1. Introduction
The large database reported on here was originally assembled for improving the statistics on aircraft icing conditions aloft. This paper reports on some of the findings that will be of general interest to the cloud physics community. In particular, the results should be of use to experimentalists and modelers, icing forecasters, and perhaps climate researchers.
a. Historical data
The first extensive set of cloud physics research flights ever undertaken in the United States was that conducted by researchers from the U.S. Weather Bureau and the National Advisory Committee for Aeronautics (NACA) during the winters from 1946 to 1950. Hacker and Dorsch (1951) summarize the results. These flights were dedicated to characterizing icing clouds for the rapidly expanding postwar commercial airline industry. They collected ice on rotating multidiameter cylinders (Jones and Lewis 1949; Ludlam 1951; Brun et al. 1955) from which they computed average values of supercooled liquid water content (SLWC) and approximate values of droplet mass-median diameter (MMD) over 1- to 5-min in-cloud exposures. About 4700 n mi of useful measurements were obtained, primarily over the north-central and northwestern regions of the United States at altitudes up to about 7 km (22 000 ft). In the 1940s and 1950s, the rotating multicylinder (RMC) method was the standard against which other liquid water content (LWC) sensors were calibrated. Today, as then, it is still a standard for calibrating icing wind tunnels, with the accuracy of the RMC-indicated SLWCs within ±10% (SAE 2003).
During the period between 1950 and 1970, a number of airborne cloud physics research projects were conducted by universities and government laboratories with instrumentation that was evolving to more automated, electronic- and optically based probes and sensors. One of these projects was a follow-on NACA project during the early 1950s in which a number of commercial airliners and weather reconnaissance aircraft were equipped with perforated-tube icing rate meters (Perkins 1959). These meters were designed for nearly unattended operation along routine flight routes whenever the aircraft encountered icing conditions, mainly over Alaska and the Aleutians, and the North Atlantic, with a smaller number of measurements from Europe and the northwestern Pacific Ocean. These flights provided icing rates (from which SLWC was obtained), horizontal extents of icing conditions, and in-cloud temperatures at various altitudes. Drop size information was not available. The indicated SLWCs were within ±0.1 g m−3 of the RMC during in-flight comparisons (Perkins 1959).
Altogether, more than 14 000 n mi of measurements from the various NACA flights of the 1940s and 1950s have been obtained from the NACA technical reports, as indicated in Table 1. These were included in the database for comparison with the more modern data described next.
b. Modern data
Beginning in 1973, new types of automated, electro-optical, cloud particle size spectrometers became commercially available from Particle Measuring Systems (PMS), Inc., of Boulder, Colorado. The Forward Scattering Spectrometer Probe (FSSP) and other “optical array,” single particle size spectrometers soon became standard equipment for most airborne cloud physics research. These provide droplet size distributions and number densities from which the LWC, MMD, and other variables can be computed. During the years 1977 to 1984, Russian researchers used similar modern instruments to collect an additional 54 000 n mi of cloud measurements over the former Soviet Union (Mazin 1995).
For present purposes, modern data are defined here as measurements obtained after 1973 from flight research projects using these PMS probes along with hot-wire LWC meters and other complementary sensors. Existing or archived data were obtained from a number of diverse projects (Jeck 1986). Individual flights were carefully screened for usefulness and data quality. Data from individual probes and sensors were corrected or adjusted, as necessary, using best practices and instructions from the source organization. Further details are given in the appendix.
The modern data thus incorporated into the database consist of about 5800 n mi of measurements over parts of North America and about 7800 n mi over parts of Europe and South Africa. Table 1 summarizes the data collected according to geographic region and contributing agency.
The variables common to both the old and the new measurements include SLWC, MMD, temperature, altitude, and other information on the clouds (type, phase, base and top heights, and temperatures), synoptic and geographic setting (weather and airmass, location and surface elevation), data source (project name and performing laboratory or university), and sample-related variables (date, start time, averaging distance).
Scatterplots, presented here later, show that the NACA data and modern data compare favorably with each other in the determination of LWC and MMD, even though the measuring techniques were radically different. The NACA and modern data both indicate an average MMD of ∼15 μm for layer clouds and 18 or 19 μm for convective clouds.
2. Results
This paper is concerned with ordinary cloud droplets (nominally smaller than 50-μm diameter) in supercooled and mixed phase clouds. The primary interest is in the range and frequency of SLWC and MMD values, depending on cloud type (stratiform or convective), in-cloud averaging distance (scale), air temperature, altitude, and freezing level height. The following figures and tables present the results in several different ways.
a. Supercooled liquid water content
1) Stratiform clouds (St, Sc, As, Ac, Ns)
The flight patterns through stratiform (layer) clouds were a mixture of vertical profiles and level segments. Because of the underlying interest in aircraft icing conditions, thin cloud layers were usually ignored and measurements in the middle and upper parts of thicker layers were generally preferred.
The observed range and frequency of SLWC values in 23 000 n mi of flight in these layer clouds is presented in Table 2a. Column 2 gives the number of nautical miles (data miles) recorded in the database for each 0.1 g m−3 increment in SLWC. The rationale for using accumulated distance as a measure of frequency is explained in the appendix. Columns 4 and 5 give the average and maximum observed extents of uniform cloud intervals (see the appendix) having the average SLWC listed in column 1. This supplemental information indicates the typical (average) and the possible (maximum) extent of different specific LWC values in clouds. The last four columns in Table 2a give incidentals about where the maximum extents occurred and who observed them.
For layer clouds in this database, the largest recorded values of SLWC are three momentary (less than 1 n mi in extent) patches (probably embedded convection) of 1.6 to 1.7 g m−3. Ninety percent of the accumulated data miles is in SLWCs smaller than 0.35 g m−3 and half are in SLWCs smaller than 0.12 g m−3. Table 2b gives the breakdown in terms of selected SLWC percentiles.
These percentiles were obtained by interpolation and extrapolation from a Weibull distribution (Kapur and Lamberson 1977, 291–308) fitted to the cumulative frequencies in column 3 of Table 2a. Of the two distributions commonly used for this purpose (Wilks 1995, 93–98), the Weibull describes the LWC frequency distributions better than the Gumbel. The Weibull distribution is an exponential, P(%) = 100[1 − exp(−aLWCb)], and the Gumbel is a double exponential, P(%) = 100{1 − exp[−exp(−aLWC)]}, where P(%) are the LWC cumulative frequency percentile levels (50%, 90%, 95%, etc.) and a and b are experimental parameters. It is easy to decide whether a variable such as LWC follows a Weibull or a Gumbel distribution. The probability levels P(%) written in the double logarithm form loglog[100/(100 − P)] will plot as a straight line against LWC for a Gumbel and against log(LWC) for a Weibull distribution. The difference is readily apparent, graphically. The advantages of a linear function are the ease of using simple regression methods to fit it to the experimental frequency distribution and the confidence it gives to extrapolating it beyond the observed data for estimating the extreme (99% and 99.9%) values of LWC.
2) Convective clouds (Cu, Cg, TCu, Cb)
The observed range and frequency of SLWC values in convective clouds is given in Table 3a. The largest value of SLWC that has been documented in this database is a brief (0.2 n mi) 5.2 g m−3, but 99.9% of the distance in convective clouds was in SLWCs smaller than 3.2 g m−3 and 99% was smaller than 2.1 g m−3. Table 3b gives selected percentiles based on a Weibull fit to column 3 in Table 3a. The relative number of SLWC values larger than about 2 g m−3 should not be interpreted as the natural frequency to be expected in random encounters with convective clouds. Many of these larger LWCs were deliberately and arbitrarily selected from summertime clouds over Florida to help estimate the largest values of SLWC that can be found in summer cumuliform clouds.
b. Droplet mass-median diameter
FSSP data indicate that cloud droplets are routinely found in the diameter range of 1–50 μm, with the largest concentrations around 5–20 μm and few, if any, found with diameters greater than about 50 μm, excluding drizzle or rain.
For economy of computer memory and simplification of the database, drop-size distributions (available only in the modern data) were not stored as part of the database. Instead, they are represented by the MMD or, in aircraft icing usage, the equivalent median-volume diameter (MVD).
It has been customary in aircraft icing computations to represent cloud droplet populations by the MMD because, for droplets smaller than about 100 μm in diameter, the MMD gives practically the same ice accretions as when using the full LWC versus drop-size distributions (Finstad et al. 1988). Thus, the MMD is a convenient simplification.
For those who prefer the arithmetic mean diameter or other representative drop diameters, these can be obtained approximately from the MMD for drop-size distributions described by the Khrgian–Mazin distribution n(r) = (27N/2r3av)r 2 exp(−3r/rav), where r is the droplet radius, rav is the distribution-average radius, and N is the total number of drops in the distribution (see Pruppacher and Klett 1980, p. 11).
For distributions not extending much beyond 50 μm in diameter, it is found by inspection that 1) the MMD ≈ 1.8 times the mean diameter and 2) the MMD is about 10% larger than the effective diameter (ratio of the third to second moments). It can also be shown (Borovikov et al. 1963, pp. 68, 84) that the mode diameter is two-thirds of the mean diameter.
Figures 1a and 1b show the observed frequency of occurrence for MMDs in the database. Frequencies are expressed in terms of the number of nautical miles that has been recorded for each increment in MMD. The solid curve is the cumulative frequency of occurrence according to the right-hand ordinate scale.
The MMD distribution peaks strongly near 14 μm for layer clouds and near 18 μm for convective clouds. Most of the MMDs fall within a 15-μm interval centered at the mode value. This may be because droplets smaller than 30 μm in diameter are slow to grow via collision–coalescence processes: this tends to keep the droplet distribution almost unchanged around the MMD of the initial droplet distribution (Almeida 1979, p. 1562), except for the gradual increase in MMD with height above cloud base.
Phenomenologically, a narrow range of MMDs is consistent with the relatively narrow range of droplet average diameters, dav, that is observed in clouds. Borovikov et al. (1963; Table 3, p. 69) reported that, out of more than a half million droplets measured on slide exposures in stratiform clouds, dav fell in the range from 8 to 12 μm. Using MMD = 1.8dav, this translates into a MMD range from 14 to 20 μm. Similarly, Lewis (1951, p. 1201) reported average MMDs in the range 12–20 μm from 567 RMC exposures in layer clouds and 17–20 μm from 330 exposures in Cu and Cb.
1) Stratiform clouds
Figure 1a shows that about 80% of all MMDs fall in the 10-μm interval from 10 to 20 μm. This means that MMDs are not as variable as may be expected and, for cloud parameterization, one could assume that the MMD is within the 10–20-μm range with 80% confidence. (About 50% of the MMDs are contained within a narrower 5-μm interval centered at 14 μm.) About 55% of the MMDs are smaller than 14 μm, but only about 10% are smaller than 10 μm. Only about 10% of MMDs are larger than 20 μm, and the few (1.5%) MMDs larger than 30 μm are probably due to occasional occurrences of freezing drizzle. Ninety percent of MMDs larger than 30 μm are from maritime air masses, as determined by the at-sea or coastal locations of the clouds and by their characteristically low droplet concentrations.
Another way of looking at MMD probabilities is shown in Fig. 2. There, the 99th-percentile SLWC for various MMDs is displayed as well as the longest distance that a given combination of LWC and MMD can be expected to last. The larger the MMD, the shorter its horizontal extent will be, the rarer its occurrence, and the lower the maximum LWC that can be present. MMDs near 14 or 15 μm appear to be a stable condition for stratiform clouds and are also where LWCs can be the largest and last the longest.
2) Convective clouds
In this case, the MMDs are a little larger, and Fig. 1b shows that the mode is now about 18 μm. About 80% of all MMDs fall within the 13-μm interval from 12 to 25 μm. This means that in nonprecipitating convective clouds, one could assume that the MMD is within the 12–25-μm range with 80% confidence. (About 50% of the MMDs are confined to the narrower 7-μm interval centered at 18 μm.) In convective clouds, about 25% of the MMDs are smaller than 15 μm, but only about 10% are smaller than 12 μm. The few (3%) MMDs larger than 30 μm may be due to drizzle-size drops forming in strong updrafts in some of these convective clouds.
3) Large droplets
The MMDs that are 35 μm and larger represent only 1% of all the data miles (or 0.5% of all the records) in the entire database. These percentages probably represent about how often freezing drizzle occurred in the mix of supercooled clouds sampled in this data collection.
In this database, the only modern data with supercooled droplets in the range 50–300-μm diameter are those few that have been identified in some flights by the University of Wyoming (Sand et al. 1984; Politovich 1989) over California. Despite the presence of the large droplets, the MMD remained smaller than 35 μm.
It may be possible that other cases of freezing drizzle have gone undetected in some of the modern flights, because not all the research aircraft carried a 1D-C or 2D-C probe. None of the flights involved freezing rain.
c. SLWC versus MMD
Figures 1a and 1b show that MMDs peak sharply about the mode values of 14 and 18 μm for layer and convective clouds, respectively. But what about the LWCs? At what MMDs do the largest LWCs occur?
Figure 3b shows that, for convective clouds, the largest LWCs occur at MMDs near the mode—between 18 and 25 μm. That is, the most common MMDs also contain the largest LWCs, and the LWCs decline rather sharply either side of the mode MMD. The reason for this congruency is unknown, but the Khrgian–Mazin distribution is consistent with it in that the MMD depends only on dav and not on the LWC. That is, the MMDs cluster near their mode value no matter what the LWC. One could argue that not enough large MMDs have been found so that any large LWCs at large MMDs have gone undiscovered. The author believes that the trends seen in Figs. 1 –3 make that situation unlikely.
The narrow peak shown in Fig. 3b means that, if drop sizes were not available for a given application, as a useful generalization one could reasonably assume that LWCs greater than 1 g m−3 belong to MMDs between about 15 and 25 μm for rain- or drizzle-free zones in convective clouds.
For the largest LWCs in stratiform clouds (Fig. 3a) the MMD distribution is wider, although taking into account the frequencies of occurrence in Fig. 1a, most of the time spent in the larger SLWCs is still in the vicinity of the mode MMD.
Figures 1 and 3 indicate that MMDs above 30 μm or below 10 μm are relatively infrequent and the LWCs there are generally small, and Fig. 2 shows that MMDs larger than 35 μm do not extend very far anyway—less than about 10 n mi on each occasion.
d. Air temperature
The frequency of occurrence of various recorded temperatures is given in Figs. 4a and 4b.1 The air temperatures in the database are most frequently within the range −5° to −15°C, whereas the lowest temperature for any event in the database is about −39°C for both convective clouds and layer clouds.
The frequencies of occurrence for temperature do not represent the natural frequencies that would result from truly random samples in supercooled clouds. There are some sampling biases. The modes near −10°C are partly due to the popularity of the −10°C flight level among researchers in cloud-seeding (weather modification) experiments (Smith et al. 1984). About 35% or more of the modern data came from cloud-seeding projects.
Figures 4a and 4b also show that only about 10% of the samples occurred at temperatures above −3°C and 10% below −20°C. The shortage of data at temperatures between −3° and 0°C is due to the intentional avoidance of this temperature interval by both the modern and the NACA flights. The NACA researchers required lower temperatures so as to avoid runoff or shedding of ice from their ice-accreting devices. The low frequency of measurements at temperatures below −20°C is due to the difficulty in finding clouds that have not already glaciated at those temperatures. Clouds that are composed entirely of snow or ice crystals (i.e., no supercooled droplets) are not included here.
e. SLWC versus temperature
1) Stratiform clouds
Figure 5a shows the observed variation of SLWC with temperature. The largest SLWCs occur between 0° and −15°C, with maximum SLWCs decreasing more or less linearly with decreasing temperature below −15°C. The dashed lines in Fig. 5a are the SLWC values from column 2 in Table 2b. These apply to the temperature ranges in column 3. Below these temperature ranges, the number of samples is too few to compute reliable SLWC percentiles, so the percentile values are simply estimated by reducing the SLWCs linearly with temperature to a minimum value of about 0.05 g m−3 at −40°C.
This temperature dependence of cloud water content has been studied recently by several investigators using other large datasets. Mazin (1995) analyzed some 54 000 n mi of total (liquid + ice) water content (TWC) measurements from 1977 to 1984 over the former Soviet Union and compared the temperature dependence to that of earlier LWC measurements from 1957 to 1963. Gultepe and Isaac (1997) analyzed about 8500 n mi of their own LWC measurements from 1983 to 1993 in stratiform clouds over eastern Canada and compared the results to the two Russian datasets. The temperature-stratified LWC percentiles differed somewhat from one dataset to another, apparently due to differences in LWC sensors, averaging scale, and the type of curve fitted to the cumulative LWC distribution for each 5°C temperature interval.
Comparisons are difficult owing to the difference between LWC and TWC and the mismatch in averaging scales, but the 50th and 95th percentile SLWCs in Fig. 5a agree more closely with the 1978–84 Russian TWC values near 0°C (Mazin 1995). The roll-offs of SLWC with temperature are different, however. The percentile SLWCs obtained here remain a bit larger than their TWCs below 0°C and do not appear to decrease until the temperature drops below −15° or −20°C.
2) Convective clouds
Figure 5b shows the observed variation of SLWC with temperature for convective clouds. The largest SLWCs occurred between −5° and −20°C, with maximum SLWCs appearing to decrease more or less linearly with temperature below −10° or −15°C. As before, the dashed lines in Fig. 5b are the SLWC values from column 2 of Table 3b. At temperatures below the ranges listed in column 3, the percentile values are estimated by reducing the SLWCs linearly down to a minimum value of 0.3 g m−3 at −30°C.
f. SLWC versus averaging distance
In the course of compiling this database from a variety of sources, it became clear that it is not possible to directly compare individual LWC measurements with each other if they are averaged over different distances. This is because relatively large LWCs may exist over short intervals in cloud, but average values will decrease as the averaging distance increases. This problem has also been pointed out recently by Gultepe and Isaac (1997, 1999) and Korolev et al. (2001).
In cloud physics practice, measurements have never been standardized to a common averaging distance. Some researchers report peak values of LWC recorded during a cloud penetration, especially for convective clouds, and some use pass averages or other arbitrary fixed or variable intervals. Typically, LWCs are presented as averages over 1, 5, or 10 s, and occasionally over distances up to 10 km. This makes it difficult to compare measurements reported from one source to another. The only way to put measurements from various sources into perspective is to plot the reported LWCs as a function of their averaging distance. The scatterplots in Figs. 6a and 6b show all LWC averages contained in the database. It is easy to see that the largest LWCs are confined to the shorter averaging intervals. The plots also show the largest LWCs that have been recorded (in this database) for any particular averaging distance. This is the first time since the early NACA reports that LWCs have been plotted and compared over a wide range of averaging distances.
The LWC percentile curves were obtained from a Weibull distribution fitted to cumulative LWC frequencies in each of several distance intervals (0.2–1, 1–5, 5–15, 15–50, 50–120, and 120–200 n mi for layer clouds and 0.1–1.5, 1.5–3, 3–6, 6–12, 12–24, and 24–48 n mi for convective clouds). The indicated percentile values of LWC were read off the linear Weibull fit and plotted (solid triangles) at the center of their respective distance interval. The smooth curves were faired through the plotted points for each percentile across the distance scale down to the center of the first interval, which for layer clouds is 0.5 n mi. Averaging distances shorter than 1 n mi mostly represent a mixture of embedded convection and 150-m vertical segments during ascent or descent through stratiform cloud decks.
These are actually hybrid graphs—the plotted points are individual averages over uniform cloud intervals to show the basic elements of the database (see the appendix). The curves depict the cumulative LWC probability for generally longer cloud transects consisting of one or more uniform intervals strung together until the research airplane leaves the cloud or reverses direction. This has the effect of reducing the number of data points and shifting the overall averages toward the lower right in the graph.
The scatterplots in Figs. 6a and 6b are recommended for use by experimentalists who wish to compare their LWC measurements to the background of those made by many others. (Figures 8, 10, 11 and 12, in terms of LWC percentiles, are also good for this purpose.) They may be useful for selecting realistic LWCs for atmospheric models in which information on scale effects for LWC has been wanting.
g. Seasonal variations
Aircraft icing is primarily a wintertime problem, so most of the data for this collection has been from cold-season clouds. Table 4 indicates the amounts of data, in terms of in-cloud flight distances, that have been compiled here for the different seasons of the year. These amounts of data are expected to be adequate for good statistics in cold-season supercooled clouds, but they are of questionable adequacy for warmer-season supercooled clouds. The latter contain the largest values of SLWC but are also confined to higher altitudes in localized, convective clouds.
The altitudes at which supercooled clouds occur are dependent, of course, on the season of the year and the geographical location. Supercooling occurs only above the 0°C level, which in summerlike weather is well above 3 km (10 000 ft) above ground level (AGL). This limits the occurrence of summertime icing primarily to thunderstorms or to other convective clouds reaching above the freezing level. In the winter, icing conditions may be found at all altitudes down to ground level, but the layer clouds predominate, and thunderstorms (with their potentially large LWCs) are rare when surface temperatures are low. It is informative to explore this behavior further, as is done in the following paragraphs.
1) Seasonal definitions
A practical way of analyzing for seasonal effects is to separate the data according to the height of the 0°C level at the time and place of the measurements. Measurements obtained where the 0°C level is low can be considered winterlike data. High 0°C levels correspond to summerlike conditions. That is, for some applications, the seasons may be defined in terms of a measurable property of the atmosphere rather than by the calendar. This way, any ambiguities due to latitude or geographic location are conveniently removed. For example, data from Florida in January would be correctly grouped with the warm-season data if the 0°C level there was high enough at the time. For present purposes, the seasons are arbitrarily defined in Table 5.
2) SLWC versus freezing-level height
One type of plot that helps to predict the maximum SLWC expected for each season is shown in Figs. 7a and 7b. Each plotted symbol in these two figures represents a measurement at an altitude somewhere above the indicated 0°C level. For example, the points plotted at 1 km (3300 ft) were all obtained from a variety of altitudes for cases in which the 0°C level was known or estimated to be at 1 km AGL.2 The data can be used to estimate the maximum SLWCs expected for each season or for a given height of the 0°C level. For example, during the cold season, the largest expected SLWC is indicated by the largest observed SLWCs for freezing levels in the range 0–1.5 km AGL. For the mild season, the largest SLWC to be expected is indicated by the data from freezing levels from 1.5 to 3 km AGL.
Figures 7a and 7b demonstrate opposite trends for the two classes of cloud types. Not surprisingly, the maximum probable LWC increases for convective clouds as the freezing level rises. This, of course, simply reflects the fact that convective clouds tend to be shallow in the cold season and deeper in the warm seasons. For layer clouds, however, the probable maximum values of SLWC decrease from winter to summer, that is, as the freezing level rises. This is due to the fact that the deeper, nonglaciated layer clouds occur in the lower altitudes (e.g., below 3 km or so). Only thinner clouds (altostratus, cirrostratus, etc.) are found at the higher altitudes.
(i) Stratiform clouds
All layer cloud data (Fig. 7a) show a gradual trend toward smaller SLWCs with increasing freezing level height above 1.5 km AGL. Although there are progressively fewer data available for higher freezing levels, this trend toward smaller SLWCs is believed to be real and not just a result of inadequate sampling. The largest SLWCs appear to be confined to conditions when freezing levels are below 6000 or 7000 ft (2 km) AGL.
Another way of displaying the seasonal dependence is shown in Fig. 8a. There, the lines simply circumscribe the largest SLWCs recorded in the database for stratiform encounters. (The cold-season limit drawn on the graph applies to layer clouds below 3 km AGL because that is where the largest SLWCs lie. Otherwise, this curve overestimates the limiting SLWCs for higher stratiform clouds in the cold season.)
(ii) Convective clouds
According to the data in Fig. 7b, as long as the freezing level is below 1.5 km AGL (i.e., winter conditions), the maximum value of SLWC should be less than about 2–2.5 g m−3 for convective encounters at any altitude. Similarly, the maximum SLWC for the mild season is 2.5–3 g m−3, and for summer conditions it is up to 5 g m−3. These numbers are not sorted by averaging distance, however, so the larger LWCs are likely to be from short distances. A distance-based plot like that in Fig. 6b reveals this fact.
Figure 8b shows the seasonal dependence of maximum observed SLWC as a function of averaging distance for convective cloud encounters. The effect of summer clouds is marked, but it is only important for short distances. For encounters of 10 n mi or longer, the seasonal differences are negligible.
h. SLWC variations with altitude
The knowledge that temperatures generally decrease with increasing altitude can lead one to falsely conclude that LWC extremes also decrease with altitude. The overall altitude dependence of SLWC is presented in Figs. 9. The importance of these plots is that they emphasize, again, the fact that the maximum expected SLWCs are altitude-dependent.
1) Stratiform clouds
The data show that for stratiform-type clouds, the maximum LWC decreases only above about 3 km. Figure 9a shows that the largest SLWCs in layer clouds occur below 3 km AGL.
2) Convective clouds
For convective clouds, Fig. 9b shows that the maximum possible LWC actually increases with altitude up to at least 6 km (20 000 ft), and the largest SLWCs occur only well above 3 km. The largest SLWCs to be expected in any season in supercooled convective clouds at 3 km AGL are perhaps 2 g m−3.
The SLWC percentiles in Table 3b are for all convective clouds regardless of altitude. But in convective clouds between 4.5 km (15 000 ft) and 7.6 km (25 000 ft) any given SLWC may be exceeded considerably more often than indicated by the percentiles. This is because more often the largest SLWCs are present only in these higher altitude clouds, as Fig. 9b shows.
3) All clouds together
Figure 10 shows another way of presenting the altitude dependence of SLWC. In this case, it is for both layer and convective clouds together, except summer convective clouds have been excluded, making the graph applicable to cold and mild season conditions. Individual curves show the 99th-percentile SLWC as a function of averaging distance near the indicated altitude. The solid portions of the curves in Fig. 10 are obtained using a Weibull fit to the data where enough measurements are available for reliable statistics. The dashed portions are best estimates for combinations of altitude and averaging distance where measurements are sparse.
The curves show that maximum SLWCs increase with altitude up to about 3 km and then decrease for higher altitudes.
Some other conclusions about the curves in Fig. 10 are that in the range from 1.5 to 4.5 km, altitude makes little difference for encounters of about 50 n mi or longer. The curves come together for these long encounters. Similarly, for icing encounters at 0.75 km (2500 ft) or 6 km (20 000 ft), the probable maximum SLWCs are practically the same for encounters longer than about 8 n mi.
i. SLWC probabilities
Figures 11 and 12 show an alternate way to depict the probability of encountering a selected value of SLWC, depending on the temperature and averaging distance. The percentile curves were obtained by interpolation along a Weibull function fitted to the cumulative LWC distributions in each of several distance intervals, as explained in section 2f. The confidence in the curves is strongest where the data points are plentiful. From there the curves have simply been judiciously extrapolated into the data-sparse regions.
1) Stratiform clouds
Figure 11a applies to flight level temperatures from 0° to about −10°C. The 50% curve indicates, for example, that in the 0° to −10°C temperature range, half of the SLWCs will be less than about 0.17 g m−3 when averaged over 10 n mi and less than about 0.08 g m−3 when averaged over 100 n mi, if a cloud can be found that extends that far.
Figure 11b shows percentile curves for clouds in which the flight level temperatures are near −20°C. The curves are less certain due to the sparseness of observations at these lower temperatures.
In both Figs. 11a and 11b, the indicated percentile curves were obtained from linear Weibull fits to the cumulative LWC frequencies in each of the more populated distance intervals (0.2–1, 1–5, 5–15, and 15–50 n mi). In both Figs. 11a and 11b the curves flatten or even decrease at the shorter distances. This is based on the observations and is probably due to narrower layer cloud parcels being shallower too, thus not containing as much LWC as broader and deeper clouds.
2) Convective clouds
For convective clouds, it must be decided whether to include warm season (summer) clouds in the mix. Practically all LWCs above about 2 g m−3 are from summer convective clouds, and these obviously highly skew the distribution for averaging distances shorter than about 2.5 n mi.
Figures 12a and 12b show SLWC percentiles with summer clouds excluded. Figures 12c and 12d include the summer clouds in the database. As before, the percentile curves are obtained from a linear Weibull fit to the cumulative LWCs in each of the more populated distance intervals. A trend line extends the curves out to larger averaging distances.
In any case, in convective clouds the larger average LWCs may be expected over shorter averaging distances down to the limit of our observations at about 0.1 or 0.2 n mi, at least. Higher sampling rates (e.g., 0.1 s) may reveal momentarily larger LWCs in some clouds, but these are outside the range of averaging distances considered here.
These figures make useful reference standards for cloud researchers. Any LWC measurements can be plotted on these figures for comparison to the measurements compiled in this large database.
3. Summary
This paper has presented some new characteristics of supercooled clouds, such as the range, frequency, and duration of LWC versus temperature, droplet mass-median diameter, altitude, season, and cloud type, based on 28 000 n mi of in-cloud measurements of these variables.
MMDs near 15 μm are most common, and it is only for these MMDs that the LWC appears to be the largest. Smaller or larger MMDs are rarer and occur over shorter distances in cloud. The largest supercooled LWCs in stratiform clouds are found only below 3 km AGL, while the largest SLWCs in convective clouds occur above 3 km AGL.
Several innovations for preparing and presenting the data have been introduced and are recommended for general use by the cloud physics community:
Uniform cloud intervals (averages over variable distances for which the droplet concentration, MMD, altitude, temperature, etc., stay within defined limits) provide an economical way to organize large numbers of 1-s samples into a manageable set of averages. These preserve essential features of the cloud without sacrificing horizontal or vertical resolution where it is needed.
Averaging distance or duration as a variable weighting factor is used for frequency-of-occurrence tabulations so that short and long averages are not counted the same.
Distance-based graphing solves the dual problem of 1) comparing values of a given variable (e.g., LWC) averaged over different distances from different sources and 2) depicting limiting values of LWC and MMD as a function of averaging distance.
Seasons (cold, mild, and warm) are defined not by the calendar months but by the height of the local freezing level AGL (<1.5 km, 1.5–3 km, or >3 km, respectively).
Originally compiled for characterizing aircraft icing conditions, this large combined dataset of cloud microphysical variables should also be useful for cloud modeling and parameterization by providing realistic percentile values of SLWC and MMD, especially by showing the dependence of SLWC on horizontal extent or averaging distance.
Tables and graphs of SLWC percentiles as a function of temperature, altitude, MMD, averaging distance, season or height of the 0°C level, and averaging distance in stratiform and convective clouds can serve as a standard of comparison for other cloud researchers who wish to compare their measurements to LWC probabilities based on this large dataset.
The computerized 28 000 n mi dataset is available for analyses other than those presented here. It is a unique resource for cloud physics research.
Acknowledgments
The author is indebted to the numerous organizations from which the modern data were obtained and to the following scientists, affiliated with those organizations, who assisted in providing the data and assuring its quality: Roelof Bruintjes, Todd Cerni, William A. Cooper, James Dye, Jean-Francois Gayet, Glenn Gordon, Cedric A. Grainger, John Hallett, Peter Hobbs, Hans E. Hoffmann, Robert Ide, John Latham, John Marwitz, Myron Oleskiw, Marcia Politovich, Lawrence Radke, Wayne Sand, Jeffrey Stith, Walter Strapp, and Don Takeuchi. Special thanks to James T. Riley of the FAA Airport and Aircraft Safety Research & Development Division at the William J. Hughes Technical Center, who helped process and compile all the varieties of data.
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APPENDIX
Data Management
Basic screening procedure
Most of the modern data were obtained from various sources on digital tapes. The NACA data, and some of the modern data (FACE-II, DLR) were only available as already-processed results in tabular reports. The latter had to be accepted as is, but the modern 1-Hz digital data were screened to avoid the occasional defects due to iced probes, ice-particle contamination, faulty operation, etc. The usual correction procedures for the PMS drop-size spectrometers and hot-wire LWC sensors are referenced elsewhere (Nagel et al. 2007; Brenguier et al. 1994) and need not be repeated here. The procedures that may be unique to this work are explained below.
LWC acceptance test
As part of the quality assurance procedure, the following LWC acceptance test was used: Only the modern flights with LWC redundancy [a working Johnson-Williams (J-W) or Commonwealth Scientific and Industrial Research Organization (CSIRO) “King” LWC meter in addition to an FSSP] were considered for use, except for a few flights or projects which were desirable because of their high LWCs even though only one LWC sensor was available. Otherwise, individual data records were accepted only if the hot-wire LWCs and the FSSP-computed LWC were separated by no more than 0.4 g m−3. Uncertainties in LWC among the probes are further mitigated in the statistics by using a consensus value—that is, the average LWC from all the available probes.
Contamination by ice particles
The NACA (rotating cylinder and perforated tube) probes, being ice accretion devices, were insensitive to ice particles, so they responded only to supercooled drops whether ice particles were present or not. Thus, totally glaciated clouds were automatically eliminated (no icing formed on the probes), and in mixed phase clouds the probes responded only to the cloud drops.
The LWCs and MMDs in the modern data represent ordinary cloud droplets nominally smaller than 50 μm in diameter. The presence of any ice particles is therefore immaterial, except as they may induce small, residual responses in the hot-wire LWC probes and add a few counts in the upper channels of the FSSP (Gardiner and Hallett 1985; Cober et al. 2001). Although many clouds were mixed phase, any false LWC due to the ice particles is of little concern here because of its small contribution to the hot-wire or FSSP-computed LWCs. The ice particles usually add fewer than about 5 cm−3 to the FSSP, so their contribution to the FSSP-computed LWC is negligible. Even in a worst-case situation with, say, an indicated ice particle concentration of 15 cm−3 (15 000 per liter) distributed with 1 cm−3 in each of the 15 size channels (3–45 μm), only 0.15 g m−3 of “false” LWC is added to the droplet LWC. Most of the time, the IWC in the FSSP range is much smaller than this. The FSSP-computed MMD may be overestimated by a few microns in the presence of ice crystals, but the only effect may be a broadening of the LWC versus MMD scatterplots in Fig. 3 of this paper.
When they were available, the optical array probes (OAPs) were used mainly to reveal the presence or absence of large particles and their abundance (concentration). No specialized particle shape recognition software was needed. All particles larger than 0.5 mm were assumed to be ice and were not used for any LWC or MMD computation, but were an indicator of mixed phase conditions. No freezing rain was encountered. Drizzle (which appeared to be rare) was declared only when all particles were confined to below 250 μm on the 1D-C or 2D-C, there was LWC in the cloud sample, and the entire cloud was warmer than −15°C.
In any case, in the data screening procedure, whenever the SLWC was low and ice particle contamination appeared to be a concern, the data record(s) were not used.
Large drops (drizzle)
In the modern data, the MMD is computed only from the FSSP size distributions, except for the few cases when drizzle was known to be present. In those cases, an OAP (1D-C or 2D-C) was used in addition to the FSSP. The hot-wire probes are known to respond to larger drops, but with declining sensitivity above 30 to 50 μm. Practically all of the drop size distributions were well within the limits of the FSSP so that it and the LWC probes were measuring the same thing.
In the historical data (rotating multicylinders) the MMD was routinely estimated as part of the original data processing. The NACA rotating multicylinders and perforated-tube icing rate meters will collect larger drops too, but such cases seem to have been seldom encountered. The small number of MMDs above 30 or 40 μm probably represent these occasional exposures to freezing drizzle in the NACA data.
Accuracy of the LWC and MMD measurements and computations
The data all come from experienced cloud physics organizations participating in major research projects, so usually the cloud physics probes were suitably calibrated, maintained, installed, and operated. Any instrument failures or other problems during flight were usually recognized by the responsible scientists. Nevertheless, as an extra precaution for the LWC reliability, flights with redundant LWC sensors were used as much as possible.
The error in LWC indicated by the FSSPs and J-Ws has been reported to be as much as ±20% to 40% (Baumgardner 1983; Strapp and Schemenauer 1982) for probes routinely calibrated by the user. For present purposes, this makes little difference for small LWCs (less than about 0.5 g m−3, which includes 70% and 95% of the LWCs observed in convective and stratiform clouds, respectively). Even for a LWC of 0.5 g m−3, a 40% error would shift the reading by only 0.2 g m−3. Nevertheless, to mitigate any errors, we use the average LWC from available probes for our statistical analyses.
The hot-wire LWC probes are subject to saturation at high LWCs, and the ice accretion probes (Rosemount ice detector and the NACA probes) are susceptible to LWC underestimates when the probe surface temperature is near 0°C (Ludlam 1951). But the Rosemount ice detector was not used as a quantitative LWC indicator here and the NACA probes were generally not used at temperatures above about −5°C, so the Ludlam effects are not a concern as a source of error. The largest indicated LWCs were the short-duration values up to 4 and 5 g m−3 found in Florida and Montana summer Cb. The Florida (1978–80 FACE-II project) flights had only a J-W for LWC measurements and the accuracy at these high LWCs was not given. [The data were taken directly from published tables in the FACE-II data report (Jordan et al. 1981)]. In the Montana flights (1981 CCOPE project) both a J-W and FSSP were available so that they could be used to cross-check each other’s LWC. But the FSSP usually became temporarily iced up when these high LWCs were encountered and only the J-W LWC was temporarily usable. The heavy icing reported by the crew during these times indicates that the SLWC was, indeed, unusually high, but the exact accuracy of the J-W LWCs in these conditions is unknown. The tendency of the J-W to saturate at LWCs above about 3 g m−3 implies that the actual LWC may have been even greater than the record indicates.
The error in the LWC obtained from the rotating multicylinders is estimated to be within ±5%; the error in the MMD increases with increasing MMD but is estimated to be within ±10% for MMDs smaller than 20 μm (Jones and Lewis 1949). The error in the SLWCs computed from NACA icing rate meters in the 1950s was estimated to be within ±30% for the flights selected for use here (Perkins 1959).
Variable averaging intervals
For the high-resolution (1 Hz) data available in digital form, the following averaging scheme has been devised to condense the number of records to a manageable set.
Each variable (LWC, MMD, air temperature, droplet number density, etc.) is averaged over continuous, uniform portions of clouds as defined in Table A1. These are variable length intervals termed uniform cloud intervals, and each constitutes an individual record in the database. If the aircraft is still in continuous clouds at the end of one uniform interval, then a new averaging interval is immediately begun and continued until the next significant change in cloud properties occurs. Otherwise, the next averaging interval is not begun until the aircraft enters another continuous, uniform section of cloud. This scheme results in variable averaging distances overall, and the averaging distance is retained as one of 43 variables in each data record.
A minimum acceptance rule also had to be established to avoid overloading the database with numerous, brief, and insignificant events. Thus, measurements are included only if (i) the average LWC is at least 0.01 g m−3 and (ii) the product of LWC and averaging distance is at least 0.01 g m−3 n mi. That is, a LWC as low as 0.01 g m−3 must last at least 1 n mi (30 s at 120 kt or 18 s at 200 kt). This still allows for resolution of significant microphysical changes within clouds, such as cells containing large amounts of LWC. For example, a LWC of 1 g m−3 need only last 0.01 n mi (19 m, or 0.3 s at 120 kt). At a 1-Hz sampling rate, a LWC of 1 g m−3 lasting for 1 s would qualify as a separate record, if desired. In practice, as seen in Table 3a, the average extent was about 0.8 n mi for LWCs larger than 1 g m−3 in convective clouds. That distance corresponds to about 24 s at 120 kt or 14 s at 200 kt.
Although these rules were designed for the modern data, pretabulated data from reports or other publications can be formally accommodated as well. The reported averaging distance is used in that case.
This averaging scheme has a number of advantages:
It avoids inflexible, fixed intervals such as 1-min averages or averages over entire cloud passes. (These are undesirable if they wash out useful detail otherwise available with modern, high-resolution measurements.)
The intervals can be short enough to resolve any significant changes in cloud characteristics along the flight path—that is, the natural variability in clouds can be preserved and documented.
Intervals of uniform, constant conditions within clouds can be preserved whole so that their durations and characteristics can be documented without the ambiguity that would occur if the average included voids or adjacent parcels having significantly different or variable properties.
The averages can resolve extremes of LWC or other variables without dilution.
The averages can preserve altitude-dependent changes in cloud properties observed during ascents or descents through clouds.
The scheme can accommodate broken or scattered cloud conditions without including voids or clear-air gaps that would dilute the averages.
The overall horizontal extent of continuous or semicontinuous cloud conditions is available simply by summing the extents of consecutive uniform intervals.
Data miles as a measure of frequency of occurrence
With variable averaging intervals, it is unsatisfactory to define frequencies of occurrence simply as the number of records having a particular value of a given variable. The deficiency was twofold. First, momentary cloud intervals would incorrectly carry just as much statistical weight as long averages. Thus, there is no way to emphasize the statistical importance of an extended encounter with an extreme value of LWC, for example, compared to a relatively insignificant, brief encounter. Second, the reader would have no information as to whether a given number of records represented 5 or 500 n mi of in-flight measurements.
Data miles were therefore chosen as the most informative measure of frequency of occurrence. It is simply the averaging distance (in nautical miles), or sum of averaging distances, for any subset of the data. This convention automatically weights each record (or LWC measurement, e.g.) by its duration or averaging distance. The other principal advantage is that the reader can easily gauge the relative significance of a dataset by the number of data miles it represents.
MMD frequencies in supercooled clouds: (a) stratiform clouds (12 400 n mi contributing), and (b) convective clouds (4300 n mi contributing).
Citation: Journal of the Atmospheric Sciences 65, 7; 10.1175/2007JAS2522.1
The 99th percentile limits to SLWC, and duration of same, for MMDs equal or larger than indicated in supercooled stratiform clouds from 0° to −10°C. (Curves will be lower for temperatures below −10°C.) Percentages give the relative frequency of MMDs larger than the indicated MMD. Dashed lines are tentative due to the low frequency of MMDs 25 μm and larger.
Citation: Journal of the Atmospheric Sciences 65, 7; 10.1175/2007JAS2522.1
Supercooled LWC averages sorted by MMD, regardless of temperature and averaging distance: (a) stratiform clouds (12 400 n mi contributing) and (b) convective clouds (4300 n mi contributing).
Citation: Journal of the Atmospheric Sciences 65, 7; 10.1175/2007JAS2522.1
Air temperature frequencies for clouds in the database: (a) stratiform clouds (23 000 n mi contributing) and (b) convective clouds (5000 n mi contributing).
Citation: Journal of the Atmospheric Sciences 65, 7; 10.1175/2007JAS2522.1
Supercooled LWC averages sorted by temperature, regardless of averaging distance: (a) stratiform clouds (3500 averages or 23 000 n mi contributing), and (b) convective clouds (3200 averages, or 5000 n mi contributing).
Citation: Journal of the Atmospheric Sciences 65, 7; 10.1175/2007JAS2522.1
Hybrid graph showing local supercooled LWC averages (points) overlaid by SLWC percentiles (solid curves) for combined averages over complete cloud passes: (a) stratiform clouds (3500 averages, or 23 000 n mi) and (b) convective clouds (3200 averages, or 5000 n mi).
Citation: Journal of the Atmospheric Sciences 65, 7; 10.1175/2007JAS2522.1
Supercooled LWC averages recorded in clouds somewhere above the indicated 0°C level, regardless of the averaging distance: (a) stratiform clouds (23 000 n mi contributing) and (b) convective clouds (5000 n mi contributing).
Citation: Journal of the Atmospheric Sciences 65, 7; 10.1175/2007JAS2522.1
Observed seasonal limits to supercooled LWC, and duration of the same, in clouds above the local 0°C level in (a) stratiform clouds and (b) convective clouds.
Citation: Journal of the Atmospheric Sciences 65, 7; 10.1175/2007JAS2522.1
Supercooled LWC averages sorted by altitude, regardless of averaging distance: (a) stratiform clouds (23 000 n mi) and (b) convective clouds (5000 n mi).
Citation: Journal of the Atmospheric Sciences 65, 7; 10.1175/2007JAS2522.1
The 99th percentile limits to SLWC, and duration of the same, at selected altitudes AGL for entire supercooled cloud database except for warm season convective clouds. Dashed lines or extensions are tentative because of the small number of samples at those combinations of altitude and duration.
Citation: Journal of the Atmospheric Sciences 65, 7; 10.1175/2007JAS2522.1
Hybrid graphs showing local supercooled LWC averages (points) in stratiform clouds with MMDs from 10 to 20 μm overlaid by SLWC percentiles (curves) for combined averages over complete cloud passes: (a) for temperatures from about −10°C to 0°C (11 000 n mi) and (b) for temperatures up to −20°C (2750 n mi). Dashed curves indicate tentative values.
Citation: Journal of the Atmospheric Sciences 65, 7; 10.1175/2007JAS2522.1
Hybrid graphs showing local supercooled LWC averages (points) in convective clouds with MMDs from 10 to 25 μm overlaid by SLWC percentiles (lines) for combined averages over complete cloud passes: (a) for temperatures from about −10°C to 0°C (2450 n mi, with warm season clouds excluded); (b) for temperatures up to −20°C (415 n mi, with warm season clouds excluded); (c) for temperatures from about −10°C to 0°C (2675 n mi, including warm season clouds); (d) (450 n mi, including warm season clouds). Dashed lines indicate tentative values.
Citation: Journal of the Atmospheric Sciences 65, 7; 10.1175/2007JAS2522.1
Composition of the supercooled cloud database.*
Table 2a. SLWC frequencies in 23 000 n mi of supercooled stratiform clouds.
Table 2b. SLWC in 23 000 n mi of layer clouds.
Table 3a. SLWC frequencies in 5000 n mi of supercooled convective clouds.
Table 3b. SLWC in 5000 n mi of convective clouds.
Seasonal origins of the data.
Definition of the seasons in terms of the 0°C level height.
Table A1. Rules for defining uniform cloud intervals.
These are true air temperatures, sometimes called static or outside air temperature (OAT) and not total or indicated air temperatures.
The 0°C level was either observed during flight or estimated by extrapolating from the observed temperature at the flight altitude closest to the 0° level. In the latter case, the following formula was used, based on the standard atmospheric lapse rate (6.6°C km−1): estimated 0°C level (m) = altitude (m) + 150 (m/°C) × temperature (°C).
