Characterization of Aircraft Icing Environments with Supercooled Large Drops for Application to Commercial Aircraft Certification

Stewart G. Cober Cloud Physics and Severe Weather Research Section, Environment Canada, Toronto, Ontario, Canada

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George A. Isaac Cloud Physics and Severe Weather Research Section, Environment Canada, Toronto, Ontario, Canada

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Abstract

Observations of aircraft icing environments that included supercooled large drops (SLD) greater than 100 μm in diameter have been analyzed. The observations were collected by instrumented research aircraft from 134 flights during six field programs in three different geographic regions of North America. The research aircraft were specifically instrumented to accurately measure the microphysics characteristics of SLD conditions. In total 2444 SLD icing environments were observed at 3-km resolution. Each observation had an average liquid water content (LWC) > 0.005 g m−3, drops > 100 μm in diameter, ice crystal concentrations <1 L−1, and an average static temperature ≤0°C. SLD conditions were observed approximately 5% of the in-flight time. The SLD observations were segregated into four subsets, which included conditions with maximum drop sizes <500 μm and >500 μm in diameter, each with median drop volume diameters <40 μm and >40 μm. For each SLD subset, the observations were used to develop envelopes of maximum LWC values as a function of horizontal extent and temperature. In addition, characteristic drop size distributions were developed for each SLD subset. The maximum LWC values physically represent either the 99% or 99.9% LWC values, as determined from an extreme value analysis of the data. The analysis is sufficient for simulation of SLD environments with either numerical icing accretion models or wind-tunnel icing simulations. The SLD envelopes are similar in structure and supplemental to existing aircraft icing envelopes, the difference being that the existing envelopes did not explicitly incorporate SLD conditions.

Corresponding author address: Stewart Cober, Cloud Physics and Severe Weather Research Section, Science and Technology Branch, Environment Canada, 4905 Dufferin Street, Toronto, ON M3H 5T4, Canada. E-mail: stewart.cober@ec.gc.ca

A comment/reply has been published regarding this article and can be found at http://journals.ametsoc.org/doi/abs/10.1175/JAMC-D-12-096.1 and http://journals.ametsoc.org/doi/abs/10.1175/JAMC-D-12-0213.1

Abstract

Observations of aircraft icing environments that included supercooled large drops (SLD) greater than 100 μm in diameter have been analyzed. The observations were collected by instrumented research aircraft from 134 flights during six field programs in three different geographic regions of North America. The research aircraft were specifically instrumented to accurately measure the microphysics characteristics of SLD conditions. In total 2444 SLD icing environments were observed at 3-km resolution. Each observation had an average liquid water content (LWC) > 0.005 g m−3, drops > 100 μm in diameter, ice crystal concentrations <1 L−1, and an average static temperature ≤0°C. SLD conditions were observed approximately 5% of the in-flight time. The SLD observations were segregated into four subsets, which included conditions with maximum drop sizes <500 μm and >500 μm in diameter, each with median drop volume diameters <40 μm and >40 μm. For each SLD subset, the observations were used to develop envelopes of maximum LWC values as a function of horizontal extent and temperature. In addition, characteristic drop size distributions were developed for each SLD subset. The maximum LWC values physically represent either the 99% or 99.9% LWC values, as determined from an extreme value analysis of the data. The analysis is sufficient for simulation of SLD environments with either numerical icing accretion models or wind-tunnel icing simulations. The SLD envelopes are similar in structure and supplemental to existing aircraft icing envelopes, the difference being that the existing envelopes did not explicitly incorporate SLD conditions.

Corresponding author address: Stewart Cober, Cloud Physics and Severe Weather Research Section, Science and Technology Branch, Environment Canada, 4905 Dufferin Street, Toronto, ON M3H 5T4, Canada. E-mail: stewart.cober@ec.gc.ca

A comment/reply has been published regarding this article and can be found at http://journals.ametsoc.org/doi/abs/10.1175/JAMC-D-12-096.1 and http://journals.ametsoc.org/doi/abs/10.1175/JAMC-D-12-0213.1

1. Introduction

The Code of Federal Regulations Title 14 Chapter 1 Part 25 Appendix C (FAR 25-C) (Federal Aviation Administration 1999) presents characterizations of aircraft icing environments for continuous maximum (stratiform) and intermittent maximum (convective) clouds. The icing environments are defined as functions of air temperature, maximum liquid water content (LWC), droplet mean effective drop diameter (MED), and horizontal extent. Note that MED and drop median volume diameter (MVD) are considered to be equivalent (Finstad and Lozowski 1988). The FAR 25-C characterizations of stratiform cloud environments only included MED values up to 40 μm, likely because it was not possible to accurately measure larger MED values during the 1940s when the observations were collected. The maximum icing envelopes (nominally ≥99 percentile for LWC) included in FAR 25-C have been used for the certification of commercial aircraft since the mid-1950s. While an upper MVD limit of 40 μm for stratiform clouds has been used for aircraft certifications, hazards associated with supercooled large drops (SLD) >100 μm in diameter and icing environments with drop MVD > 40 μm have been documented in numerous reports (Sand et al. 1984; Cooper et al. 1984; Politovich 1989; Pobanz et al. 1994; Cober et al. 1996, 2001c; Ashenden and Marwitz 1998). Collectively, these reports have demonstrated that the FAR 25-C envelopes do not adequately capture all aircraft icing environments that include SLD conditions. This led to a series of measurement programs in the past 15 years that were designed in part to adequately characterize icing environments that contained SLD conditions.

Following the crash of a turboprop commuter aircraft near Roselawn, Indiana, in 1994, the National Transportation Safety Board report (National Transportation Safety Board 1996) suggested that the aircraft encountered SLD >100 μm in diameter and that these drops contributed to the development of a ridge of ice that accumulated behind the deicing boots of the aircraft (Marwitz et al. 1997). Subsequent to the Roselawn accident, the Federal Aviation Administration developed an In-flight Aircraft Icing Plan (Federal Aviation Administration 1997), which contained specific recommendations for preventing accidents caused by in-flight icing. One recommendation of this plan was to consider a comprehensive redefinition of the current aircraft icing certification envelopes when sufficient information was available worldwide on SLD and other icing conditions.

The plan also recommended the establishment of an aviation rulemaking advisory committee harmonization working group (HWG), which was to be given the task of developing certification criteria and advisory material for the safe operation of airplanes in SLD icing conditions. An Ice Protection HWG was subsequently established with the specific task of “defining an icing environment that includes SLD aloft, near the surface, and in mixed-phase (supercooled liquid drops and ice crystals) conditions if such conditions are determined to be more hazardous than the supercooled liquid-phase icing environment.” In support of the Ice Protection HWG, a large database of aircraft icing observations was acquired and analyzed, and the data were used to characterize aircraft icing environments that included SLD. The primary analysis undertaken in support of the Ice Protection HWG is presented here. This characterization has been proposed as a new aircraft certification standard.

2. Field projects

Observations of aircraft icing environments that included SLD were made during six field projects conducted by researchers from Environment Canada (EC) and the National Aeronautics and Space Administration (NASA) Glenn Icing Technology Branch during the period from 1995 through 2000. These field projects included the following:

  1. The First Canadian Freezing Drizzle Experiment (CFDE I) was conducted by EC during March 1995 (Isaac et al. 2001b; Cober et al. 2001c). It was based from St. John’s, Newfoundland, Canada, and consisted of 12 research flights with the National Research Council of Canada (NRC) Convair-580 research aircraft; St. John’s was chosen as the center for operations because it receives in excess of 150 h yr−1 of freezing precipitation (McKay and Thompson 1969; Stuart and Isaac 1999) with a peak frequency in February and March.

  2. The Third Canadian Freezing Drizzle Experiment (CFDE III) was conducted by EC during the period of December 1997 to February 1998 (Isaac et al. 2001b; Cober et al. 2001c). The NRC Convair-580 research aircraft was based out of Ottawa, Ontario, Canada, and 26 flights were conducted over southern Ontario, southern Quebec (Canada), Lake Ontario, and Lake Erie. The geographical region was selected for two reasons: 1) to obtain data in a continental region where there was considerable air traffic and 2) the region around Ottawa and Montreal, Quebec, has a high frequency of freezing precipitation with 50–75 h yr−1 observed at the surface (Stuart and Isaac 1999).

  3. The First International Satellite Cloud Climatology Project (ISCCP) Regional Experiment Arctic Cloud Experiment (FIRE-ACE) was conducted by EC in April 1998 (Curry et al. 2000). The NRC Convair-580 research aircraft was based out of Inuvik of the Northwest Territories, Canada, and 18 flights were conducted into boundary layer and midlevel Arctic clouds.

  4. The First Alliance Icing Research Study (AIRS I) was conducted by EC during December 1999 and February 2000 (Isaac et al. 2001a,b). AIRS I was based from Ottawa and the majority of the 25 research flights with the NRC Convair-580 research aircraft were conducted in the vicinity of Mirabel, Quebec, where a variety of remote sensing instruments were located.

  5. The First Alliance Icing Research Study (AIRS I NASA) was conducted by NASA Glenn during December 1999 (Isaac et al. 2001a,b). The NASA Glenn Icing group also participated in AIRS I and conducted 16 flights in the Ottawa and Mirabel areas with their Twin Otter research aircraft.

  6. The SLD Flight Research Study was conducted by NASA Glenn during January 1997 through February 1998 (Miller et al. 1998). Using a Twin Otter research aircraft, 37 flights in the southern Great Lakes region were specifically targeted at environments nowcasted to have SLD conditions.

With the exception of FIRE-ACE, each of these projects had a specific objective to gather in situ observations with instrumented research aircraft in winter storm environments where SLD was forecast or observed to exist. The instrumentation on the aircraft was specifically oriented to adequately measure the SLD environment including the concentrations, sizes, and LWC of the entire drop spectrum. While this objective was not inherent to the FIRE-ACE project, this project followed closely the CFDE III project and the same instrumentation suite was employed. Hence, FIRE-ACE was considered a viable project for adequately measuring SLD conditions.

3. Instrumentation

Common instruments were mounted on the NRC Convair-580 research aircraft during CFDE I, CFDE III, FIRE-ACE, and AIRS I. These included two King hot-wire LWC) probes, a Nevzorov hot-wire LWC probe, a Nevzorov hot-wire total water content (TWC) probe, a Rosemount Icing Detector (RID), two Particle Measuring Systems, Inc., (PMS) Forward Scattering Spectrometer Probes (FSSP), two PMS 2D Cloud Particle Imaging Probes (2D-C and 2D-G), a PMS 2D Precipitation Particle Imaging Probe (2D-P), and two Rosemount Temperature Probes. The instruments were mounted on three underwing pylons including a dedicated pylon for the LWC probes and two pylons that could each hold four PMS-type probes.

The NASA Glenn Twin Otter research aircraft flew with a similar instrumentation suite for AIRS I and the NASA SLD study, although there were fewer duplicate instruments. Its instruments included a King LWC Probe, Nevzorov LWC and TWC Probe, FSSP, 2D-G, RID, and Rosemount Temperature Probe. The temperature, LWC, and RID instruments were mounted on the forward fuselage, while the FSSP and 2D probes were mounted on small underwing pylons.

Table 1 summarizes the instruments on each aircraft that were used in the analysis. The measurements associated with each instrument in Table 1 will be briefly described below, along with the accuracy, sensitivity, references, and known limitations.

Table 1.

Summary of instruments used for analyzing the icing environments.

Table 1.

King LWC probes have been described by King et al. (1978) and King et al. (1985). Calibration and utilization of the Environment Canada King probes have been described by Cober et al. (1995, 2001b) and Strapp et al. (2001). The King LWC measurements are believed to be accurate to within 15% for drops <30 μm in diameter when baseline drift is corrected for. There is an increasing underestimate of LWC for increasing MVD (Biter et al. 1987), and Strapp et al. (2003) showed that the King probe experienced a 70%, 60%, and 45% underestimate of the LWC for MVD of 50, 100, and 200 μm, respectively. For this reason, the King probes were not used to measure LWC in icing environments where significant LWC existed in drop sizes greater than 30 μm.

The Nevzorov LWC and TWC probes have been described by Korolev et al. (1998b). Utilization of the Nevzorov LWC and TWC probes for analyzing aircraft icing environments has been described by Cober et al. (2001b). These probes are believed to be accurate to within 15% with a sensitivity of 0.003–0.005 g m−3 when baseline drift and ice crystal effects are corrected for. Similar to the King probe, the Nevzorov LWC probe underestimates the LWC associated with drops >40 μm. Strapp et al. (2003) showed that the Nevzorov LWC probe experienced a 70%, 60%, and 50% underestimate of the LWC for median volume diameters of 50, 100, and 200 μm, respectively. Conversely, the Nevzorov TWC probe was designed to minimize this effect (Korolev et al. 1998b) and this was confirmed by Strapp et al. (2003) who showed that the Nevzorov TWC probe measured the LWC within 30% of calibrated wind-tunnel values for MVDs up to 250 μm.

Since the Nevzorov TWC probe was not believed to underestimate the LWC in SLD environments with MVD values larger than 50 μm, it was used as the primary LWC measurement in SLD conditions. The King and Nevzorov LWC probes were used to confirm consistency of the Nevzorov TWC probe and the FSSPs. The Nevzorov TWC probe does respond to ice crystals (Cober et al. 2001b). However, since the majority of mixed-phase conditions were eliminated from the SLD analysis, the Nevzorov TWC response to ice did not impact the LWC estimates in SLD environments.

The RID, which is manufactured by B.F. Goodrich, has been described by Baumgardner and Rodi (1989), Heymsfield and Miloshevich (1989), Cober et al. (2001a), and Mazin et al. (2001). It is extremely useful for helping to segregate liquid-, mixed-, and glaciated-phase conditions (Cober et al. 2001a) since it is not believed to respond to ice crystals (Heymsfield and Miloshevich 1989). A limitation of the RID is that the combination of dynamic heating and latent heat release from supercooled droplets that are freezing on the sensing cylinder can cause the ice surface temperature to reach 0°C (Ludlam 1951). This causes the interpretation of the RID signal to be difficult at temperatures warmer than the Ludlum limit. For the analysis presented here, the RID was mainly used to help assess the phase of each cloud environment.

The FSSP instruments were used to determine the sizes and concentrations of cloud drops over various diameter ranges. Glass bead calibrations were used to correct for under- or oversizing (Cober et al. 1995), while the concentrations were corrected for dead time and coincidence errors following Baumgardner et al. (1985). Two FSSPs on ranges 3–45 and 5–95 μm were normally used for flights with the NRC Convair-580. Having two FSSP instruments allowed for redundancy in the event of fogging or malfunction of one of the probes. It also allowed for real-time and postflight consistency checking. The FSSPs were believed to measure concentration within ±17%, droplet size within ±15%, and LWC within ±43% (Baumgardner 1983). Application of the FSSP probes for the analysis of aircraft icing conditions has been described by Cober et al. (2001b).

FSSPs respond to ice crystals and the ice crystal responses can be incorrectly interpreted as drops. Gardiner and Hallett (1985) showed that PMS FSSP probes responded significantly to ice crystals, while the misinterpretation of droplets as ice crystals with 2D-C measurements has been discussed by Rauber and Heggli (1988). On the basis of mixed-phase conditions observed during CFDE I and CFDE III with ice crystal concentrations ≥1–5 L−1 (for crystals observed with the 2D probes), Cober et al. (2001b) found that the FSSP measurements were assessed to be biased by ice particles, and hence unreliable for sizes above 35 μm. This observation was similar for both FSSP instruments and independent of the measurement range used. When the data were averaged over the collective CFDE dataset, the FSSP measurements in cloud conditions with ice crystal concentration ≥1–5 L−1 were found to have concentrations of particles larger than 35 μm that were up to 10 times the concentrations for conditions with no ice crystals. For ice crystal concentrations in the range 0–1 L−1 the drop spectrum was not significantly biased by ice crystals. Cober et al. (2001b) concluded that the FSSPs should not be used to infer drop spectrum characteristics for diameters larger than 35 μm when the ice crystal concentration measured with the 2D probes exceeded 1 L−1.

The 2D cloud (2D-C and 2D-G) and 2D precipitation (2D-P) probes were used to provide shape, size, and concentrations for particles within their respective size ranges. The first four channels of each 2D probe were discarded because of depth of field uncertainties associated with these channels (Joe and List 1987; Korolev et al. 1998a) and because of the significant sizing errors that occur in these channels (Korolev et al. 1991; Korolev et al. 1998a). Strapp et al. (2001) showed that distribution measurement errors for the 2D-C mono, when expressed as sizing errors, were <10% for particles ≥5 pixels (125 μm).

The hydrometeor images obtained with the 2D probes were processed following the center-in technique of Heymsfield and Parrish (1978). This technique uses circular geometry computations that allow the effective photodiode width to be at least a factor of 2 larger than the actual photodiode width. Since the technique assumes circular geometry, it is only valid for measuring circular particles such as drops. The data from the 2D-C gray probe were processed using two shadow levels (approximately 40%–50%), simulating a 2D-C mono probe response, although with a smaller sample volume.

A technique for assessing drops, ice crystals and erroneous particles from 2D images greater than 4 pixels in diameter has been described by Cober et al. (2001b). Images were separated into circles (assumed to be drops), noncircles (assumed to be ice crystals), and erroneous images (zero area images, out of focus, time bar errors, embedded blank slices, etc.) using diameter, area, perimeter, and symmetry algorithms described by Cober et al. (2001b). They showed that in liquid-phase conditions at temperatures >0°C, where every particle image was assumed to be a circular drop, in excess of 85% of the images were assessed as circles and hence interpreted correctly as drops. Conversely, in glaciated-phase conditions, where every particle image was assumed to be an ice crystal, between 5% and 40% of the processed images were assessed as circles, which could be incorrectly interpreted as drops. The relative fractions of circles and noncircles were strongly dependent on particle size, with particles ≤8 pixels in diameter having the largest potential errors. The larger a particle is, the higher is the resolution of its shape, and hence the higher is the accuracy in distinguishing circles from noncircles. In glaciated clouds a particle size of 11 pixels was required before the average fraction of circular particles dropped below 0.2. The application of such a technique is necessary if 2D images are to be used for deriving drop spectra associated with SLD conditions.

For this study the analysis method for 2D images described by Cober et al. (2001b) was followed. Only 2D images of cloud particles that were ≥5 pixels in diameter and that were obtained in liquid-phase clouds or in mixed-phase clouds with ice crystal concentration <1 L−1, were assumed to be drops and were subsequently used to develop SLD drop spectra. SLD spectra were not determined when the cloud conditions were assessed as glaciated or contained ice crystal concentrations >1 L−1. In all cases 2D images that represented out-of-focus particles or other erroneous images were removed from the data and were not included in the analysis.

4. Database of icing and SLD observations

The data from each flight were averaged in sequential 30-s intervals, corresponding to a horizontal length scale of 2.9 ±0.3 km for the Convair-580 data and 2.1 ±0.2 km for the Twin Otter data. The error represents the standard deviation from the mean. The 30-s averaging scale was chosen because it represented a short averaging scale and a scale that generally allowed sufficient 2D measurements for statistical significance (i.e., >100 counts). The phase of each 30-s data point was determined following Cober et al. (2001b). For each 30-s data point that was assessed to be liquid phase or mixed phase with an ice crystal concentration <1 L−1, the entire FSSP spectrum, 2D-C spectrum ≥5 pixels (125 μm for the EC 2D-C), and 2D-P spectrum ≥5 pixels (1000 μm) were used to produce a binned drop spectrum. The midpoint diameters of each bin were used to interpolate a normalized drop spectrum at 1-μm resolution, from 1 μm to the maximum drop diameter observed. The interpolation was based on a linear fit between logarithmic diameter and concentration pairs. For regions where the 3–45- and 5–95-μm FSSP measurements overlapped, the 3–45-μm data were used unless they were assessed to have been biased because of probe icing or fogging. The spectra were interpolated in two locations including 1) between the last FSSP channel (≤95 μm depending on where the spectrum is truncated because of insufficient particle counts) and the first useful 2D-C channel (125 μm), and 2) between the last useful 2D-C channel (which varies, depending on where the spectrum is truncated because of insufficient particle counts) and the first useful 2D-P channel (1000 μm). FSSP and 2D channels were required to have 10 counts before they were used in the analysis. When the number of counts per bin fell below 10, bins were combined until 10 counts were obtained. The spectra were truncated when there were fewer than 10 counts in sizes larger than the last useful bin. The maximum diameter (Dmax) for each spectrum was assessed as the midpoint of the last useful bin. Each data point with a temperature ≤0°C and with at least one measurement bin of drops larger than 100 μm in diameter was considered as an SLD environment. For each such SLD environment, the 1-μm drop spectrum was used to compute the LWC, mean, mean volume, median volume, and 95% and 99% mass diameters. An example of an integrated drop spectrum for an SLD environment observed during AIRS I is shown in Fig. 1.

Fig. 1.
Fig. 1.

Example of an SLD drop spectrum determined from several instruments. Individual channels from the two FSSP and three 2D probes are shown as circles. Combined bins with a minimum of 10 counts are shown as ×s. The 1-μm spectrum is shown as a solid line. The MVD for this spectrum is 141 μm, and the maximum drop diameter for the 1-μm spectrum is 1100 μm.

Citation: Journal of Applied Meteorology and Climatology 51, 2; 10.1175/JAMC-D-11-022.1

In total, there were 48 301 30-s in-flight data points (approximately 400 h) collected during the six flight campaigns. Of these, 27 497 (57%) data points were assessed as being in cloud with a TWC > 0.005 g m−3. There were 22 263 in-cloud observations (46% of in flight) with an average static temperature ≤0°C, and 14 199 observations (29% of in flight) where supercooled liquid water was assessed to exist. There were 10 128 in-cloud in-icing data points with ice crystal concentrations <1 L−1 where the drop spectra could be accurately determined. Finally, there were 2444 observations with an average static temperature ≤0°C, an average LWC > 0.005 g m−3, an ice crystal concentration <1 L−1, an assessment of either liquid or mixed phase, and drops >100 μm in diameter. The latter data points, which represent 5% of the in-flight observations, represent the SLD database used for the analysis. Only data points with adequate measurements of both LWC and the drop spectrum were included in the SLD database.

A comparison between the measured LWC and spectrum-derived LWC is shown in Fig. 2 for the 2444 SLD observations. The best fit has a slope of 0.95, which suggests a good agreement between the measurements. The spectrum-derived LWC has an estimated error of approximately 40% (Cober et al. 2001c; Baumgardner 1983), and the measured LWC has an error of ±15%, for a combined error of 43% (Baumgardner 1983). Eighty-five percent of the observations with LWC > 0.1 g m−3 fall within the expected error estimates. Consistency between the measured and spectrum-derived LWC values is demonstrated in Fig. 2, which is extremely important for providing confidence when applying these observations to the development of certification envelopes. Other databases with SLD observations were not used in the analysis because the same level of confidence in the observations was not established.

Fig. 2.
Fig. 2.

Scatterplot of measured LWC vs the spectrum-derived LWC for each 30-s SLD measurement (2444 observations). The solid center line is the best fit while the two outer lines represent ±43% to the best fit. The measured LWC was based on the Nevzorov LWC and TWC measurements.

Citation: Journal of Applied Meteorology and Climatology 51, 2; 10.1175/JAMC-D-11-022.1

5. Segregation of SLD environments

There have been several different suggestions regarding how to develop SLD envelopes, or how to characterize icing or SLD environments, including Newton (1978), Jeck (1996), Politovich (1996), Shah et al. (2000), and Ashenden and Marwitz (1998). Comparisons of in situ data with several of these envelopes have been reported by Cober et al. (2001c) and Isaac et al. (2001b). While the SLD data were being acquired, the aviation community requested that the existing icing certification envelopes contained in FAR 25-C should remain unchanged and that any characterization of SLD conditions should be supplementary and distinct. The decision to leave FAR 25-C unchanged was based on the fact that all of the existing certification programs, facilities, and experience was based on certification to FAR 25-C. To conduct realistic wind-tunnel or numerical icing simulation experiments that mimic cloud environments that contain SLD, it is necessary to characterize the data in a form that is both practical and realistic. Practical implies a minimum number of representative drop spectra, while realistic implies that a wide range of natural icing conditions should be included in the characteristic spectra.

The majority of reports of SLD measurements have simply presented the drop size distributions that were observed (Politovich 1989; Ashenden and Marwitz 1998; Cober et al. 1996), with no attempt to reconcile or average different environments. Icing environment characterizations such as Cober et al. (2001c) have typically followed the averaging approach of FAR 25-C. Jeck (1996) suggested that reported drop spectra could be averaged together in specific diameter bins (i.e., 50–100 μm, 100–200 μm, etc.). Shah et al. (2000) suggested that in situ SLD data could be segregated into distinct subsets by varying only two parameters including Dmax and the drop MVD. They suggested that by varying Dmax and MVD, the SLD environments could be classified into four distinct subsets that physically represented environments with freezing drizzle or freezing rain, with high or low MVD values, respectively, and that these four environments would be unique from, and supplemental to FAR 25-C. This was recognized as being practical to the aviation community and hence the approach of Shah et al. (2000) was followed. After a number of sensitivity studies to assess the impact of using different thresholds of Dmax and MVD (Cober et al. 2003), the SLD data were segregated into four subsets as listed in Table 2.

Table 2.

Number of SLD observations, MVD, and Dmax values for each average SLD spectrum.

Table 2.

In Table 2 the MVD threshold of 40 μm was chosen to be consistent with the maximum MVD limits of FAR 25-C for continuous maximum icing, since this more closely corresponded to conditions in the in situ SLD data collected in the research programs. The Dmax threshold of 500 μm was selected to be consistent with the meteorological definitions of freezing drizzle and freezing rain. Freezing drizzle is defined in the Glossary of Meteorology (Glickman 2000) as supercooled drops between 200 and 500 μm in diameter while freezing rain is defined as supercooled drops larger than 500 μm in diameter. The lower Dmax threshold of 100 μm was selected because it is commonly used as a definition of SLD. Shah et al. (2000) suggested a value of 135 μm for the Dmax threshold based on the assumption that FAR 25-C conditions could be described with a Langmuir E distribution, and a Langmuir E distribution with an MVD of 50 μm would have a maximum drop diameter of 135 μm. Cober et al. (2003) showed that there were no significant differences in the analysis by using thresholds between 100 and 135 μm. A methodology that focused only on freezing drizzle conditions could have used a Dmax lower threshold of 200 μm; however, that would not have incorporated SLD conditions with smaller diameters. There is no way to know the drop spectra characteristics for the original FAR 25-C conditions and hence selection of the lower Dmax threshold choice of 100 μm was arbitrary.

These SLD environments can be considered distinct from FAR 25-C if the latter is assumed to only include drops <100 μm in diameter and if there are no environments with Dmax < 100 μm and MVD > 40 μm. In the icing database collected there were 90 observations at 30-s resolution with Dmax < 100 μm and MVD > 40 μm. This represents only 4% of the SLD observations, and these conditions are neglected by assuming that they are close enough to FAR 25-C conditions that FAR 25-C adequately describes them.

6. Characterization of drop spectra for SLD conditions

Each SLD data point at 30-s resolution had a drop spectrum at 1-μm resolution that was derived from the combination of FSSP and 2D probes and that spanned the range from 1 μm to the maximum drop diameter observed. Following the methodology described in Cober et al. (2003), for each of the four SLD subsets, all of the drop spectra concentrations for each subset were averaged together to derive a single drop spectrum that was considered representative of the SLD subset. For ease of comparison, the LWC of each average spectrum was scaled to a constant value of 0.2 g m−3. The average drop size distribution at 1-μm resolution was then used to derive the mass spectrum, cumulative mass spectrum, mass distribution, and characteristic diameters such as the MVD. Table 2 also shows the MVD and Dmax values for each of the four average SLD spectra.

The cumulative mass distribution, as a fraction of the LWC, for each of the freezing drizzle and freezing rain spectra appear in Figs. 3a and 3b, respectively. For application of these average SLD spectra in numerical ice accretion codes, or in wind tunnel experiments, the cumulative mass spectra shown in Fig. 3 can be used to develop numerical or sprayed drop distributions that have similar shapes and characteristics. The actual mass distributions for each of the freezing drizzle and freezing rain spectra are shown in Figs. 4a and 4b, respectively.

Fig. 3.
Fig. 3.

Cumulative mass fraction distributions for SLD environments that include (a) freezing drizzle drops > 100 μm, and with MVD < 40 μm and MVD > 40 μm and (b) freezing rain drops > 500 μm, and with MVD < 40 μm and MVD > 40 μm.

Citation: Journal of Applied Meteorology and Climatology 51, 2; 10.1175/JAMC-D-11-022.1

Fig. 4.
Fig. 4.

Mass distributions for SLD environments that include (a) freezing drizzle drops > 100 μm, and with MVD < 40 μm and MVD > 40 μm and (b) freezing rain drops > 500 μm, and with MVD < 40 μm and MVD > 40 μm.

Citation: Journal of Applied Meteorology and Climatology 51, 2; 10.1175/JAMC-D-11-022.1

The normalized mass distributions, representing Δ(LWC)/Δlog(diameter) versus diameter, for each of the freezing drizzle and rain spectra are shown in Figs. 5a and 5b, respectively. The normalization adjusts for the log scale on the horizontal axis in such a way that area is proportional to LWC, so that the features such as bimodality are readily apparent.

Fig. 5.
Fig. 5.

Normalized mass distributions [Δ(LWC)/Δlog(diameter)], where LWC is in grams per meter cubed and diameter is in micrometers, for SLD environments that include (a) freezing drizzle drops > 100 μm, and with MVD < 40 μm and MVD > 40 μm and (b) freezing rain drops > 500 μm, and with MVD < 40 μm and MVD > 40 μm.

Citation: Journal of Applied Meteorology and Climatology 51, 2; 10.1175/JAMC-D-11-022.1

The bimodal natures of the SLD spectra are clearly evident in these plots. For freezing drizzle and rain conditions with MVD < 40 μm the cloud drop mass peak around 20 μm is the dominant one. For freezing drizzle conditions with MVD > 40 μm and freezing rain conditions with MVD > 40 μm, the dominant peak for mass is in the peak that occurs in the drizzle (around 200–300 μm) or rain (around 700–800 μm) size ranges.

The wide variation in the cumulative mass curves suggests that the four spectra have distinct characteristics, and that they collectively appear to represent a wide range of naturally observed SLD icing conditions. Using the aircraft-based observed vertical temperature profiles, the formation mechanism for each 30-s SLD data point was assessed as either classical, implying that it formed through a melting and resupercooling mechanism, or nonclassical, implying that it formed through a condensation and collision–coalescence mechanism. For freezing drizzle conditions, 88% were observed to have formed through a nonclassical process. Conversely, for freezing rain conditions, 92% were observed to have formed through a classical process. This highlights that the freezing drizzle and freezing rain conditions observed are relatively distinct in that they primarily formed through fundamentally different mechanisms in the atmosphere.

7. Horizontal scale factor for LWC in SLD conditions

To simulate SLD conditions in a wind tunnel or a numerical ice accretion model for aircraft certification, it is necessary to have both a drop spectrum and a maximum LWC where the maximum LWC value is normally associated with a high percentile value such as 99% or 99.9%. The determination of a maximum LWC value predicted for each SLD condition was complicated by the requirement to have a horizontal scale factor that would project the maximum LWC value at one length scale to different length scales. It was also considered necessary to determine the maximum LWC value as a function of temperature. FAR 25-C includes a horizontal scale factor and a temperature dependency for LWC.

Each data point was first normalized to a standard temperature of 0°C following Isaac et al. (2004). The normalization was done by assuming that the liquid water mixing ratio would remain constant for any change in temperature or pressure. Starting with an observed temperature and pressure, assuming that the pressure did not change so that Pobs = P0C, and assuming that the mixing ratio remained constant, the following equation could then be applied:
e1
where LWC is the liquid water content, ρ is the density of dry air, T is the temperature, and P is the pressure. The subscript “obs” refers to the value of the parameter observed and the subscript “0C” refers to the value of the parameter at 0°C. Since Tobs and T0C were normally within 5% of each other, the normalization of the data to 0°C had a minimal effect on the analysis. No normalization was done with respect to pressure for the observed data, hence the assumption that Pobs = P0C. Once the data were normalized to 0°C, the 99% LWC values were determined using an extreme value analysis technique as described in section 9. The 99% LWC value at 0°C was then used to derive the temperature dependency.

For each averaging interval, including the 30-, 60-, 120-, and 300-s averages, which corresponded to horizontal extents of 3, 6, 12, and 30 km, respectively, the collective SLD LWC observations, normalized to 0°C, were used to compute the 99% LWC value following the extreme value analysis described in section 9. It is important to note that all four SLD subsets were grouped together for this analysis and Table 3 gives the number of SLD observations for each averaging interval or length scale. The SLD 99% LWC values, along with the 95% confidence limits, are plotted against the averaging distance in Fig. 6.

Table 3.

Sample size of SLD conditions for each length scale.

Table 3.
Fig. 6.
Fig. 6.

Plot of 97% (squares), 99% (diamonds), and 99.9% (circles) LWC vs averaging distance for SLD conditions. All SLD conditions were used for each data point. The linear best fits for each are shown. The vertical solid lines are the 95% confidence limits for each data point.

Citation: Journal of Applied Meteorology and Climatology 51, 2; 10.1175/JAMC-D-11-022.1

The data in Fig. 6 were fit to a linear best fit as
e2
where dHkm is the horizontal averaging distance in kilometers and LWC99 is the 99% LWC in grams per meter cubed at the averaging distance dHkm. From Eq. (2), at a horizontal extent of 32.2 km (17.4 n mi) the LWC is 0.418 g m−3. It is possible to define a dimensionless scale factor so that Eq. (2) can be rewritten as follows:
e3
e4
where SF99 is the scale factor for the 99% LWC data, and LWC32.2 is the value of LWC99 at a horizontal extent of 32.2 km (17.4 n mi). Note that the scale factor has been defined so that it is equal to 1 at 32.2 km so that it parallels the dimensionless scale factor in FAR 25-C.
To determine whether Eqs. (3) and (4) were valid for other low-probability LWC values, extreme value analysis was used to compute the 97% and 99.9% LWC values for each of the four averaging periods. The best fits of LWC versus averaging distance are also shown in Fig. 6. When the 97% and 99.9% fits in Fig. 6 are transformed into dimensionless scale factors such as Eq. (4), the equations for the scale factors are as follows:
e5
e6
where SF97 and SF99.9 are the scale factors for the 97% LWC and 99.9% LWC data, respectively. These equations are within 3% of Eq. (4), which suggests that Eq. (4) is valid for LWC probabilities between 97% and 99.9%. The three dimensionless scale factors for 97%, 99%, and 99.9% are plotted in Fig. 7 where they are indistinguishable. The scale factors for the SLD conditions and from FAR 25-C are compared in Fig. 7. The difference in the slope between the two scale factors may be caused by differences in how the observations were averaged and in differences in the primary length scales that the data were collected on.
Fig. 7.
Fig. 7.

Dimensionless scale factors for 97%, 99%, and 99.9% LWC vs averaging distance for SLD conditions. The dimensionless scale factor from FAR 25-C is also shown for comparison.

Citation: Journal of Applied Meteorology and Climatology 51, 2; 10.1175/JAMC-D-11-022.1

To ensure that Eq. (4) was valid for each subset of SLD conditions, an extreme value analysis was performed for each horizontal extent for each of the four SLD subsets to assess the 99% LWC values. The 99% LWC values along with their 95% confidence limits are shown in Fig. 8. The uncertainty intervals in Fig. 8 are larger than those in Fig. 6 because there were fewer data points for each fit. For the freezing drizzle with MVD > 40 μm at 30-km resolution and the freezing rain with MVD < 40 μm at 30-km resolution there were insufficient data points to undertake an extreme value analysis. The fits shown in Fig. 8 are not the statistical best fits as derived in Fig. 6. Rather they are the eye-estimated best fit of Eq. (4) to each SLD subset. Each of the four SLD subsets seems to be well represented by the fits in Fig. 8 and it is concluded that the dimensionless scale factor given in Eq. (4) adequately represents each of the four SLD subsets. The LWC values for each SLD subset at 32.2 km can be determined from Fig. 8 and are given in Table 4. The dimensionless scale factor in Eq. (4) must be used in conjunction with the LWC at 32.2 km in Eq. (3). These are given in Table 4. Using the dimensionless scale factor from Eqs. (4) and (3) and the LWC for 32.2 km from Table 4, the 99% LWC value at 0°C can be computed for any SLD subset at any horizontal extent.

Fig. 8.
Fig. 8.

The 99% LWC as a function of horizontal extent for each subset of SLD conditions. The vertical lines represent the 95% confidence limits for each data point. The fitted lines are not the statistical best fits, but rather are the best fit assuming a slope given by Eq. (4).

Citation: Journal of Applied Meteorology and Climatology 51, 2; 10.1175/JAMC-D-11-022.1

Table 4.

The 99% LWC values for each SLD subset at 32.2 km (17.4 n mi).

Table 4.

8. Temperature dependency of LWC in SLD conditions

Using the 99% LWC values in Table 4, a LWC–temperature relationship was developed using the following methodology. The mean temperature and pressure of all of the 30-s SLD data observed were −4.2°C and 865 hPa, respectively. These values were used to modify the U.S. Standard Atmosphere, which provides a relationship between temperature and pressure, so that the U.S. Standard Atmosphere temperature at 865 hPa was also equal to −4.2°C. The modification required was a systematic reduction of the temperature profile by 11.0°C, which represents a cooler atmosphere than the U.S. Standard Atmosphere. This is consistent with the winter nature of the SLD observations. The modified U.S. Standard Atmosphere equation for computing pressure from temperature is as follows:
e7
where P is the pressure in pascals and T is the temperature in kelvins. The 0°C LWC values from Table 4 were assigned a pressure of 939 hPa, which is consistent with the pressure at 0°C in the modified U.S. Standard Atmosphere described above. For temperatures between 0° and −25°C the corresponding pressures were determined using the equation provided above. For each temperature–pressure pair, the LWC was computed by assuming that the liquid water mixing ratio remained constant for the changes in temperature and pressure from 0°C and 939 hPa. The LWC calculation is given by the following equation:
e8
where LWC is the liquid water content, ρ is the density of dry air, T is the temperature, and P is the pressure. The subscript “0C” refers to the values at 0°C and 939 hPa while the subscript “SA” refers to the values at temperature–pressure pairs of the modified U.S. Standard Atmosphere. The LWC0C values are taken from Table 4.

Figure 9 shows a plot of temperature versus LWC for freezing drizzle environments with MVD < 40 μm and MVD > 40 μm. The values of LWC at 0°C are valid for the reference distances of 32.2 km and are taken from Table 4. Figure 10 shows a similar plot for freezing rain environments. The in situ observations at 300 s (30 km) are shown for comparison. The data are adequately bounded by the temperature–LWC curves. The curves are truncated at −25°C for freezing drizzle and −13°C for freezing rain because there are no or negligible numbers of observations at lower temperatures. These limits are consistent with climatologies of surface observations for freezing drizzle and freezing rain (Stuart and Isaac 1999; McKay and Thompson 1969).

Fig. 9.
Fig. 9.

The 99% LWC envelopes vs temperature for freezing drizzle environments compared with 300-s data. The number of data points observed for each subset of SLD data are shown in the caption.

Citation: Journal of Applied Meteorology and Climatology 51, 2; 10.1175/JAMC-D-11-022.1

Fig. 10.
Fig. 10.

As in Fig. 9, but for freezing rain environments.

Citation: Journal of Applied Meteorology and Climatology 51, 2; 10.1175/JAMC-D-11-022.1

9. Determination of maximum LWC environments for SLD conditions

The FAR 25-C icing curves were based on in situ data collected in the 1940s (Jones and Lewis 1949; Lewis and Bergrun 1952). Several icing cylinders of different diameter were used to infer the LWC and MVD of the observed icing environments. These envelopes for continuous maximum (extreme) icing conditions were developed for a horizontal distance of 17.4 n mi (approximately 32.2 km). For a given temperature–LWC–MVD point on the envelopes, there is some uncertainty regarding the probability of simultaneously observing temperatures that are colder, LWC values that are larger, and MVD values that are larger. Simultaneous exceedance probabilities of 0.01 and 0.001 have commonly been associated with these envelopes. To extrapolate their data to estimate the 99.0% or 99.9% icing environments, Lewis and Bergrun (1952) followed Gumbel (1942) and fitted the cumulative probability distributions of the observed LWC values to a distribution of the form
e9
where P is the probability distribution function for x and α and μ are constants. This distribution is generally referred to as the Gumbel or EV-I distribution and it represents the generalized extreme value distribution (GEV) with shape parameter 0.
Masters (1983) used a different database of icing measurements to estimate the 99.9% icing environments for cloud conditions at altitudes less than 10 000 ft above ground level. He fitted the cumulative probability distributions of observed LWC values to a distribution of the form
e10
where k, α, and μ are constants. Equation (10) is a form of the Weibull distribution.
Extreme value statistical analysis (Coles 2001) allows quantification of the nature of distributions in the tails of the distributions, and hence provides a more accurate method for determining extreme values, and their associated confidence limits. Extreme value analysis is based on the “three types theorem” of Fisher and Tippett (1928), which states that there are only three types of distributions that can arise as limiting distributions of extremes in random samples. The Fisher–Tippett theorem suggests that the asymptotic distribution of the maxima belongs to one of the three distributions regardless of the original distribution of the observed data. The three types of extreme value distributions can be combined into a single family known as the GEV (Coles 2001), which is of the form
e11
where μ is called the location parameter, ψ is called the scale parameter, and ξ is called the shape parameter. The nature of the tail of the distribution is determined by ξ, and the three types of extreme value distributions are related to whether ξ = 0 (Gumbel family), ξ > 0 (Fréchet family), or ξ < 0 (Weibull family).

The Gumbel or EV-I family of distributions have “medium”-tailed distributions. That is, the distribution of the maximum of a sample of size n from one of the distributions in the domain of convergence will eventually have the EV-1 distribution as n becomes large. The Fréchet or EV-II family of distributions have tails that are wider, or longer, than the Gumbel family. The Weibull or EV-III family of distributions have tails that are narrower, or shorter, than the Gumbel family.

There are several techniques for estimating the parameters associated with the GEV (Coles 2001). The technique of threshold selection is used here. This involved sorting the data from the smallest to the largest value, then choosing a threshold value, and fitting a generalized Pareto distribution (GPD) to all of the observations that exceed the threshold value. The distribution of values above a threshold u can be approximated by GPD (Gencay et al. 2002), which is given by
e12
where ξ is the shape parameter, σ′ is proportional to u, and μ and σ are constants. It can be shown that the GPD is analogous to the GEV with both distributions having a similar form and the same shape parameter ξ (Coles 2001). When choosing a threshold, care must be taken to balance the number of exceedances of the threshold with the number of data points necessary for a good fit. Choosing a low threshold will allow more data points for the fit but may incorporate data from the center of the distribution, rather than from only the tail. Choosing a high threshold will better represent the tail; however, there may be insufficient data points for an adequate fit. Sensitivity studies are required to ensure that the choice of threshold provides results that are reasonable and robust.

The in situ aircraft icing data were analyzed using the Extreme Value Analysis in MATLAB (EVIM) software described by Gencay et al. (2002). The method of fitting the data to the GPD and of estimating the shape of the tail of the distribution is discussed in Cober and Isaac (2006). A brief summary of the methodology follows. Following Gencay et al. (2002) the shape of the tail of each SLD distribution was estimated as a function of the threshold (exceedance value) by fitting the data to a GPD. A threshold value was selected above which the shape factor was observed to be relatively stable. The LWC values greater than the threshold, representing the tail of the original LWC distribution, were then fit using a GPD. The 99% and 99.9% LWC values were determined from the fit with corresponding 95% confidence intervals. Sensitivity studies were done with different threshold values to ensure that the choice of threshold did not significantly influence the results.

The number of data points at 30-s resolution for the four SLD subsets ranged from 193 to 1469. To maximize the number of data points used in the analysis no further subdividing of the SLD subsets (i.e., as a function of temperature or MVD) was undertaken. Table 5 shows, for each SLD subset, the threshold values that were used when fitting the data to a GPD. Table 5 also shows the maximum observed LWC, the LWC corresponding to the threshold selection and the shape factor determined for each fit. The standard deviation σ for each shape factor is listed in Table 5. The shape factors were fairly similar and generally agreed within their standard deviations. The shape factors suggested narrow to medium tailed distributions.

Table 5.

Threshold characteristics for the GPD for each SLD subset.

Table 5.

The 99% and 99.9% LWC values were estimated for each of the four SLD subsets. The fits along with the 99% estimates and 95% confidence limits are shown in Fig. 11 for each SLD subset for the 3-km-resolution data. Similarly, the fits along with the 99.9% estimates and 95% confidence limits are shown in Fig. 12. Similar fits were done for each SLD subset at 6-, 12-, and 30-km resolution. The 95% confidence limits are much wider for the 99.9% analysis and reflect a significantly greater uncertainty. The size of the database was sufficient for determining the 99% LWC values, since for a given fit there were generally several LWC observations that were above the 99% limits. Conversely, the size of the database was generally too small to determine the 99.9% LWC values within a narrow 95% confidence limit. This can be seen in Fig. 12. There were no observations of SLD environments where the LWC was greater than the upper bound of the 95% confidence limit of the 99.9% LWC value [1 − F(x) = 0.001]. To reduce the uncertainty of the 99.9% estimates, a significant number of new SLD observations would need to be collected. Regardless, the fits shown in Fig. 12 appear to represent the observations quite well. Sensitivity studies were done with different threshold values to ensure that the choice of threshold did not significantly influence the results.

Fig. 11.
Fig. 11.

Estimation of the 99% or [1 − F(x)] = 0.01 probability values with 95% confidence limits, by fitting the exceedance values of LWC(x) above a threshold LWC to a GPD for each SLD subset: (a) freezing drizzle with MVD < 40 μm; (b) freezing drizzle with MVD > 40 μm; (c) freezing rain with MVD < 40 μm; (d) freezing rain with MVD > 40 μm. These fits were based on 3-km data. The data are shown as dots, and the best fit is shown as a solid line. The 95% confidence limits are shown as a solid horizontal bar. The values of LWC associated with the best-fit probability value and the associated 95% confidence limits are shown along the top axis of each plot.

Citation: Journal of Applied Meteorology and Climatology 51, 2; 10.1175/JAMC-D-11-022.1

Fig. 12.
Fig. 12.

As in Fig. 11, but for the 99.9% or [1 − F(x)] = 0.001 probability values.

Citation: Journal of Applied Meteorology and Climatology 51, 2; 10.1175/JAMC-D-11-022.1

The numerical values of the 99.0% and 99.9% LWC values for each of the SLD subsets valid for 32.2 km (17.4 n mi) are listed in Table 6. Note that the maximum LWC values in Table 4 are equal to the 99.0% LWC values in Table 6.

Table 6.

The 99.0% and 99.9% LWC values for 32.2 km determined using GPD.

Table 6.

10. Comparison of icing envelopes

The FAR 25-C envelopes only include MVD values up to 40 μm, although Jones and Lewis (1949) suggested that extreme freezing rain conditions could be represented by a droplet MVD of 1000 μm, LWC of 0.15 grams per centimeter squared per hour. and a horizontal extent >100 km. Newton (1978) described icing accumulation envelopes, which physically represented the sweep out LWC and the potential accumulations of ice on a 3-in. diameter icing cylinder in grams per centimeter squared per hour. The potential accumulation rate would depend on the collision-collection efficiency of the hydrometeor spectra, which is a function of aircraft speed and droplet size. However, for drops greater than approximately 50 μm in diameter the collision efficiency would be essentially 1, and there would be no way to distinguish the accumulation associated with 50-μm drops from that from 500- or 1000-μm drops.

The SLD observations for freezing drizzle and freezing rain conditions for horizontal extents of 300-s (30 km) are compared with the FAR 25-C and the potential accumulation envelopes in Figs. 13 and 14, respectively. The 99% and 99.9% LWC limits from Table 6 for 32.2 km (17.4 n mi) horizontal extents are also shown for the MVD < 40 μm and MVD > 40 μm conditions. Note that the FAR 25-C envelopes and the EVD determined LWC limits are valid for 32.2 km, while the individual data points are valid for 30 km. The comparison is acceptable because the difference in length scales is quite small. Since the SLD observations are not segregated by temperature and include all observations at temperatures <0°C, it is only valid to compare the observations and envelopes with the 0°C envelope for FAR 25-C.

Fig. 13.
Fig. 13.

Plot of MVD vs LWC for 300-s (30 km) averaged data for freezing drizzle conditions. The 99% and 99.9% LWC values from Table 6 are shown. The FAR 25-C envelopes for 0°, −10°, and −20°C and the Newton (1978) potential accumulation envelopes for 1, 6, and 12 g cm−2 h−1 are also shown for comparison and labeled accordingly. The LWC limits (envelopes) are shown as boxes ranging from 7 to 40 μm (for MVD < 40 μm) and from 40 to 500 μm (for MVD > 40 μm). The 99% LWC limits are shown as solid lines while the 99.9% LWC limits are shown as dotted black lines.

Citation: Journal of Applied Meteorology and Climatology 51, 2; 10.1175/JAMC-D-11-022.1

Fig. 14.
Fig. 14.

As in Fig. 13, but for the freezing rain conditions. The upper limit of the LWC envelope/box for MVD > 40 μm is not shown because it is > 1000 μm.

Citation: Journal of Applied Meteorology and Climatology 51, 2; 10.1175/JAMC-D-11-022.1

For the SLD observations (both drizzle and rain) with MVD < 40 μm the FAR 25-C envelope for 0°C seems to capture the data extremely well. For MVD > 40 μm conditions, the potential accumulation envelope of approximately 10 g cm−2 h−1 bounds the data very well. Newton (1978) suggested that a potential accumulation of 12 g cm−2 h−1 could be interpreted as severe icing. The 99% and 99.9% LWC limits derived are smaller than the qualitatively named severe icing potential accumulation envelope. It is interesting to note that a single potential accumulation envelope of 10 g cm−2 h−1 would have captured all but one of the observed 300-s SLD observations at all MVD values. The potential accumulation envelopes are more physically based than those in FAR 25-C. The consistency of the SLD observations with the potential accumulation envelopes suggests that a maximum potential accumulation envelope could have formed the basis of an alternative SLD environmental characterization. A more detailed comparison of the CFDE I and CFDE III data with these and other icing envelopes was given by Cober et al. (2001c).

Because of the limited number of SLD conditions at 300-s or 30 km resolution, it can be difficult to visually reconcile the individual data shown in Figs. 13 and 14 with the 99% and/or 99.9% LWC envelopes. Figures 15 and 16 show the MVD versus LWC for 30-s (3-km) averaged data for freezing drizzle and freezing rain conditions, respectively. The 99% and 99.9% LWC envelopes were computed using the scale factor in Eq. (4) and the 99% and 99.9% LWC values for 32.2 km (17.4 n mi) from Table 6. The 95% confidence limits for the 99% and 99.9% SLD LWC values are shown as solid and dotted vertical bars, respectively. Note that the potential accumulation envelopes for 1, 6, and 12 g cm−2 h−1 are also shown for comparison however, the FAR 25-C envelopes are not shown because they were not valid at 3 km. The applicability of the 99% envelopes to the data is much clearer to visualize in these figures. It can be seen that approximately 1% of the SLD observations exceed the 99% LWC envelopes, which is consistent with the 99% analysis. There are enough data points to have a high degree of confidence in the 99% LWC analysis. This is further demonstrated by the small width of the 95% confidence limits for the 99% LWC analysis. The 99.9% LWC analysis had significantly wider 95% confidence limits and there were no SLD observations that exceeded the upper confidence limit of the 99.9% LWC envelopes. A potential accumulation envelope of 12 g cm−2 h−1 would bound all of the freezing rain observations and 99.5% of the freezing drizzle observations at 3-km resolution.

Fig. 15.
Fig. 15.

Plot of MVD vs LWC for 30-s (3 km) averaged data for freezing drizzle conditions. The Newton (1978) potential accumulation envelopes for 1, 6, and 12 g cm−2 h−1 are also shown for comparison. The LWC limits (envelopes) are shown as boxes ranging from 7 to 40 μm (for MVD < 40 μm) and from 40 to 500 μm (for MVD > 40 μm). The 99% LWC limits are shown as solid lines while the 99.9% LWC limits are shown as dotted black lines. The 95% confidence limits to the 99% and 99.9% LWC limits are shown as vertical solid and dotted lines, respectively.

Citation: Journal of Applied Meteorology and Climatology 51, 2; 10.1175/JAMC-D-11-022.1

Fig. 16.
Fig. 16.

As in Fig. 15, but for freezing rain conditions. The upper limit of the LWC envelope/box for MVD > 40 μm is not shown because it is > 1000 μm.

Citation: Journal of Applied Meteorology and Climatology 51, 2; 10.1175/JAMC-D-11-022.1

11. Representativeness of the data

It could be argued that the SLD database is biased toward extreme values because the aircraft was deliberately flown into the most severe conditions. To test this hypothesis, a comparison was done between the SLD database and datasets obtained from surface measurements of freezing precipitation. The surface measurements were not biased but represent two long-term series of data obtained by using a Precipitation Occurrence Sensor System (POSS) (Sheppard 1990) at St. John’s from 1997 to 2004 and a regular weighing gauge used at six stations in Quebec from 1997 to 2003. The data were provided by private communication from B. Sheppard of Environment Canada and B. Myers of Transport Canada.

Table 7 shows that the 99th percentiles for freezing drizzle and freezing rain based on unbiased surface measurements are very similar to those obtained from the in-flight measurements. The in-flight values were obtained by integrating each individually measured 30-s spectra to obtain rainfall rate. The two freezing drizzle environments were combined into a single category. Similarly, the two freezing rain environments were combined into a single category. Using the Marshall and Palmer (1948) relationship, rainfall rate (mm h−1) can also be empirically related to LWC (g m−3) through the equation, M = 0.072R0.88. So for the 99% value for measured surface freezing rainfall rate of 4.3 mm h−1, the LWC mass is 0.26 g m−3, which is quite close to the 99% value for freezing rain conditions in Table 6. This analysis suggests that the 99% SLD LWC values are not overly biased by the sampling strategy used to collect the in-flight data.

Table 7.

Percentiles of precipitation rate for SLD environments as obtained from rain gauges, POSS, and in-flight instruments.

Table 7.

Determining the actual frequency of occurrence of SLD in the atmosphere is difficult using the in situ data. It is recognized that there are geographic differences and changes with season. For maritime environments, based on all flights conducted during CFDE I, SLD environments (which included drops larger than 100 μm in diameter) were observed 6.8% of the in-flight time. For continental environments, based on all flights conducted during CFDE III, AIRS, and the NASA SLD project, SLD environments were observed 5.9% of the in-flight time. The percentage of in-flight time with median volume diameters greater than 40 μm (outside FAR 25-C) was 3.8% for the maritime clouds and 1.7% for the continental clouds. Similar results using different subsets of the same data were reported by Isaac et al. (2001b). These percentages are likely overestimates in comparison with random encounters because the research flights were targeted at areas where SLD was expected. Consequently, the random probability of encountering a SLD environment should be lower.

The frequency of occurrence of freezing precipitation at the ground represents approximately 1% of the time averaged over the winter season for most of Canada with greater values occurring in the Great Lakes area (2%) and in Newfoundland (5%) (Stuart and Isaac 1999). The surface climatology and in situ observations of SLD are similar in magnitude, with the in situ observations being slightly higher.

The SLD conditions analyzed here were for liquid-phase and mixed-phase environments with ice crystal concentrations <1 L−1. Mixed-phase SLD conditions with ice crystal concentrations >1 L−1 were not included in the analysis. To assess whether this may have excluded some potentially extreme SLD environments the TWC frequency distributions and extreme values for liquid- and mixed-phase conditions for the entire dataset were compared. They were very similar, suggesting that the mixed-phase conditions did not include extreme values of TWC that were larger than those observed in the liquid-phase conditions.

Finally, it is important to note that the SLD data were collected in a limited number of research flights (134) in three different geographic locations including maritime, continental, and Arctic regions. Hence, the data may not be representative of all geographic regions. Some SLD forming conditions such as those associated with orographic lift are not represented in this dataset. The data were collected entirely in winter cloud systems (primarily stratiform in nature), hence the dataset contains no cases from convective (intermittent maximum) regions.

12. Conclusions

Observations of aircraft icing environments that included supercooled large drops greater than 100 μm in diameter have been collected by instrumented research aircraft from 134 flights during six field programs in three different geographic regions of North America. In total 2444 SLD icing environments were observed at 3-km resolution that had an average LWC > 0.005 g m−3, drops >100 μm in diameter, ice crystal concentrations <1 L−1, and an average static temperature ≤0°C. The research aircraft were highly instrumented to accurately measure the microphysics of the icing environments and there was a high degree of consistency observed between the direct measurements of LWC and the spectrum-derived LWC. SLD conditions were observed approximately 5% of the in-flight time of the research aircraft. These observations were used to determine potential aircraft icing certification envelopes that would be supplementary to those envelopes currently used for commercial aircraft certification. The data were analyzed to develop a characterization of aircraft icing environments that included SLD. The analysis has the following conclusions:

  1. The observations with SLD > 100 μm were subdivided into four categories including freezing drizzle conditions where the maximum drop sizes were < 500 μm in diameter and freezing rain conditions where the maximum drop sizes were > 500 μm in diameter, each of which had MVD < 40 μm and MVD > 40 μm. These four subsets appear to capture the full range of SLD conditions that were observed, especially the bimodal drop distributions that are characteristic of SLD environments. In general there is a formation mechanism distinction between freezing drizzle and freezing rain conditions, based on the fact that 88% of the freezing drizzle conditions formed through a condensation and collision–coalescence mechanism while 92% of the freezing rain conditions formed through a melting and supercooling process.

  2. Extreme value analysis was used to determine the 99% and 99.9% LWC values for four different horizontal length scales. The method of threshold selection was used, whereby for a specific subset of data, LWC observations above a high threshold value were fitted to a generalized Pareto distribution. The quality of the fits was generally quite good and the 99% and 99.9% LWC percentiles along with 95% confidence limits were determined. The size of the 95% confidence limits is rather large for the 99.9% LWC values because of the limited size of the database. Conversely, the 95% confidence limits for the 99% LWC values are relatively narrow. The 99% LWC values were used as the basis for the development of a horizontal scale factor and a LWC–temperature relationship.

  3. A horizontal scale factor was developed that allows a maximum LWC value at one length scale to be translated into another length scale. The scale factor was independent of LWC percentile in the range from 97% to 99.9%.

  4. The observations were compared with temperature to develop a LWC-temperature relationship that bounded the majority of observations. This allows the translation of a maximum LWC at 0°C to a lower temperature. It is suggested that freezing drizzle environments do not need to be considered at temperatures <−25°C while freezing rain environments do not need to be considered at temperatures <−13°C.

  5. The SLD environments were compared with the original FAR 25-C envelopes and to the potential accumulation envelopes described by Newton (1978). A potential accumulation envelope of 12 g cm−2 h−1 would bound 99.5% of the SLD observations at 3-km resolution and 99.8% of the SLD observations at 30-km resolution. The FAR 25-C envelops that are valid for 32.2 km and MVD < 40 μm capture all of the 30-km SLD observations with MVD < 40 μm, demonstrating consistency between the two characterizations.

The results are being used to develop a new standard for aircraft certification (Cober et al. 2009). The analysis is sufficient for simulation of SLD environments with either numerical icing accretion models or wind tunnel icing simulations. The characteristic drop spectra can be used to define the desired SLD environment. The maximum LWC values (i.e., either 99% or 99.9%) can be determined for any desired horizontal length scale or temperature. In terms of temperature, LWC, and horizontal length scale, the SLD icing envelopes are similar in structure to the original aircraft icing envelopes described in FAR 25-C, the latter having been used for aircraft certification for the past 50 years.

Acknowledgments

Funding for this research was provided by Environment Canada (EC), the National Research Council of Canada (NRC), Transport Canada (TC), the Canadian National Search and Rescue Secretariat, NASA Glenn, the Federal Aviation Administration, and Boeing Commercial Airplane Group. Walter Strapp, Alexei Korolev, Tom Ratvasky, Dave Marcotte, and Jim Riley are acknowledged for their assistance in collecting the data and/or their reviews of this manuscript. Francis Zwiers is thanked for his assistance with the extreme value analysis. Brian Sheppard and Barry Myers are thanked for providing data related to surface precipitation observations. Mohammed Wasey and his technical team are thanked for their long-term support to the various measurement programs.

REFERENCES

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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
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    • Search Google Scholar
    • Export Citation
  • Isaac, G. A., I. Gultepe, and S. G. Cober, 2004: Use of mass versus volume units for cloud microphysical parameters. Proc. 14th Int. Conf. on Clouds and Precipitation, Bologna, Italy, International Commission on Clouds and Precipitation, 800–803.

    • Search Google Scholar
    • Export Citation
  • Jeck, R. K., 1996: Representative values of icing-related variables aloft in freezing rain and freezing drizzle. FAA Tech. Note DOT/FAA/AR-TN95/119, 45 pp.

    • Search Google Scholar
    • Export Citation
  • Joe, P., and R. List, 1987: Testing and performance of two-dimensional optical array spectrometers with greyscale. J. Atmos. Oceanic Technol., 4, 139150.

    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
  • King, W. D., D. A. Parkin, and R. J. Handsworth, 1978: A hot-wire liquid water device having fully calculable response characteristics. J. Appl. Meteor., 17, 18091813.

    • Search Google Scholar
    • Export Citation
  • King, W. D., J. E. Dye, J. W. Strapp, D. Baumgardner, and D. Huffman, 1985: Icing wind tunnel tests on the CSIRO liquid water probe. J. Atmos. Oceanic Technol., 2, 340352.

    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Export Citation
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    • Search Google Scholar
    • Export Citation
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Save
  • Ashenden, R., and J. D. Marwitz, 1998: Characterizing the supercooled large droplet environment with corresponding turboprop aircraft response. J. Aircr., 35, 912920.

    • Search Google Scholar
    • Export Citation
  • Baumgardner, D., 1983: An analysis and comparison of five water droplet measuring instruments. J. Climate Appl. Meteor., 22, 891910.

  • Baumgardner, D., and A. Rodi, 1989: Laboratory and wind tunnel evaluations of the Rosemount icing detector. J. Atmos. Oceanic Technol., 6, 971979.

    • Search Google Scholar
    • Export Citation
  • Baumgardner, D., W. Strapp, and J. E. Dye, 1985: Evaluation of the forward scattering spectrometer probe. Part II: Corrections for coincidence and dead-time losses. J. Atmos. Oceanic Technol., 2, 626632.

    • Search Google Scholar
    • Export Citation
  • Biter, C. J., J. E. Dye, D. Huffman, and W. D. King, 1987: The drop-size response of the CSIRO liquid water probe. J. Atmos. Oceanic Technol., 4, 359367.

    • Search Google Scholar
    • Export Citation
  • Cober, S. G., and G. A. Isaac, 2006: Estimating maximum aircraft icing environments using a large data base of in-situ observations. Proc. AIAA 44th Aerospace Sciences Meeting and Exhibit, Reno, NV, AIAA, AIAA 2006-0266, 14 pp. [Available online at http://airs-icing.org/AIRS_II/AIAAReno2006/AIAA-2006-266-268.pdf.]

    • Search Google Scholar
    • Export Citation
  • Cober, S. G., G. A. Isaac, and J. W. Strapp, 1995: Aircraft icing measurements in East Coast winter storms. J. Appl. Meteor., 34, 88100.

    • Search Google Scholar
    • Export Citation
  • Cober, S. G., J. W. Strapp, and G. A. Isaac, 1996: An example of supercooled drizzle drops formed through a collision-coalescence process. J. Appl. Meteor., 35, 22502260.

    • Search Google Scholar
    • Export Citation
  • Cober, S. G., G. A. Isaac, and A. V. Korolev, 2001a: Assessing the Rosemount Icing Detector with in situ measurements. J. Atmos. Oceanic Technol., 18, 515528.

    • Search Google Scholar
    • Export Citation
  • Cober, S. G., G. A. Isaac, A. V. Korolev, and J. W. Strapp, 2001b: Assessing cloud-phase conditions. J. Appl. Meteor., 40, 19671983.

  • Cober, S. G., G. A. Isaac, and J. W. Strapp, 2001c: Characterizations of aircraft icing environments that include supercooled large drops. J. Appl. Meteor., 40, 19842002.

    • Search Google Scholar
    • Export Citation
  • Cober, S. G., G. A. Isaac, A. D. Shah, and R. Jeck, 2003: Defining characteristic cloud drop spectra from in-situ measurements. Proc. AIAA 41st Aerospace Science Meeting and Exhibit, Reno, NV, AIAA, AIAA 2003-0561, 12 pp. [Available online at http://icingalliance.org/collaborations/documents/Cober_Spectra_AIAA_2003.pdf.]

    • Search Google Scholar
    • Export Citation
  • Cober, S. G., B. Bernstein, R. Jeck, E. Hill, G. Isaac, J. Riley, and A. Shah, 2009: Data and analysis for the development of an engineering standard for supercooled large drop conditions. FAA Tech. Rep. DOT/FAA/AR-09/10, 89 pp. [Available online at http://www.tc.faa.gov/its/worldpac/techrpt/ar0910.pdf.]

    • Search Google Scholar
    • Export Citation
  • Coles, S., 2001: An Introduction to Statistical Modeling of Extreme Values. Springer, 205 pp.

  • Cooper, W. A., W. R. Sand, M. K. Politovich, and D. L. Veal, 1984: Effects of icing on performance of a research aircraft. J. Aircr., 21, 708715.

    • Search Google Scholar
    • Export Citation
  • Curry, J. A., and Coauthors, 2000: FIRE Arctic Clouds Experiment. Bull. Amer. Meteor. Soc., 81, 529.

  • Federal Aviation Administration, 1997: FAA inflight aircraft icing plan. FAA Tech. Rep., 60 pp. [Available online at http://www.faa.gov/aircraft/air_cert/design_approvals/transport/media/Inflight_Icing_Plan.pdf.]

    • Search Google Scholar
    • Export Citation
  • Federal Aviation Administration, 1999: Part 25: Airworthiness Standard: Transport Category Airplanes, Appendix C. Title 14: Aeronautics and Space, U.S. Code of Federal Regulations, 9 pp. [Available from the Office of the Federal Register, National Archives and Records Administration, Washington, DC 20402-9328.]

    • Search Google Scholar
    • Export Citation
  • Finstad, K. J., and E. P. Lozowski, 1988: A computational investigation of water droplet trajectories. J. Atmos. Oceanic Technol., 5, 160170.

    • Search Google Scholar
    • Export Citation
  • Fisher, R. A., and L. H. C. Tippett, 1928: Limiting forms of the frequency distribution of the largest or smallest members of a sample. Proc. Cambridge Philos. Soc., 24, 180190.

    • Search Google Scholar
    • Export Citation
  • Gardiner, B. A., and J. Hallett, 1985: Degradation of in-cloud forward scattering spectrometer probe measurements in the presence of ice particles. J. Atmos. Oceanic Technol., 2, 171180.

    • Search Google Scholar
    • Export Citation
  • Gencay, R., F. Selcuk, and A. Ulugulyagci, 2002: EVIM: A software package for extreme value analysis in MATLAB. Stud. Nonlinear Dyn. Econometrics, 5, 213239.

    • Search Google Scholar
    • Export Citation
  • Glickman, T., Ed., 2000: Glossary of Meteorology. 2nd ed. Amer. Meteor. Soc., 855 pp.

  • Gumbel, E. J., 1942: On the frequency distribution of extreme values in meteorological data. Bull. Amer. Meteor. Soc., 23, 95105.

  • Heymsfield, A. J., and J. L. Parrish, 1978: A computational technique for increasing the effective sampling volume of the PMS two-dimensional particle size spectrometer. J. Appl. Meteor., 17, 15661572.

    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., and L. M. Miloshevich, 1989: Evaluation of liquid water measuring instruments in cold clouds sampled during FIRE. J. Atmos. Oceanic Technol., 6, 378388.

    • Search Google Scholar
    • Export Citation
  • Isaac, G. A., S. G. Cober, J. W. Strapp, D. Hudak, T. P. Ratvasky, D. L. Marcotte, and F. Fabry, 2001a: Preliminary results from the Alliance Icing Research Study (AIRS). Proc. AIAA 39th Aerospace Science Meeting and Exhibit, Reno, NV, AIAA, AIAA 2001-0393, 12 pp. [Available from http://airs-icing.org/publications/Isaac%20-%20AIAA2001.pdf.]

    • Search Google Scholar
    • Export Citation
  • Isaac, G. A., S. G. Cober, J. W. Strapp, A. V. Korolev, A. Tremblay, and D. L. Marcotte, 2001b: Recent Canadian research on aircraft in-flight icing. Can. Aeronaut. Space J., 47, 213221.

    • Search Google Scholar
    • Export Citation
  • Isaac, G. A., I. Gultepe, and S. G. Cober, 2004: Use of mass versus volume units for cloud microphysical parameters. Proc. 14th Int. Conf. on Clouds and Precipitation, Bologna, Italy, International Commission on Clouds and Precipitation, 800–803.

    • Search Google Scholar
    • Export Citation
  • Jeck, R. K., 1996: Representative values of icing-related variables aloft in freezing rain and freezing drizzle. FAA Tech. Note DOT/FAA/AR-TN95/119, 45 pp.

    • Search Google Scholar
    • Export Citation
  • Joe, P., and R. List, 1987: Testing and performance of two-dimensional optical array spectrometers with greyscale. J. Atmos. Oceanic Technol., 4, 139150.

    • Search Google Scholar
    • Export Citation
  • Jones, A. R., and W. Lewis, 1949: Recommended values of meteorological factors to be considered in the design of aircraft ice-prevention equipment. NASA Tech. Rep. NACA-TN-1855, 15 pp.

    • Search Google Scholar
    • Export Citation
  • King, W. D., D. A. Parkin, and R. J. Handsworth, 1978: A hot-wire liquid water device having fully calculable response characteristics. J. Appl. Meteor., 17, 18091813.

    • Search Google Scholar
    • Export Citation
  • King, W. D., J. E. Dye, J. W. Strapp, D. Baumgardner, and D. Huffman, 1985: Icing wind tunnel tests on the CSIRO liquid water probe. J. Atmos. Oceanic Technol., 2, 340352.

    • Search Google Scholar
    • Export Citation
  • Korolev, A. V., S. V. Kuznetsov, Y. E. Makarov, and V. S. Novikov, 1991: Evaluation of measurements of particle size and sample area from optical array probes. J. Atmos. Oceanic Technol., 8, 514522.

    • Search Google Scholar
    • Export Citation
  • Korolev, A. V., J. W. Strapp, and G. A. Isaac, 1998a: Evaluation of the accuracy of PMS optical array probes. J. Atmos. Oceanic Technol., 15, 708720.

    • Search Google Scholar
    • Export Citation
  • Korolev, A. V., J. W. Strapp, G. A. Isaac, and A. N. Nevzorov, 1998b: The Nevzorov airborne hot-wire LWC–TWC probe: Principle of operation and performance characteristics. J. Atmos. Oceanic Technol., 15, 14951510.

    • Search Google Scholar
    • Export Citation
  • Lewis, W., and N. R. Bergrun, 1952: A probability analysis of the meteorological factors conducive to aircraft icing in the United States. NACA Tech. Note 2738, 93 pp.

    • Search Google Scholar
    • Export Citation
  • Ludlam, F. H., 1951: The heat economy of a rimed cylinder. Quart. J. Roy. Meteor. Soc., 77, 663666.

  • Marshall, J. S., and W. M. Palmer, 1948: The distribution of raindrops with size. J. Atmos. Sci., 5, 165166.

  • Marwitz, J., M. Politovich, B. Bernstein, F. Ralph, P. Neiman, R. Ashenden, and J. Bresch, 1997: Meteorological conditions associated with the ATR72 aircraft accident near Roselawn, Indiana, on 31 October 1994. Bull. Amer. Meteor. Soc., 78, 4152.

    • Search Google Scholar
    • Export Citation
  • Masters, C. O., 1983: A new characterization of supercooled clouds below 10,000 feet AGL. FAA Tech. Rep. DOT/FAA/CT-83/22, 47 pp.

  • Mazin, I. P., A. V. Korolev, A. Heymsfield, G. A. Isaac, and S. G. Cober, 2001: Thermodynamics of icing cylinder for measurements of liquid water content in supercooled clouds. J. Atmos. Oceanic Technol., 18, 543558.

    • Search Google Scholar
    • Export Citation
  • McKay, G. A., and H. A. Thompson, 1969: Estimating the hazard of ice accretion in Canada from climatological data. J. Appl. Meteor., 8, 927935.

    • Search Google Scholar
    • Export Citation
  • Miller, D., T. Ratvasky, B. Bernstein, F. McDonough, and J. W. Strapp, 1998: NASA/FAA/NCAR supercooled large droplet icing flight research: Summary of winter 96–97 flight operations. Extended Abstracts, 36th Aerospace Science Meeting and Exhibit, Reno, NV, American Institute of Aeronautics and Astronautics, AIAA 98-0577, 24 pp. [Available from http://gltrs.grc.nasa.gov/reports/1998/TM-1998-206620.pdf.]

    • Search Google Scholar
    • Export Citation
  • National Transportation Safety Board, 1996: Aircraft accident report. In-flight icing encounter and loss of control, Simmons Airlines, d.b.a. American Eagle flight 4184, Avions de Transport Regional (ATR) Model 72-212, N401MA, Roselawn, IN, October 31 1994, Vol. 1, Safety Board Rep. NTSB/AAR-96/01, PB96-910401, DCA95MA001, 322 pp. [Available from National Transportation Safety Board, Public Inquiries Section RE-51, 490 L’Enfant Plaza S.W., Washington, DC 20594.]

    • Search Google Scholar
    • Export Citation
  • Newton, D. W., 1978: An integrated approach to the problem of aircraft icing. J. Aircr., 15, 374380.

  • Pobanz, B. M., J. D. Marwitz, and M. K. Politovich, 1994: Conditions associated with large-drop regions. J. Appl. Meteor., 33, 13661372.

    • Search Google Scholar
    • Export Citation
  • Politovich, M. K., 1989: Aircraft icing caused by large supercooled droplets. J. Appl. Meteor., 28, 856868.

  • Politovich, M. K., 1996: Response of a research aircraft to icing and evaluation of severity indices. J. Aircr., 33, 291297.

  • Rauber, R. M., and M. F. Heggli, 1988: The influence of cloud droplets on the measurement of ice particle concentrations with a Particle Measuring System’s 2DC optical array probe. J. Atmos. Oceanic Technol., 5, 123128.