed and comparisons were performed during post processing. During the data quality control process, we identified the best particle probe to be used in the output dataset for each flight based on an assessment of their minute-by-minute performance. If the performances of redundant OAPs were equally good, we gave preference to the 2D-S, since this probe has a better pixel resolution (10 μm) compared to other similar instruments.

As a result, the 2D-S data were used for identifying SLD conditions. The liquid and ice phases were segregated based on the assumption that liquid droplets produce circular images, whereas ice particles have noncircular images only. This assumption was used for separate calculations of size distributions of liquid drops and ice particles measured by the 2D-S. One of the flaws of this technique lies in the ambiguity of identifying liquid phase in general, since images of quasi-spherical ice particles (e.g., frozen drops, compact irregulars, short columns) or compact out-of-focus ice particles may appear as circles and, therefore, can be confused with liquid. Typically, such misidentification of particle phase may occur for 2D-S images of ice particles smaller than approximately 200 μm. To mitigate the effect of phase misidentification, the images were manually inspected for each flight, especially for periods when the observed liquid Dmax was unrealistically large (>1 mm). Based upon this manual inspection, we imposed an additional criterion that the CDP (or FSSP) liquid water content must be >0.01 g m−3 at the time that 2D-S liquid particles are detected to avoid ice being misidentified as liquid.4 This additional criterion eliminated 66% of the processed 2D-S data and helped reduce misidentified ice from being classified as liquid that would have biased the Dmax observations as being higher than they are. However, there may still be some periods with misidentified ice included in the analysis as it is very challenging to discriminate liquid from ice in 2D-S data in a completely objective manner.

The 2D-S data processing employed in this study was arranged into a two-stage process. During the first stage, the processing software extracted numerous properties of all image frames and all individual images inside the image frames, including interarrival times, number of images per frame, various image sizes, areas, perimeters, hollowness, roundness, etc. The outcome of the first stage is a table of properties of each individual image measured by the 2D-S. During the second stage the processing software performed a sequence of procedures of acceptance and rejection of particle images, aiming to filter out various image artifacts. These artifacts are typically caused by ice shattering, diffraction effects, electronic noise, optics contamination, and liquid shedding. After this, for the accepted liquid droplets and ice particles, separate size distributions were calculated for each averaging (1-s) time interval. More details on the specific steps to process the 2D-S data are outlined in Table 1.

Table 1.

2D-S data processing steps to create separate liquid (circular) and ice (noncircular) particle size distributions.

Table 1.

These steps result in a drop size distribution of liquid drops every second, with each size bin of the distribution providing the number concentration of drops in the given bin. We calculated the observed Dmax for every 30-s average of the 1-Hz 2D-S liquid size distributions by integrating particle concentrations from the largest size bin until a cumulative particle concentration of at least 85 m−3 was met, following a similar approach as Cober and Isaac (2012).5 The observed Dmax is defined as the mean size of the bin where integration stopped. A 30-s average was used to reflect a horizontal scale of approximately 3 km (the horizontal resolution of the HRRR) based on typical aircraft flight speeds of ~100 m s−1.

3. Model data and methodology

The HRRR v2 forecast model (Benjamin et al. 2016b) ran operationally during the winter of 2017, and the hourly forecast model output files were archived at the National Center for Atmospheric Research (NCAR). This version of HRRR employed the TE14 bulk microphysics scheme that predicts both number concentration and mass mixing ratio of cloud and rainwater. In the TE14 scheme, the cloud droplet category falls under the appendix C icing regulations (based on the size range assumed), while those in the rain category fall under the appendix O size range (Thompson et al. 2017; Xu et al. 2019). As a result, only the prognosed rain category is needed to diagnose FZDZ and FZRA. However, the microphysical characteristics (i.e., DSD) of the cloud water category influences the collision–coalescence process, which is the basis for the nonclassical SLD formation mechanism. The DSD for cloud droplets in TE14 is assumed to follow a generalized gamma size distribution and the size distribution for rain is assumed to follow the inverse-exponential distribution6 (cf. Marshall and Palmer 1948; Thompson et al. 2008; TE14).

The goal is to calculate the Dmax of the supercooled rain size distribution. If Dmax is greater than 100 μm we assume that FZDZ is present, and if larger than 500 μm, then FZRA is present. Given that appendix O contains two categories of SLD icing conditions, further delineation between FZDZ and FZRA is desired and the focus of this study is to determine whether this is possible in the HRRR model. The challenge is that the functional form of the model DSD is infinite, albeit negligible in number for large droplets, thereby having no predetermined Dmax (Fig. 1 illustrates examples of gamma DSDs for rain from the model). This study aims to demonstrate a method to extract a Dmax from a HRRR model forecast and evaluate the model’s ability to distinguish FZDZ from FZRA.

Fig. 1.
Fig. 1.

Sample rain drop size distributions for a FZDZ (blue) and FZRA (red) scenario, as well as a scenario that would be classified differently based upon the percentile used (purple). The 95th, 99th, and 99.9th percentiles of these distributions are noted by the dots (from left to right). Number concentration is equal to 1 cm−3 in these example DSDs.

Citation: Weather and Forecasting 36, 4; 10.1175/WAF-D-20-0138.1

a. Method to extract Dmax from the HRRR model

In the absence of a finite size distribution in the model, where a maximum value is certain, the approach used here is to estimate Dmax based upon a very large (e.g., >95th) percentile of the distribution. Dmax is estimated from the model rain size distribution based upon a percentile of the number of rain drops and comparing this model calculation to the observations. A benefit of this method is that it is computationally efficient since it can be solved directly using the following equation:
D(PN)=1λln(1PN100),
where PN is the chosen percentile (from 0% to 100%), ln is the natural logarithm, and λ is the slope parameter of the gamma distribution for the rain category. The slope parameter λ is then defined by
λ=[πρw6NrqrΓ(4+μ)Γ(1+μ)]1/3,
where Nr is the rain droplet number concentration (m−3), qr is the rainwater content (kg m−3), ρw is the density of water (1000 kg m−3), μ is the shape factor, and Γ is the gamma function in the form of Γ(x) = EXP[GAMMALN(x)]. In the TE14 microphysics scheme, μ = 0 for rain, which results in an inverse-exponential distribution and a simplified form of the equation for λ:
λ=(πρwNrqr)1/3.
Using Eq. (3) in place of λ in Eq. (1), the complete formula for the diameter for a chosen percentile is
D(PN)=(qrπρwNr)1/3ln(1PN100).
The main question is then what percentile to use to define the Dmax from the model size distribution? In Tessendorf et al. (2017), several percentiles, from the 50th to the 99th, were explored in two FZDZ case studies. The study recommended that the 99th percentile be considered for further evaluation since it produced Dmax values that qualitatively compared best with the observations in the two cases. Herein, we evaluate three percentiles surrounding the 99th percentile (PN = 95, 99, 99.9) for the entire dataset from SNOWIE and BAIRS II, which includes FZDZ and FZRA cases.

To illustrate this method of extracting Dmax for these three percentiles, two rain DSDs from the HRRR model are shown in Fig. 1, with the blue one having all extracted percentiles (from 95% to 99.9%) resulting in a Dmax < 500 μm, therefore classified as FZDZ, and the red one having all percentiles falling > 500 μm classifying it as FZRA. For DSDs that fall in between these two examples, the choice of percentile can make the difference in determining FZDZ versus FZRA, such that a smaller percentile would yield FZDZ while a larger percentile would yield FZRA for the exact same DSD. An example of this is illustrated by the purple DSD in Fig. 1, where the 95th and 99th percentiles result in Dmax < 500 μm (FZDZ), and the 99.9th percentile yields Dmax > 500 μm (FZRA). Therefore, it is important to carefully determine the optimal percentile to calculate Dmax, which is the purpose of the evaluation presented in the present study.

b. Model and observations matching methods

Each 30-s average observational data point was compared to model output variables (e.g., Dmax) from all model points within ± 1000 ft from the aircraft altitude with a horizontal neighborhood of 9 × 9 grid boxes. The neighborhood of 9 × 9 grid points translates to a footprint area of 27 × 27 km2, which is comparable to a similar HRRR model evaluation study (Xu et al. 2019). The 1000-ft vertical neighborhood is also consistent with Xu et al. (2019) and corresponds to 1.6 model vertical levels on average. Xu et al. (2019) showed that using a time-lagged ensemble method can improve the model’s skill at predicting icing. As a result, we also consider multiple forecast lead times (1, 3, 6, and 12 h), though performance trends by lead time are beyond the scope of this paper. For each lead time, 81 grid boxes in the horizontal neighborhood and an average of 1.6 vertical levels, each 30-s observation was compared to an average of 130 model points. The four lead times are considered as independent model forecasts for a given observation data point for the contingency table statistics. However, when analyzing the joint distribution of observed and modeled Dmax, each of the ~518 (~130 total grid points × 4 lead times) possible Dmax values from the model are compared against the same observed (30-s average) Dmax.

4. Examples of SLD icing scenarios

Two case studies are presented to examine how the HRRR model predicts the observed SLD icing conditions within classical and nonclassical SLD environments. A common aspect of these two cases was that the HRRR performed well in predicting the thermodynamic environments that were conducive to classical and nonclassical SLD formation.

a. Classical SLD formation

In situ sampling of classical FZRA scenarios are not commonly done due to their occurrence close to the ground (below a warm layer) where it is challenging to fly an aircraft safely. This greatly limited the number of cases with in situ measurements in classical FZRA events, though this was achieved during the BAIRS II campaign. One such case occurred on 24 January 2017, on a flight between 0245 and 0645 UTC, when the NRC Convair-580 was able to sample the warm layer and profile the atmosphere just below it. The cloud was a deep stratiform cloud on the north side of a large extratropical cyclone (not shown). The warm layer was present in an inversion between 1–2 km MSL based on flight temperature data between 0245 and 0345 UTC (Fig. 2). The heights of the warm layer in the HRRR compared well with the observations, although the model underestimated the strength of the temperature inversion (Fig. 2). The magnitude of the maximum temperature in the forecast warm layer at this location and time varied based upon model lead time, but was generally on the order of 1°C, whereas the observations were as warm as 5°C. This inversion was also evident (although closer to 2 km and just above) in the Albany, New York, sounding launched operationally a few hours earlier at 0000 UTC by the local National Weather Service (NWS) office (Fig. 2). At Albany, the HRRR model forecast compared fairly well with the observations, showing a deep cloud with an inversion in the temperature profile that peaked at 0°C around 760 hPa, while the observed inversion peaked slightly >0°C at 800 hPa (Fig. 2).

Fig. 2.
Fig. 2.

(left) Skew T–logp profile showing the 3-h lead time HRRR forecast model sounding from a spiral descent segment (at the loop in the north–south leg of the Convair-580 flight track in Fig. 3) at 0300 UTC, with observed temperature from the Convair-580 between 0245 and 0345 UTC overlaid and (right) the operational sounding observations from Albany, NY, at 0000 UTC 24 Jan 2017 compared to the 3-h lead time forecast from the HRRR model (valid at 0100 UTC) at the same location.

Citation: Weather and Forecasting 36, 4; 10.1175/WAF-D-20-0138.1

The HRRR forecast had both supercooled liquid cloud water and snow above the warm nose, while below the warm nose, the model predicted supercooled rainwater, including in the area that the Convair-580 flight sampled the FZRA conditions (Fig. 3). Convair-580 measurements indicated the observed conditions were FZRA with a maximum Dmax of 915 μm during the flight. The Dmax from the model was correctly classified as FZRA when defined using the 99th or 99.9th percentile (Fig. 4a). Using the 99th percentile definition (shown in Fig. 3d), the model clearly predicted the entire supercooled rain area below the warm nose along the flight path and to the southeast as FZRA (>500 μm). This region of FZRA resulted from the classical process of snow melting into rain that fell into the subfreezing layer near the surface (Fig. 3). This process yielded a notable bimodal DSD in the observations, which was represented well by the model (Fig. 4a).

Fig. 3.
Fig. 3.

Maps of composite (a) supercooled cloud water content, (b) snow water content, (c) supercooled rainwater content, and (d) Dmax (left) above and (right) below the warm nose (WN) from the HRRR 3-h forecast valid at 0400 UTC 24 Jan 2017 during a BAIRS II flight (black line shows flight path). Asterisks indicate the nearest NWS sounding sites at Buffalo (western point) and Albany (eastern point). The top of the WN is defined as the highest level where pressure > 300 hPa and temperature > 0°C in every vertical column. Everything above that (where temperature < 0°C) is “above WN.” The bottom of the WN is the highest level below the WN top where temperature < 0°C again. This level and all the lower ones are “below WN.”

Citation: Weather and Forecasting 36, 4; 10.1175/WAF-D-20-0138.1

Fig. 4.
Fig. 4.

Example drop size distributions from the HRRR model (black) and from the aircraft observations (red) for (a) the 24 Jan 2017 FZRA case from BAIRS II and (b) the 9 Mar 2017 FZDZ from SNOWIE. The observed Dmax (see section 2) is shown as a red dot on the red curve at 895 μm in (a) and 385 μm in (b). The 95th, 99th, and 99.9th percentiles are indicated on the HRRR curve by the black dots (from left to right, respectively) as 415, 637, and 956 μm in (a) and 313, 481, and 721 μm in (b). Note that the HRRR curve is made up of two hydrometeor categories in the model: the cloud water and rainwater category gamma distributions.

Citation: Weather and Forecasting 36, 4; 10.1175/WAF-D-20-0138.1

b. Nonclassical SLD formation

An example of nonclassical FZDZ occurred on 9 March 2017 during the SNOWIE field program. The HRRR model predicted a shallow, entirely subfreezing, cloud layer between 2.5 and ~4 km with a cloud-top temperature of −10°C (Fig. 5), which represented the observed cloud layer on this day well (albeit the model was unable to resolve all the observed fluctuations in the profile). A broad area of supercooled cloud water was predicted around the flight path, with only some isolated pockets of SLD (Fig. 6).

Fig. 5.
Fig. 5.

Skew T–logp profile showing the observed sounding data from Crouch, ID, at 1600 UTC 9 Mar 2017 compared to the 1-h lead-time forecast from the HRRR model at the same location. The HRRR model cloud-top temperature was −10°C and the observed cloud top was −11°C.

Citation: Weather and Forecasting 36, 4; 10.1175/WAF-D-20-0138.1

Fig. 6.
Fig. 6.

Maps of composite supercooled (a) cloud water content and (b) rainwater content, and (c) Dmax from the 3-h forecast valid at 1500 UTC 9 Mar 2017 for the SNOWIE campaign flight that day (black line showing flight path) north of Boise, ID. The asterisk indicates the sounding site at Crouch.

Citation: Weather and Forecasting 36, 4; 10.1175/WAF-D-20-0138.1

The Dmax of the SLD predicted by the HRRR was correctly categorized as FZDZ using the 95th and 99th percentiles (Fig. 4b), with maximum sizes < 500 μm. The observed DSD in this case shows a broad droplet spectrum formed by collision–coalescence processes (Fig. 4b). While the model does not reproduce the DSD perfectly (primarily due to the fact that the model DSD is made up of two bulk DSDs from the cloud and rain categories), the model produced a narrower rain DSD with mostly small (drizzle-sized) raindrops, as observed. The median cloud number concentration predicted in this case was between 22 and 75 cm−3, which compared well with the in situ observations in this case (<52 cm−3), despite the predicted LWC being slightly low along the flight path (0.1–0.2 g m−3 compared to observations up to 0.33 g m−3). We attribute the model’s success in forecasting the nonclassical SLD on this day to the representative thermodynamic structure and comparable cloud drop number concentration that allowed the autoconversion and collision–coalescence processes in the model microphysics to grow FZDZ-sized drops as observed.

5. Results of Dmax in SLD icing

This analysis indicated the HRRR model correctly identified 23% of the observed SLD in the SNOWIE dataset and 9% of the observed SLD in the BAIRS II dataset. Recall in Xu et al. (2019) they showed that the HRRR correctly forecast 45%–50% of the SLD observed at the surface in METAR observations. It needs to be clarified that their observations were dominated by FZRA, whereas in the present study the datasets were dominated by FZDZ. This indicates that the HRRR could use improvement in forecasting environments conducive to SLD, especially nonclassical FZDZ environments. This analysis revealed the model has challenges in accurately capturing the dynamic and thermodynamic aspects of the SLD-producing environments. It is beyond the scope of this paper to address these issues. Rather, this analysis focuses on points in which the model correctly predicted the presence of SLD, in order to concentrate on the microphysics in the model and its ability to distinguish FZDZ and FZRA.

Nearly all (99.7%) of the SNOWIE SLD observations included in this analysis were classified as FZDZ, with the few remaining SLD measurements classified as FZRA sizes. All of the SLD icing environments observed during SNOWIE were nonclassical SLD icing environments. As a result, the few FZRA sizes that were observed formed by collision–coalescence processes due to very low observed cloud drop concentrations and large MVDs (see Fig. 11 in Tessendorf et al. 2019). In the BAIRS II dataset, FZDZ was observed in 98% of the SLD observations, while the remaining 2% were FZRA. The FZRA observed in BAIRS II occurred in classical SLD environments (Fig. 2), while the FZDZ occurred in nonclassical environments (Fig. 7).

Fig. 7.
Fig. 7.

Skew T–logp profile showing the observed sounding data from Buffalo, NY, at 1200 UTC 7 Feb 2017 compared to the 6-h lead-time forecast from the HRRR model at the same location. The HRRR model cloud-top temperature matched the observed cloud top quite well, at −8°C.

Citation: Weather and Forecasting 36, 4; 10.1175/WAF-D-20-0138.1

a. Contingency table statistics of SLD categories

The accuracy7 of the model Dmax to correctly classify the SLD category of FZDZ or FZRA varied from 74% to 99% for the SNOWIE dataset, and from 53% to 73% for the BAIRS II dataset depending on the percentile used to define Dmax (Table 2). In both datasets, the accuracy was highest (99% in SNOWIE and 73% in BAIRS II) using the 95th percentile definition for model Dmax. In SNOWIE, the accuracy using the 99th percentile was also still very high, at 97%. Table 2 provides the Heidke skill score8 (HSS), which is helpful to determine the accuracy relative to random chance. The HSS also shows that the 95th percentile is most skillful in both datasets, and again the 99th percentile also performs well in the SNOWIE dataset.

Table 2.

Contingency table and error statistics for the HRRR Dmax based upon the three percentiles (PN) evaluated for each of the field campaign datasets. Note that this table does not include false alarm ratio (FAR) because the FAR for one category is equivalent to 1 − POD for the other category. The sign of the mean error is based upon observations minus model, so positive indicates observations are greater than the model. The 99th percentile results for each dataset are highlighted (bold italics) as the percentile that yielded the most optimal results overall in both FZDZ and FZRA conditions.

Table 2.

The probability of detection9 (POD) for each of the two SLD categories (FZDZ and FZRA) for each of the three percentiles evaluated are also shown in Table 2. Similar to the results of the accuracy and HSS, the SNOWIE dataset has the highest POD (POD = 99%) for detecting FZDZ when using the 95th percentile. The POD for FZDZ from SNOWIE using the 99th percentile Dmax method is still quite high at 97%, while for the 99.9th percentile it decreases to 74%. The POD for FZRA in SNOWIE, however, is quite variable (13%–93% for the three percentiles). In the few cases where the collision–coalescence process produced FZRA-sized drops, the model did not perform well except when using the 99.9th percentile. In BAIRS II, the POD for FZRA was highest, at 93% and 90%, also using the 99.9th and 99th percentile definition of Dmax, respectively (Table 2). The POD for FZDZ in the BAIRS II data for these two upper percentiles was lower (<50%) and, similar to in SNOWIE, it was highest for FZDZ (POD = 81%) using the 95th percentile.

The Pierce skill score10 (PSS) is a useful metric in distinguishing yes from no (in this case, FZDZ from FZRA). In the SNOWIE dataset, the 99.9th percentile was most skillful with PSS = 0.67, whereas in the BAIRS II dataset the 95th percentile was most skillful (PSS = 0.39). In general, the model does have skill in distinguishing the two categories of SLD icing; however, the skill varies by dataset and percentile for Dmax.

In summary, the POD statistics show that the greater percentile used in the Dmax definition is better at detecting FZRA, while a slightly lower percentile (95th in this case) outperforms the higher percentiles when detecting FZDZ. These results may simply be due to the fact that a greater percentile yields a larger model Dmax, which increases the likelihood of classifying the Dmax as FZRA as opposed to FZDZ, and vice versa. It is possible that the formulation for the rain DSD cannot get narrow enough in FZDZ scenarios to be accurately forecast using a larger percentile. For operational aircraft icing forecasting applications, if the goal is to err on the side of predicting the more severe form of icing to avoid missed severe events, then a greater percentile to define Dmax would be recommended. However, there can be financial implications (canceled, delayed, or rerouted flights) that must also be considered by those making aviation weather decisions, which is beyond the scope of this analysis. Nonetheless, under this assumption, the 99th percentile would be a reasonable compromise to yield optimal results in both FZDZ and FZRA conditions.

b. Evaluation of Dmax size

The Dmax values extracted from the model using the three percentiles are compared with the Dmax calculated from the in situ aircraft observations in Fig. 8. In the SNOWIE campaign, the observed Dmax values overwhelmingly fell within the FZDZ category, as noted above. The model predicted the observed FZDZ size category quite well using the 99th and 95th percentiles, with the majority of the HRRR Dmax values also falling within the FZDZ category (POD FZDZ of 97% and 99%, respectively, Table 2). The root mean squared error (RMSE) was lowest for these two percentiles as well (Table 2). The model Dmax was too large and more often fell outside of the FZDZ size range when using the 99.9th percentile. The mean error was always negative, for all three percentiles, indicating the model produced larger sizes for Dmax than observed (Table 2).

Fig. 8.
Fig. 8.

Scatterplots presented as a heat map to show the density of points in a given size bin, colored using a log scale as a percentage of total points, comparing the observed Dmax (μm) with the Dmax extracted from the HRRR model for the (a) 95th percentile, (b) 99th percentile, and (c) 99.9th percentile. Data from the SNOWIE campaign on the left column and from BAIRS II on the right column. The 1:1 line is illustrated as a white solid line down the diagonal of the plots. The key size thresholds (100 and 500 μm) used to define FZDZ and FZRA are highlighted with red and magenta solid lines, respectively. The POD (from Table 2) for FZRA and FZDZ are labeled on each panel.

Citation: Weather and Forecasting 36, 4; 10.1175/WAF-D-20-0138.1

For the BAIRS II dataset, the observed and predicted Dmax values were closest to the 1:1 line using the 95th and 99th percentiles. The 95th percentile Dmax produced the least RMSE, but the RMSE was larger overall for the BAIRS II data than in SNOWIE for all percentiles (Fig. 8, Table 2). Notably, the FZRA category, which was observed more often in BAIRS II than SNOWIE, was most accurately predicted in a categorical sense (POD = 93%) using the 99.9th percentile; however, the majority of FZRA points were centered about the 1:1 line using the 99th percentile (Fig. 8). The mean error shows that Dmax was generally overestimated using the 99th and 99.9th percentiles, but was actually slightly underestimated using the 95th percentile. The BAIRS II dataset includes classical SLD environments leading to FZRA (Figs. 2 and 3), which have been shown to be well predicted by HRRR (Xu et al. 2019).

Regardless of the percentile used, the model had a tendency to produce a mode of Dmax (e.g., 250–350 μm using the 99th percentile), while the observed Dmax values were more distributed between 100 and 500 μm (Fig. 8). This mode of model Dmax in FZDZ cases was not the result of just one case dominating the results, but rather a systematic result as shown by the distribution of inverse slope parameter values (Fig. 9a for SNOWIE, as well as in the BAIRS II FZDZ data as shown in Fig. 9b). The inverse of the slope parameter λ is a key variable in the calculation of Dmax, as shown in Eq. (1), which is proportional to the ratio of qr and Nr [Eq. (4)]. The narrow distribution of λ is the result of the TE14 parameterization autoconversion process, which creates rain from cloud water once cloud drops have grown to a large enough size. The production of rain number concentration by autoconversion (p_NAC) is based upon the following formula:
p_NAC=dNrdt=6p_qACπρwνcD0r3,
where p_qAC is the production of rainwater content (kg m−3; see appendix), νc is a variable dispersion factor (m3), and D0r is the minimum diameter of rain (in m; set equal to 50 μm in the scheme), and all other coefficients have been previously defined. Equation (5) indicates that the production of rain number is directly proportional to the amount of rainwater content produced by autoconversion, with the only other variable being the dispersion factor νc. In the TE14 scheme, νc is determined from the number concentration of cloud drops Nc in the model using Eq. (6) and varies between 2 (for high cloud number concentrations, such as polluted clouds) and 15 (for low cloud drop number concentration, such as from maritime clouds):
νc=MIN[15,NINT(1000×106Nc+2)].
This formula, which uses FORTRAN functions, was defined in Thompson et al. (2008) and was based upon Martin et al. (1994). Per the definition of νc in Eq. (6), in cases where Nc < 77 cm−3, the dispersion factor maximizes at 15, and therefore maintains a constant ratio of the production of rain number to rain mass, which results in a constant λ for the newly generated rainwater. A constant λ occurs when Nr and qr are proportional to each other, which would occur from autoconversion anytime the dispersion factor is constant at any value given Eq. (5). In all but three of the SNOWIE cases included in this analysis, the cloud drop concentrations were <100 cm−3 and most were <50 cm−3 (not shown), so the dispersion factor would be a constant value of 15, making λ (and associated Dmax) values constant in FZDZ produced by autoconversion.
Fig. 9.
Fig. 9.

Histograms of the inverse of the slope parameter (1/λ; μm) values for the rain category of the HRRR model from the (a) SNOWIE dataset and (b) BAIRS II dataset, and scatterplots of rainwater content (g m−3) vs rain number concentration (cm−3) from the (c) HRRR model and (d) 2D-S observations from both field projects combined, when supercooled rain was predicted by the model and for 2D-S data points >100 μm (to omit points where liquid vs ice discrimination is not reliable due to too few pixels detected by the instrument). Scatterplots are color coded, for illustration purposes, as blue for those in which Dmax < 500 μm (i.e., FZDZ) and red for Dmax > 500 μm (FZRA), using the 99th percentile method to define model Dmax.

Citation: Weather and Forecasting 36, 4; 10.1175/WAF-D-20-0138.1

The proportionality of Nr and qr is illustrated as a linear relation on a scatterplot of the two variables. As can be clearly seen in Fig. 9c, the majority of the model FZDZ points show that Nr and qr are linearly related (Nr = kqr), and in many cases k ~ 1 (for Nr in cm−3 and qr in g m−3) on the scatterplot. The values of Nr and qr when k ~ 1 yield an inverse λ of 68 μm, resulting in a 99th percentile Dmax of 314 μm, which corresponds with the model estimates of the modes of inverse λ and Dmax (shown in Figs. 8 and 9). This model relationship differs from the relationship in the observations (Figs. 9c,d), as the observations are completely below the k = 1 line on the scatterplot. It appears the model relationship of Nr and qr for FZRA compares fairly well though, albeit based upon very few observations of FZRA (Figs. 9c,d).

Nonclassical SLD icing environments are commonly associated with low cloud drop number concentration (Bernstein et al. 2019) and therefore the situation in which νc is essentially constant at the maximum prescribed value in the TE14 parameterization is likely to be common in FZDZ scenarios. The capped dispersion factor results in larger production of rain number compared to rainwater content for all situations with low cloud drop number concentration, as opposed to if the dispersion factor were to continue to increase with decreasing cloud number concentration, therefore skewing the relation of Nr and qr too high. Moreover, the consequence of having too narrow a distribution of Dmax (or λ) compared to the observations is that it can significantly affect how the model grows cloud and rain drops to FZDZ and FZRA sizes via collision–coalescence processes, as well as impacting particle fall speeds and evaporation processes. This is an aspect of the model that has been very challenging to evaluate in the past without detailed in situ measurements, and therefore this result opens the door for new improvements to be made in the microphysics parameterization.

6. Summary and discussion

This analysis has examined the ability of the HRRR model to predict distinct SLD icing categories of FZDZ and FZRA using in situ research data from two recent field campaigns. The results indicate that the HRRR model is capable of simulating both classical and nonclassical SLD icing environments with an accuracy as high as 99% in some cases, and that the TE14 microphysics in the HRRR is indeed capable of distinguishing FZDZ and FZRA.

Three large (>95th) percentiles were evaluated as proxies for Dmax from the model and the results showed that the accuracy of the model to predict the correct category of SLD icing was always highest for the lower (95th) percentile. The PSS showed that the Dmax percentile most skillful at distinguishing FZDZ from FZRA differed by field campaign dataset. A compromise solution to accurately predict both FZDZ and FZRA, based upon these available data, would suggest that Dmax is best defined as the 99th percentile of the rain category number distribution. Using this definition, the model Dmax correctly predicted the observed SLD icing category 62%–97% of the time when the HRRR also forecast SLD conditions. Given the skill shown in the PSS, using the model Dmax could be one way to distinguish FZDZ and FZRA in surface precipitation type algorithms using the NWP model output, such as the postprocessing algorithm used by Benjamin et al. (2016a) that currently predicts freezing precipitation as a single category.

This study revealed that the autoconversion process in TE14 produces a frequently constant shape parameter λ in nonclassical SLD scenarios, which led to a unimodal distribution of Dmax values. This result was shown to occur in situations with low cloud drop number concentration (specifically <77 cm−3), which is common to environments conducive to the production of FZDZ. Besides the accurate prediction of Dmax, the λ for rain (based upon qr and Nr) impacts the particle fall speed of the rain category and will have subsequent impacts on microphysical growth and decay processes (i.e., rain self-collection, evaporation, sedimentation, etc.), so it is an important process to accurately parameterize.

We conclude that the TE14 microphysics in the HRRR model can distinguish FZDZ and FZRA with the existing two-moment microphysical category for rain, and there is promise for the model to more accurately predict Dmax if improvements are made to the autoconversion parameterization, at a minimum by increasing the range of values for the cloud dispersion factor. While this study was limited in terms of the number and breadth of events included in the Dmax evaluation, it provides a diagnostic for Dmax that can be used to address new FAA appendix O regulations and serves as a baseline for further microphysics and other model improvements toward predicting SLD icing. In particular, this study revealed challenges with the HRRR to accurately forecast SLD overall (POD < 23%), which indicated improvements are needed in the ability of HRRR to predict the dynamics and thermodynamics of SLD-producing environments. The recent In Cloud ICing and Large-drop Experiment (ICICLE; DiVito et al. 2020) field project will provide even more data to alleviate some of the sample size constraints of this study and will allow for some of the remaining questions and issues revealed herein to be further evaluated and improved upon.

Acknowledgments

The authors are grateful for discussions with Roy Rasmussen, Matthias Steiner, Ben Bernstein, and other NCAR In Flight Icing team members (Dave Serke, George McCabe, Paul Prestopnik, Gary Cunning), SNOWIE collaborators (Jeff French, Adam Majewski, Dave Plummer), NOAA GSD collaborators (John Brown, Curtis Alexander, Steve Weygandt, Craig Hartsough, Stan Benjamin), BAIRS II scientists from MIT/LL staff (Earle Williams, Dave Smalley) and National Research Council (Mengistu Wolde), and the FAA (Danny Sims, Jim Riley, Tom Bond). This material is based upon work supported by the National Center for Atmospheric Research, which is a major facility sponsored by the National Science Foundation under Cooperative Agreement 1852977. This research is in response to requirements and funding by the Federal Aviation Administration (FAA). The views expressed are those of the authors and do not necessarily represent the official policy or position of the FAA.

Data availability statement

The SNOWIE dataset analyzed in the current study is available in the NCAR/EOL Field Catalog at https://data.eol.ucar.edu/master_lists/generated/snowie/. This dataset was collected with joint sponsorship from the National Science Foundation sponsored and Idaho Power Company. The BAIRS II dataset was collected by MIT/LL in collaboration with the Canadian National Research Council (NRC) and Environment and Climate Change Canada (ECCC) with sponsorship from the FAA. It is not currently available in a data repository. The dataset can be made available to bona fide researchers by collaboration with the MIT/LL and NRC/ECCC investigators. The specific data utilized in this study was made available by Dr. Alexei Korolev (alexei.korolev@canada.ca) at ECCC.

APPENDIX

Autoconversion Parameterization in TE14

The autoconversion process is parameterized in the TE14 microphysics scheme (microphysics option 28, mp = 28, in WRF namelist) in a similar way to how it was parameterized in the “original” Thompson scheme (microphysics option 8, mp = 8, in the WRF namelist), which is based upon that presented in Thompson et al. (2004, 2008). The process is based upon the Berry and Reinhardt autoconversion scheme (Berry and Reinhardt 1974a,b). However, the Berry and Reinhardt scheme was designed for a single-moment rain scheme, and so two-moment schemes have been shown to follow a variety of different methods even while being based upon Berry and Reinhardt (Gilmore and Straka 2008). The two-moment rain category in the Thompson scheme was not complete at the time of publication of Thompson et al. (2008), so had not been fully described in a publication. Herein, we document the autoconversion process terms in the Thompson microphysics two-moment rain parameterization.

There are two general process terms that make up the autoconversion process: production of rain mixing ratio (or rainwater content when the mixing ratio is multiplied by the density of air) and production of rain number. The production of rain number was documented in the manuscript [see Eqs. (5) and (6)]. For completeness, here we document the production of rainwater content from autoconversion (p_qAC) in Eq. (A1) below, similar to as shown in Thompson et al. (2004):
p_qAC=dqrdt=Lτ,
where the terms L and τ are defined as
L=0.027qc(6.25×1018Db3Df0.4),
τ=3.72qcρa(106Db27.5).
In Eqs. (A1)(A3), qr is the rainwater content, qc is the cloud water content, and ρa is the density of air; Db is the initial diameter of cloud droplets corresponding to the standard deviation of the mass, and Df is the mean mass diameter. The autoconversion process is not active unless qc > 0.01 g m−3.

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    • Crossref
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    • Export Citation
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1

14 Code of Federal Regulations (CFR) appendix C to Part 25 (Airworthiness Standards: Transport Category Airplanes); available online at: https://www.ecfr.gov/cgi-bin/text-idx?SID=d512b2fc852cb064fa0988a660ddffcc&mc=true&node=ap14.1.25.0000_0nbspnbspnbsp.c&rgn=div9.

3

Xu et al. (2019) compared performance of deterministic forecasts at 3- and 6-h lead times, resulting in the range of POD values presented herein, as well as used two different (1- and 8-point) thresholds for number of hits within the evaluation neighborhood. The results presented here are for the 1-point threshold only.

4

An exception was allowed to this CDP/FSSP criterion being met if the temperature was <0°C and the altitude of the aircraft was <2 km MSL in order to allow for SLD observed in a warm nose that may not have much cloud water present.

5

The method used by Cober and Isaac (2012) assigned Dmax as the midpoint of the largest “useful” size bin with at least 10 counts of particles, which translated to a concentration of 80–90 m−3 as documented in Cober et al. (2009). Herein, the 2D-S data were processed with this concentration threshold to determine Dmax using the midpoint of this range at 85 m−3.

6

The use of prescribed (e.g., gamma) functions for the size distribution is a common practice in bulk microphysics schemes in order to be more computationally efficient and therefore be able to run in a real-time NWP model.

7

Accuracy is defined as the sum of the number of “hits” plus the correct negatives all divided by the total number of points. Hits in this scenario are when the model and observations both indicated FZDZ. Correct negatives are when the model and the observations both indicated FZRA. Accuracy ranges from 0 to 1, with 1 being a perfect score.

8

HSS scores range between −1 and 1, with 1 being a perfect score and 0 indicating no skill.

9

Probability of detection is defined as the number of points from the model that were “hits” divided by the total number of “hits” plus “misses.” We calculate POD in terms of FZRA and FZDZ separately, where a “hit” for FZRA is when the model and observations both indicate FZRA, and a “miss” for FZRA when only the observations indicated FZRA; similarly, a “hit” for FZDZ is when the model and observations both indicate FZDZ, and for a “miss,” only the observations indicate FZDZ.

10

PSS scores range between −1 and 1, with 1 being a perfect score and 0 indicating no skill.

Save
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    • Crossref
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    • Crossref
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    • Export Citation
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