Abstract

The detailed microphysical processes and properties within the melting layer (ML)—the continued growth of the aggregates by the collection of the small particles, the breakup of these aggregates, the effects of relative humidity on particle melting—are largely unresolved. This study focuses on addressing these questions for in-cloud heights from just above to just below the ML. Observations from four field programs employing in situ measurements from above to below the ML are used to characterize the microphysics through this region. With increasing temperatures from about −4° to +1°C, and for saturated conditions, slope and intercept parameters of exponential fits to the particle size distributions (PSD) fitted to the data continue to decrease downward, the maximum particle size (largest particle sampled for each 5-s PSD) increases, and melting proceeds from the smallest to the largest particles. With increasing temperature from about −4° to +2°C for highly subsaturated conditions, the PSD slope and intercept continue to decrease downward, the maximum particle size increases, and there is relatively little melting, but all particles experience sublimation.

1. Introduction

The melting layer (ML), where snow melts to rain, has an important effect on the thermal structure of the troposphere. The cooling caused by the melting particles can produce deep isothermal layers (Stewart 1984). This cooling also can lead to a separation of the dynamics above and below the ML and thereby the ML can have a significant effect on the dynamics of convective systems (Fabry and Zawadzki 1995).

As ice particles fall from temperatures of −5° to 0°C in stratiform clouds, they continue to grow by aggregation, resulting in larger particles and in a reduction in the number of small particles available to be collected by the larger particles (Heymsfield et al. 2002). As these snowflakes descend into the 0°C isothermal layer, they warm and become wet; at the same time, the latent heat required to melt them cools the air, leading to a quasi-0°C temperature layer. As the particles continue to descend, they become increasingly wetter, eventually collapsing to raindrops of sizes much smaller than those of the snowflakes from which they originated. With increased fall velocity, the particle concentration decreases, and melting causes particle size but not mass to decrease. The detailed microphysical processes operating within the ML—the continued growth of the aggregates by the collection of the small particles, the breakup of the aggregates, and the effects of relative humidity on particle melting, among others—are unresolved owing to the difficulty of collecting data as particles fall through the layer.

Much of what we know about the region above, through, and below the melting layer is based on measurements with radar. From 1 km above the ML to the top of it, there is an increase in radar reflectivity of about 7 dB, with little dependence on the precipitation rate (Fabry and Zawadzki 1995). These researchers suggested that aggregation is the dominant process causing this increase, consistent with the in situ observations of Heymsfield et al. (2013), among others. Beginning at the top of the ML, where the particles begin to melt, there is an abrupt increase in the dielectric constant of the particles (Battan 1973), causing a rapid increase in the reflectivity of the particles—the radar “bright band.” From top to bottom of the ML, the dielectric constant of water versus ice, coupled with the change in the density of solid ice to liquid water, results in an increase in the reflectivity of about 5.8 dB (at X band), assuming that one-half of the snow is melted at the middle of the layer, and 6.5 dB at the bottom. Because the particles’ fall speeds increase through the ML, since their mass remains about the same but their cross-sectional area decreases, this enhancement of 6.5 dB is reduced to about 1 dB. Ice depositional growth can occur in the ML if the relative humidity is near 100%, because the water vapor pressure of the air is higher than that over ice. This growth could potentially increase the reflectivity in the ML, although this increase would be very small. Subsidence within the ML can lead to subsaturation with respect to water and a decrease in reflectivity within it (Willis and Heymsfield 1989).

According to the study of Fabry and Zawadzki (1995) and others, the reflectivity of the bright band about 250 m below the top of the ML is usually much larger than can be accounted for by these factors, up to about 10 dB. The reason for this discrepancy is unclear; it may be due to continued aggregation, the effects of particle shape, or how the water is distributed in the melting snowflake. Also puzzling is why the reflectivity of snow just above the bright band is only 1–2 dB less than the radar reflectivity at the top of the ML (Fabry and Zawadzki 1995).

There have been relatively few direct observations of ice particles undergoing melting within clouds. From ascents through the ML in clouds over California’s Central Valley, Stewart et al. (1984) found that the ratio of the number of particles with circular images to the total number of particles increased from near zero at a distance of 75 m below the top of the isothermal layer to unity at a depth of 300 m. The size of the largest particles increased rapidly within the ML, and, based on the 2D images of the particles, the largest particles were the last to become circular, indicating that they were the last to melt; melting ceased by +2°C. Because conditions in the ML were near saturation with respect to water, their observations were not influenced by particle evaporation. From a Lagrangian spiral descent through the ML together with collocated radar data, Willis and Heymsfield (1989) concluded that most of the ice mass melts, and thus most of the cooling of air occurred in a thin layer above the location of the radar bright band. Significant particle growth through aggregation was observed to occur near the top of the ML. They concluded that the radar reflectivity maximum (bright band) was due to these relatively few, very large aggregates that can survive to the warmer temperatures before fully melting. McFarquhar et al. (2007) characterized the evolution of ice particles from above to below the melting layer during 17 Lagrangian spiral-type descents in the stratiform regions of mesoscale convective systems. Most of the regions in the melting layer were subsaturated with respect to water. They found that the small ice particles in the PSDs were being removed downward in the layer by aggregation and sublimation and the PSD slope decreased with increasing temperature, consistent with aggregation downward. In a further study of these clouds, Grim et al. (2009) employed a microphysical model to evaluate the degree to which sublimation, melting, and evaporation could explain the relative humidity structure. They found that microphysical processes alone (phase change and evaporation) rather than downdrafts could produce a sharp decrease in the relative humidity across the melting layer.

According to the findings of Ohtake (1969), based on raindrop and snowflake size distributions measured at three stations along the slope of Mt. Zao, aggregation or breakup of hydrometeors did not occur within the ML; the size distribution of raindrops depended only on the precursor snowflakes above the ML. Similarly, Yokoyama et al. (1984) collected particles on filter paper along the slope of Mt. Fuji and concluded that aggregation is effective within the upper part of the ML and that breakup may have an effect within the lower part of the ML. Barthazy et al. (1998) measured the changes in the properties of particles undergoing melting along a mountain in Switzerland. At two heights, 2D video disdrometers were used to measure the cross-sectional areas and terminal velocities of the melting particles. At a lower site, a vertically pointing X-band Doppler radar measured the radar reflectivity, and a disdrometer measured the drop size distribution. Aggregation was found to be active not only above the ML but occurred at a faster rate within it. The largest aggregates were found at temperatures between 1° and 2°C at a height corresponding to the peak of the bright band. The sizes of the aggregates decreased rapidly in the lower part of the melting layer, evidently because the ice frame collapsed rapidly; but, based on particle fluxes at the top and base of the ML, the authors concluded that one snowflake yielded one raindrop. In a recent study, Misumi et al. (2014) conducted a study of the fraction of liquid water (drops and liquid in snowflakes) as a function of the ambient temperature and relative humidity using dye-treated filter paper that was kept at a temperature of 0°C. They developed relationships between this fraction and the meteorological surface data.

Several studies have described the snowflake melting process by collecting snowflakes in hexane cooled to temperatures between −10° and −15°C, so that particles freeze in the form in which they fall (Matsuo and Sasyo 1981; Knight 1979; Fujiyoshi 1986; Mitra et al. 1990). According to these studies, the first stage consists of small drops with diameters of tens of microns positioned at the tips of the particle peripheries, with most melting occurring on the edges and lower side of the flake. In stage 2, the meltwater flows from the periphery to the linkages of the snow crystals comprising the aggregate, minimizing the capillary forces and surface tension effects. The flake is not covered by water in this stage. Because the main ice frame remains intact, the snowflake has a ragged surface. In stage 3, small branches in the interior of the flake melt. The meltwater flows from these branches to the linkages between the main branches. The crystal mesh changes from one with many small openings to one with a few larger openings. The main ice frame collapses suddenly in stage 4, with the water covering the ice frame completely and pulling itself together into a drop shape. Interestingly, although breakup of the melting snowflakes generally does not occur in this stage, it does occur when there is an asymmetrical distribution of mass held together by a few crystal branches. The meltwater from these particles forms individual drops, or small drops are shed from the edges of the flakes.

Several models simulating the melting of ice particles through the melting layer have been developed, employing different assumptions of such properties as terminal velocity, bulk density, and dependence of the melted mass fraction on the environmental temperature and relative humidity (Table 1). The time rate of decrease of the snowflake diameter by melting, and the effect of ventilation on cooling the particles, are considered by all of these studies. Calculations of the terminal velocities consider the fraction of the ice melted, their physical diameter D, and their melted diameter Dm and include the relatively low bulk densities of the aggregates. Two of the studies use size distributions, and one considers continued growth in the ML through aggregation. The observational studies summarized above suggest that factors such as the relative humidity distribution in the melting layer, realistic size distributions at the top of the melting layer, and the continued growth of particles and depletion of the small ones through aggregation are important processes to consider.

Table 1.

Physics assumed in three major modeling studies.

Physics assumed in three major modeling studies.
Physics assumed in three major modeling studies.

The objective of this study is to characterize the microphysical processes as particles fall from above, through, and below the melting layer using in situ observations. In section 2, we identify the instrumentation and flight patterns used to collect data during ascents and descents through the melting layer from four field programs. In section 3, we present the observations through the melting layer conducted during these field programs. Section 4 summarizes the results and suggests ways in which the microphysics should be considered in the melting layer.

2. Data

The data collected here (available on the NASA and DOE/ARM websites) are from four field programs: the Tropical Rain Measuring Mission (TRMM) Kwajalein Field Experiment (KWAJEX), based out of Kwajalein, Marshall Islands, in 1999; the NASA Cirrus Regional Study of Tropical Anvils and Cirrus Layers–Florida-Area Cirrus Experiment (CRYSTAL-FACE) in 2002 over southern Florida and the surrounding oceanic and gulf regions; the Precipitation Measurement Mission (PMM) Midlatitude Continental Convective Cloud Experiment (MC3E) in Oklahoma in 2011 near Lamont, Oklahoma; and the PMM Global Precipitation Measurement (GPM) Cold-season Canadian Precipitation Experiment (GCPEx) near Barrie, Ontario, Canada, in 2012.

a. Flights

The University of North Dakota Citation aircraft collected data in all four field programs. A combination of Lagrangian spiral descents and ascents and Eulerian descents through the melting layer are used in the analysis. With a Lagrangian spiral descent, if conditions are quasi steady and the properties of the atmosphere are fairly uniform over a length scale somewhat larger than the diameter of the loops, then the aircraft largely samples the evolution of size distribution properties as a function of altitude (Passarelli 1978). An Eulerian descent is basically a descending path over a fixed geographic point.

To examine the vertical variability and changes in the particle populations during the melting process, we have reanalyzed data collected during three Lagrangian spiral descents from above to below the ML in stratiform ice cloud from KWAJEX (Heymsfield et al. 2002). Figure 1 shows a vertical profile of the radar reflectivities at approximately the sampling time. These measurements were made with the Jet Propulsion Laboratory’s airborne rain-mapping radar (ARMAR) downward-looking Ku-band radar (Durden et al. 1994) from the NASA DC-8 aircraft, which overflew the Citation during each of the three flights. Each loop of the spiral had nearly the same diameter during the descent for each case, ranging from about 5 to 10 km. The descent on 19 August initiated at a temperature of −14°C and concluded at +7°C. The average descent rate from −4° to +7°C was 1.2 m s−1, similar to what the mean aggregate terminal velocity would have been, but slower than what would be expected for melting and melted aggregates. For the 30 August case, where the sampling temperatures were in the range −18° < T < +6°C, the average descent rate was 2.2 m s−1 for temperatures of −4°C and above, approaching the values expected for the combination of raindrops and snow. For the 11 September case, where −39° < T < +5°C, the average descent rate was 2.6 m s−1. The strongest of the thunderstorms producing the sampled regions of these clouds was on 11 September.

Fig. 1.

Vertical sections of radar reflectivities as measured by the ARMAR Ku-band radar on board the NASA DC-8 aircraft at about the times and locations of the sampling by the Citation aircraft for the three Lagrangian spiral descents from KWAJEX. The approximate locations of sampling by the Citation are shown in the rectangular regions.

Fig. 1.

Vertical sections of radar reflectivities as measured by the ARMAR Ku-band radar on board the NASA DC-8 aircraft at about the times and locations of the sampling by the Citation aircraft for the three Lagrangian spiral descents from KWAJEX. The approximate locations of sampling by the Citation are shown in the rectangular regions.

We also examine two Lagrangian spiral descents by the UND Citation aircraft on 26 July 2002 during CRYSTAL-FACE. These spirals were in the convective outflow region of a strong thunderstorm. The aggregation process during these spirals was examined by Field et al. (2006b).

Although there was horizontal inhomogeneity during each of the spiral descents describe below, the same features were clearly sampled during each loop of the spiral. For each of the spirals, we have identified points where the properties of the measured particle size distribution were similar. The cloud properties during these times are identified in section 3.

For MC3E and GCPEX, descents and ascents were made through the melting layer, passing through the layer at mean vertical velocities of about 2 m s−1. Six cases were chosen for study: three of them were through melting layers where the relative humidity (RH) was close to saturation with respect to water and three where RH was considerably below water saturation.

All but one of the profiles were associated with widespread stratiform rain and one was associated with a convective line. We identify the dates of these cases in section 3.

b. Instrumentation

Particle size distributions and low-resolution imagery were obtained from the Particle Measuring Systems 2D-C (KWAJEX, CRYSTAL-FACE) or a Droplet Measurement Technologies cloud imaging probe (CIP, MC3E) and the SPEC high-volume particle spectrometer (HVPS) (HVPS-1, KWAJEX, and CRYSTAL-FACE; HVPS-3, MC3E, and GCPEX) probes. The PSDs were measured from about 100 μm to above 1 mm by the 2D-C and CIP and from 1 mm to 3 cm in increments of 0.2 mm from the HVPS, with composite PSDs generated from a combination of the two probes. The nominal 2D-C probe sample volume is given by the probe’s array width (about 1 mm) times the size-dependent optical depth of field, times the Citation’s true airspeed (about 120 m s−1). The “particle reconstruction” technique was used to extend this sample volume by an amount that increased roughly linearly with size [see sample volume values in Heymsfield and Parrish (1978)] by considering particles that were partially outside of the 2D-C probes’ sample volume. The HVPS swept out a sample volume given by the array width times the separation between the probes’ arms of about 20 cm times the aircraft’s true airspeed, or about 1 m3 s−1.

The methods described in Field et al. (2006a) were used to mitigate the influence of particle shattering on the observations from the imaging probes. Antishattering tips have been developed to mitigate the problem. Unfortunately, none of the imaging probes had antishattering tips. Jackson et al. (2014) have suggested that the use of the Field et al. (2006a) methods alone without the redesigned tips can lead to overestimates of particle concentrations for particles with dimensions less than 500 μm. We discuss the potential impacts later in this subsection.

Exponential size distributions of the form N = N0eλD have been fitted to the 5-s-average PSDs, corresponding to 600-m pathlengths. Although gamma PSDs can readily be fitted to the PSDs, we have chosen exponentials because they can provide more readily discernable changes in the PSDs within the ML.

The ice water content (IWC) was either measured by a Counterflow Virtual Impactor (CVI) probe (CRYSTAL-FACE) or estimated from the PSD by using the mass–dimensional relationship m = 6.21 × 10−3D2.05 from Heymsfield et al. (2010). The IWC was not directly measured for comparison with these estimates, but the relationship is thought to apply reasonably well to tropical maritime convection; the ratio r of the calculated IWC to measured IWC from the CRYSTAL-FACE spirals is r = 0.91 ± 0.30. Snow precipitation rates S were derived from this m(D) relationship and the terminal velocities derived by Heymsfield and Westbrook (2010), together with the PSD. Cross-sectional areas were derived from the 2D imaging probe data. Rain rates R have been derived using the terminal velocities from Beard and Pruppacher (1969) and Szyrmer and Zawadski (1999).

We have considered the possible effects of remnant shattered particles on the PSD slope and intercept, the IWC and snow precipitation rates, and on the total number concentration. The shattered particles, primarily smaller than 400 μm, would have affected our results only minimally because the zone from just above to just below the melting layer is dominated by large particles. Note that the HVPS is relatively insensitive to shattering because it has a wide distance between sampling arms and we use those distributions for 1 mm and above. Because these PSDs are broad, remnant small particles would have had little effect on most of the parameters we examine: slope λ (Heymsfield et al. 2008), N0, R, and S. They would affect the total concentration, but because we only are looking at trends through the melting layer and not absolute values, it is likely that the interpretations we make from the data are meaningful.

Temperature was measured with Rosemount temperature probes, and the relative humidity was taken from an EG&G chilled-mirror hygrometer (KWAJEX, CRYSTAL-FACE) or a Maycomm TDL laser hygrometer (CRYSTAL-FACE). For MC3E and GCPEx, the Citation carried the Edgetech 137 chilled-mirror dewpoint monitor and a Maycomm TDL laser hygrometer. The absolute accuracy of these hygrometers is thought to be about ±10% (Hintsa et al. 1999). The response time of the temperature probe and hygrometers is 1 Hz. Vertical winds during KWAJEX and CRYSTAL-FACE were measured by radome gust probes together with an inertial navigational system and during MC3E and GCPEX from a Rosemount 858 flow-angle probe and an Applanix POS inertial platform. The accuracy of these measurements is about ±1 m s−1.

3. Observations

This section focuses on three Lagrangian spiral descents through the ML from KWAJEX that were originally analyzed as described in Heymsfield et al. (2002); they are reanalyzed here to ascertain the detailed microphysics in the ML. Also, two Lagrangian spiral descents from CRYSTAL-FACE on 26 July 2002 are examined. In addition, four profiles through the ML were obtained for MC3E and two for GCPEX. The melting-layer regions for all of the profiles were largely devoid of updrafts or downdrafts within the measurement accuracy, other than a few times that were likely to be noise and not organized updrafts or downdrafts.

a. KWAJEX Lagrangian spiral descents

For KWAJEX, Lagrangian spiral descents were used to ascertain how the PSDs evolved in the outflow/anvil regions associated with thunderstorms on 3 days as the particles fell from layers well above the ML, into, and through the ML. Examples of particles imaged during 19 August spiral are shown in Heymsfield et al. (2002) and for the 11 September spiral in Stith et al. (2002). The particles smaller than 200 μm were irregularly shaped particles and capped columns; the larger ones aggregates of capped columns and lightly rimed particles. For the 30 August case, the small particles were similar to those for the 19 August spiral and the larger particles were lightly rimed aggregates. On 11 September, irregularly shaped crystals and moderately rimed aggregates were observed.

Figure 2 shows the profiles of relative humidity with respect to water (RHw) and ice (RHi) (left axis) and the temperature T and ice-bulb temperature Ti obtained beginning at −10°C to the end of each of the spiral descents. In each panel, RHi is plotted for all temperatures where Ti was less than 0°C. The symbol “×” denotes where the ice-bulb temperature first becomes 0°C, where the particles should begin to melt. RHi was at saturation or above where T < −4°C for all cases. For 19 and 30 August, RHw was slightly below 100% for −2° < T < +1°C, such that the ice-bulb temperature remained at Ti < 0°C until an air temperature of about 0.5° and 1°C, respectively. For the 11 September case, which was significantly subsaturated for −2° < T < 2°C, the ice-bulb temperature remained at Ti < 0°C until an air temperature of about +2.5°C.

Fig. 2.

Relative humidity with respect to water (left axis) and air temperature and ice-bulb temperature (right axis) during three Lagrangian spiral descents from above, through, and below the melting layer during KWAJEX. The average descent rates are shown. Vertical bars show the temperature at key points during the spirals.

Fig. 2.

Relative humidity with respect to water (left axis) and air temperature and ice-bulb temperature (right axis) during three Lagrangian spiral descents from above, through, and below the melting layer during KWAJEX. The average descent rates are shown. Vertical bars show the temperature at key points during the spirals.

The IWC was highest for the 19 August case and lowest for the 11 September case (Fig. 3). There were obvious pockets of higher and lower IWC during each loop of the spirals, readily ascertained from the peaks and valleys in the plots. Between each of the times of the minima and maxima, median values of IWC and variables related to the PSD have been derived and are used in later plots. The peak IWCs in these cases were about half those calculated by McFarquhar et al. (2007), although this could be in part due to the different methods of obtaining the IWC values.

Fig. 3.

Ice water content derived during the three KWAJEX spirals. Gold points show where the maximum IWCs were obtained during each loop of the spirals and blue points show the minima. In later figures, mean values of various parameters are derived from one maximum (minimum) point to midway between the previous maximum (minimum) point and, in the same way, between the next points. The lines representing the LWC assume that all ice particles are water droplets. This number is divided by 40 to show that the population-average density is about LWC/40 or 0.025 g m−3.

Fig. 3.

Ice water content derived during the three KWAJEX spirals. Gold points show where the maximum IWCs were obtained during each loop of the spirals and blue points show the minima. In later figures, mean values of various parameters are derived from one maximum (minimum) point to midway between the previous maximum (minimum) point and, in the same way, between the next points. The lines representing the LWC assume that all ice particles are water droplets. This number is divided by 40 to show that the population-average density is about LWC/40 or 0.025 g m−3.

The rapid dropoff in the IWC (calculated from the PSD, assuming that all of the particles are ice) at temperatures of +1°C for the 19 August case, at about 0°C for the 30 August case, and at almost +2°C for the relatively dry 11 September case are clearly noted. Also plotted in Fig. 3 is a hypothetical LWC, derived by assuming that all particles are liquid. The reason for doing this is to get an average bulk density of the ice particle population, IWC/LWC. The values of this hypothetical LWC plotted in Fig. 3 have been arbitrarily divided by 40 to account for the higher density of the raindrops and now match the IWCs to within a factor of 1, implying that the estimated bulk ice density is, on average, about 0.025 g cm−3.

Precipitation rates derived assuming that all particles are snow or all are water drops are plotted as a function of time for the three cases in Fig. 4. For reference, mean values of S derived for −4° < T < 0°C range from relatively heavy to light: 4.90 ± 2.1 mm h−1 for 19 August, 5.12 ± 0.93 mm h−1 for 30 August, and 1.34 ± 0.3 mm h−1 for 11 September. For the first two cases, S is relatively constant during the spirals, until abruptly decreasing at a temperature of +0.5°–1°C, signifying the change in the mass–dimensional relationship from lower-density snow to the more appropriate rain (Figs. 4a,b). This effect is more readily seen in the calculations for R: the rates are much too high for temperatures below 0°C. Above +0.5°–1°C, the values of R come in line with an extrapolation of the values of S for temperatures near 0°C. Although this comparison suggests approximate conservation of mass flux across the melting layer, such factors as variation in the cloud properties, the higher fall speeds of rain compared to snow (the descent velocity of the aircraft spiral was meant to follow descending snow), and the subsaturated conditions make a more precise comparison difficult. For the 11 September case, S increases downward, and, because of the highly subsaturated conditions, S does not decrease (converting to rain) until a temperature of about +2°C.

Fig. 4.

As in Fig. 3, but for the derived snow precipitation rate.

Fig. 4.

As in Fig. 3, but for the derived snow precipitation rate.

The slope of the exponential fit to the PSD is relatively insensitive to issues such as shattering (Heymsfield et al. 2008), which has a large effect on N0 and the total concentration Nt. Note in Fig. 5 the decrease in λ downward with height and extending into the ML, indicating spectral broadening through aggregation. The increase in the size of the largest measured particle for each PSD (Dmax) indicates this growth downward from low to warm temperatures and extending into the ML (Fig. 6). For clarity in Fig. 6, given the discreteness of the PSD size binning, mean values in time intervals corresponding to the maxima and minima in Fig. 3 are shown, along with lines fitted by eye through these points. For the cases in which the humidity is close to saturation with respect to water, 19 and 30 August, λ continues to decrease and Dmax increase to a temperature of +0.5°C, followed by abrupt increases and decreases, respectively, signifying melting. Melting is delayed until a temperature of about 1°C for the drier case of 11 September.

Fig. 5.

Time plot of the slope of the exponential PSDs fitted to the 5-s-average PSDs.

Fig. 5.

Time plot of the slope of the exponential PSDs fitted to the 5-s-average PSDs.

Fig. 6.

Size of the largest particle measured during each 5-s PSD.

Fig. 6.

Size of the largest particle measured during each 5-s PSD.

The intercept parameter decreases with increasing temperature to about +1°C, displaying a characteristic feature of aggregation, where the smaller particles are collected by the larger ones, thereby depleting them (Fig. 7). At temperatures above +1°C, N0 continues to decrease, the result of an increase in the fall speed of all particles due to their melting to water. These effects are readily seen from the total particle concentration greater than 100 µm (Fig. 8). There does not appear to be any enhancement in Nt within and below the melting level, as might be expected from breakup of the melting particles, at least for sizes 100 µm and above. We have derived the total concentrations larger than 900 μm to see if there was any enhancement in the concentrations of the large particles within the melting layer and there was no discernable increase in these concentrations, suggesting that breakup of the melting aggregates is leading to more large particles. Of course, aggregation may be removing some of these larger particles produced in this way but this possibility is not apparent in the data.

Fig. 7.

As in Fig. 5, but for the PSD intercept parameter.

Fig. 7.

As in Fig. 5, but for the PSD intercept parameter.

Fig. 8.

Total concentration (>100 μm) measured during the Lagrangian spiral descents.

Fig. 8.

Total concentration (>100 μm) measured during the Lagrangian spiral descents.

Figures 9 and 10 summarize the changes in the PSD slope, intercept parameter, total concentration, and maximum diameter as a function of temperature for the three spiral descents. Within the critical temperature range from 0° to +1°C, λ and N0 continue to decrease. Although we use exponential fits to more clearly show how λ and N0 vary through the melting layer and McFarquhar et al. (2007) use gamma fits, the magnitudes of these coefficients are quite similar, as ascertained from the gamma-function fits that we derived through the layers. There is no obvious increase in Nt in the melting layer; indeed, there is a decrease, signifying continued aggregation. The total concentrations, and their variations with altitude, are very similar to those shown in McFarquhar et al. (2007), but it is unclear from their plots whether Nt increased in the melting layer. The Dmax values continue to increase in this temperature range, consistent with the conclusion reached by McFarquhar et al. (2007) that shows aggregation is responsible for this increase. As temperature continues to increase, λ then increases because of the melting of the ice to rain, and N0 continues to decrease because of the higher fall speeds of the raindrops than of the ice particles.

Fig. 9.

Summary of the KWAJEX PSD properties with temperature during the spiral descents, by case: (a)–(c) PSD slope and (d)–(f) PSD intercept.

Fig. 9.

Summary of the KWAJEX PSD properties with temperature during the spiral descents, by case: (a)–(c) PSD slope and (d)–(f) PSD intercept.

Fig. 10.

As in Fig. 9, but for (a)–(c) the total concentration and (d)–(f) the size of the largest particle.

Fig. 10.

As in Fig. 9, but for (a)–(c) the total concentration and (d)–(f) the size of the largest particle.

The ratio of the particle area to an area of circle of the same (peak) diameter, the area ratio Ar is a very useful parameter for depicting the melting process. An area ratio of 1 would indicate a sphere, but, owing to coarse particle-probe pixel dimensions and particle stretching and canting, a sphere typically produces Ar of about 0.8. In Figs. 1113 we see the melting process unfolding in the form of plots that show the dependence of the mean value of Ar on the size bin (when a given size is measured). At temperatures above +1°C, particles become more spherical, and the largest particles in the PSD show a rapid decrease. The exception is for the 11 September case, where melting is suppressed because of the dry environment (Fig. 13). Figures 1113 also illustrate that the smaller particles melt before the larger ones.

Fig. 11.

Summary of the PSD properties as a function of temperature for the 19 Aug 1999 KWAJEX case. (a),(b) The PSD properties, as in Fig. 9. (right) The area ratio dependence on size and temperature.

Fig. 11.

Summary of the PSD properties as a function of temperature for the 19 Aug 1999 KWAJEX case. (a),(b) The PSD properties, as in Fig. 9. (right) The area ratio dependence on size and temperature.

Fig. 12.

As in Fig. 11, but for the 30 Aug 1999 case.

Fig. 12.

As in Fig. 11, but for the 30 Aug 1999 case.

Fig. 13.

As in Fig. 11, but for the 11 Sep 1999 case.

Fig. 13.

As in Fig. 11, but for the 11 Sep 1999 case.

b. CRYSTAL-FACE

Cloud properties from two of the three Lagrangian spiral descents spanning the temperature range from about –10° to 3°C on 26 July 2001 are highlighted here. In both cases, the relative humidities were substantially below water saturation (Figs. 14a and 15a), thereby providing insight into the relative roles of melting versus sublimation. Furthermore, there were direct, reliable measurements of the IWC, which provide some guidance on whether the ice particle masses that are used for the calculation of the snowfall rates can be trusted. The aircraft descent rates were 1.68 and 1.56 m s−1, comparable to the terminal velocity of millimeter-size aggregates at the observed pressure level of about 500 hPa. The ice particles were irregularly shaped small particles and the larger ones were moderately rimed aggregates.

Fig. 14.

Observations through a spiral descent during CRYSTAL-FACE for the period 77153–78556 UTC s. The average descent rate was 1.68 m s–1. (a) Relative humidity with respect to water. (b) Calculated snowfall rate. (c) Ice water content. (d) Average area ratios per size bin, for the midpoints of three size bins. Note the boxed area, where melting is beginning.

Fig. 14.

Observations through a spiral descent during CRYSTAL-FACE for the period 77153–78556 UTC s. The average descent rate was 1.68 m s–1. (a) Relative humidity with respect to water. (b) Calculated snowfall rate. (c) Ice water content. (d) Average area ratios per size bin, for the midpoints of three size bins. Note the boxed area, where melting is beginning.

Fig. 15.

As in Fig. 14, but for the period 82384–83189 UTC s. The average descent rate was 1.56 m s−1.

Fig. 15.

As in Fig. 14, but for the period 82384–83189 UTC s. The average descent rate was 1.56 m s−1.

Estimated values of S and IWC decrease throughout the spirals as a result of the highly subsaturated conditions (Figs. 14b,c and 15b,c). The ratios of calculated to measured IWC were 0.98 ± 0.35 and 0.91 ± 0.30 g m−3, respectively, indicating that the ice particle masses, and hence S, are likely to be highly accurate.

The area ratios of the millimeter- to centimeter-size particles suggest there is little melting (Figs. 14d and 15d) except perhaps at the very bottom of each of the spirals (boxed regions in Figs. 14d and 15d), indicating that melting of the ice at temperatures as warm as +2°C is minimal in these highly subsaturated conditions.

The slope of exponentials fitted to the PSDs does suggest that there is melting beginning at about 1.5°C (boxed region in Fig. 16a). Where T > 1.5°C, the PSD intercept parameter N0 increases rather than decreases as might be expected to result from melting (Fig. 16). The total concentration of particles increases where T > 1.5°C (Fig. 16c), which, together with the N0 values, suggests that sublimation is leading to some fragmentation of the larger aggregates. The size of the largest particles decreases during the spirals because of sublimation, and there is little indication that the largest aggregates melt, even at temperatures T > 2°C (Fig. 16d).

Fig. 16.

Summary of PSD property changes during the two Lagrangian spiral descents from CRYSTAL-FACE. Note that the melting takes place between the horizontal black and red lines. (a) PSD slope. (b) PSD intercept. (c) Total concentration > 100 μm. (d) Maximum diameter.

Fig. 16.

Summary of PSD property changes during the two Lagrangian spiral descents from CRYSTAL-FACE. Note that the melting takes place between the horizontal black and red lines. (a) PSD slope. (b) PSD intercept. (c) Total concentration > 100 μm. (d) Maximum diameter.

c. MC3E and GCPEX

Of the 23 ascents–descents performed by the Citation during MC3E, we examine four through the melting layer. The 27 April and 1 and 10 May cases were associated with widespread stratiform rain and the 20 May case with a convective line. Two of the ascents–descents through the melting layer from GCPEX, on 27 January, were in clouds associated with lake-effect snow squalls but not in convection. Of the six MC3E and GCPEX melting layer cases, three took place where RHw > 90% and three took place where RHw < 90%, making possible an examination of the dependence of the melting process on the relative humidity. The improved image quality from the newly developed SPEC High Volume Particle Spectrometer (HVPS-3) allows us to see the melting processes in more detail than was previously possible.

On 27 April during MC3E, during spiral 1, particles were small columns and needles, some 1–5-mm heavily rimed particles and large unrimed aggregates. Also on this day, during spiral 2, the particles smaller than 1 mm in diameter were primarily needles and moderately rimed particles and large aggregates. On 1 May, the small particles were lightly rimed, mostly aggregates, and the large particles were aggregates. On 10 May, particles smaller than 1 mm in maximum dimension were aggregates with few pristine particles and particles larger than that size were aggregates. On 20 May, there were few pristine particles and almost all were aggregates. For the 27 January GCPEX case, for both spirals, the particles smaller than 1 mm were almost all pristine needles and the larger particles were aggregates of needles. What was most noticeable from the MC3E and GCPEX data, with the associated high-quality imagery, is that the aggregation process is enhanced at the top of the melting layer, possibly because the aggregates begin to melt, primarily at their bottom surface and on their edges (Fujiyoshi 1986), providing more sticky surfaces where they collect and/or collide with other particles, which enhances the sticking process.

Because the penetrations through the melting layer were climbs and descents rather than Lagrangian spirals, from which we could ascertain aspects of the horizontal structure, we have decided to capture the general tendencies by averaging in 1°C intervals from −4° < T < −1°C and 0.5°C intervals from −1° < T < 3°C. Variability will be shown from the standard deviations plotted in the figures.

These cases demonstrate many of the same characteristics found in KWAJEX. For most of the cases with high RHw, λ and N0 continue to decrease, and Dmax continues to increase (Figs. 1718); above 1°C, λ and Dmax increase and N0 decreases. For most of the cases with lower RHw, λ and N0 and Dmax increase with warmer temperatures. That the value of N0 increases signifies a shift to smaller particles and likely sublimation. The precipitation rates, assuming snow and rain, also show features similar to those observed during KWAJEX, especially the dependence on RHw (Figs. 17d and 18d).

Fig. 17.

Summary of the PSD properties and the snow precipitation rate during three descents (solid vertical lines) and ascents (dotted vertical lines) through the melting layer, where the relative humidities were relatively high. (a) PSD slope. (b) Intercept parameter. (c) Maximum particle diameter. (d) Precipitation rates, assuming that the particles are all ice/snow and rain.

Fig. 17.

Summary of the PSD properties and the snow precipitation rate during three descents (solid vertical lines) and ascents (dotted vertical lines) through the melting layer, where the relative humidities were relatively high. (a) PSD slope. (b) Intercept parameter. (c) Maximum particle diameter. (d) Precipitation rates, assuming that the particles are all ice/snow and rain.

Fig. 18.

As in Fig. 17, but for four highly subsaturated cases.

Fig. 18.

As in Fig. 17, but for four highly subsaturated cases.

The area ratios for two of the MC3E cases, one with a relatively high average RHw at temperatures from −4° to 0°C and another where it is relatively low, are shown in Fig. 19. We see the melting process occurring for the higher-RH case at temperatures between about +0.5° and +1.0°C, whereas it does not occur until above +2°C for the lower-RH case. As with the KWAJEX spirals, melting proceeds from the smallest to the largest particles.

Fig. 19.

Area ratios as a function of temperature for (top) a relatively high-RH case and (bottom) a relatively low-RH case.

Fig. 19.

Area ratios as a function of temperature for (top) a relatively high-RH case and (bottom) a relatively low-RH case.

4. Discussion

If we consider calculations of the ice-bulb temperature and account for the heat released by deposition, we estimate that an ice particle at RHw = 90% does not begin to melt until 0.6°C; for RHw = 80%, this occurs at 1.3°C, and at RHw = 70%, it occurs at 2.0°C. The profiles of the PSD parameters and bulk properties are consistent with these temperature limits for melting, especially given the potential errors in the relative humidity measurements. As a consequence, it is obviously necessary to consider the relative humidity within the ML if models and radar retrieval algorithms are to be able to accurately estimate changes in the PSD properties through the melting layer.

From mountain-based observations that were located at different temperatures within the melting layer, Misumi et al. (2014) developed an empirically based relationship between the ratio of liquid water flux (drops and water included in the drops) to the total flux as a function of temperature and relative humidity. For a precipitation rate of 5.0 mm and RHw = 95%, similar to the conditions from the 11 September flight during KWAJEX and the low-RHw cases from MC3E and GCPEX (Figs. 13, 18, and 19b), they found that about one-half of the snow is melted when a temperature of 1.6°C is reached and all snow is melted when the temperature reaches 3.1°C. This is in excellent agreement with our observations at these lower RHw values. For a precipitation rate of 5 mm and RHw = 95%, similar to the conditions from the first two KWAJEX flights and the high-RHw cases from MC3E and GCPEX (Figs. 11, 12, 17, and 18a), about one-half of the snow melts at 0.4°C and all is melted at 1.6°C. Again, there is excellent agreement, especially given that the range of RHw for these cases is 90%–100%. For the low-RH cases from CRYSTAL-FACE, with RHw ≈ 70% and S ≈ 3 mm h−1, all particles would be melted at +3.5°C. The Misumi et al. (2014) model can therefore be used to estimate the liquid water fraction and its dependence on the temperature and humidity reasonably reliably, especially where RHw > 75%.

A question remains as to how to use our results for developing or improving radar retrieval algorithms, especially snow and rain precipitation rates. Using data from MC3E, we compared our forward models of radar reflectivity at Ku and Ka band with measurements made by the APR-2 radar (Tanelli et al. 2005) on board the NASA ER-2 aircraft overflying the UND Citation, approximately collocated in time and position, during several of the flights. We used various backscatter models for Ku and Ka band (e.g., Matrosov 2007) and consistently found that our values of the radar reflectivity Ze at each wavelength are about 6 or 7 dB too large. We are not sure whether the failure to derive more reliable radar reflectivities is due to the backscatter model, the mass–dimensional relationship used for the calculations, or an overestimate of the size of the largest measured particles, which dominate the reflectivity. Given this yet-to-be-resolved issue, we have not developed an explicit relationship between Z and S.

The ratio of the snow precipitation rate calculated as described above to the intercept parameter should be relatively immune to the problem noted above and should primarily be a function of λ. This is readily found from the KWAJEX and MC3E datasets (Figs. 20a,d). (Data from the two other field programs are not included for conciseness.) Likewise, errors in the calculated Ze should be mitigated by characterizing λ in terms of the difference in Ze at Ku and Ka band, dual-wavelength ratio (DWR). In Figs. 20b and 20e, we note a direct relationship between λ and DWR, except at the low values of DWR, where there would be radar measurement uncertainties as well. Therefore, with a value for DWR, we should be able to calculate λ and thus S/N0 with relatively little error. Fits to the relationships of S/N0 to λ and of λ to DWR are shown in Figs. 20a,b and 20d,e, respectively.

Fig. 20.

Parameters used to develop the snowfall retrieval algorithm: (a)–(c) all times from KWAJEX, at subfreezing temperatures or where we are certain that the particles are ice, and (d)–(f) as in KWAJEX, but for MC3E. (top) The ratio of the estimated snowfall rate to the PSD intercept parameter. (middle) The PSD slope as a function of the difference between the calculated radar reflectivity at 13 and 35 GHz. (bottom) The temperature dependence of the PSD intercept parameter. Fits to the observations are shown as solid curves.

Fig. 20.

Parameters used to develop the snowfall retrieval algorithm: (a)–(c) all times from KWAJEX, at subfreezing temperatures or where we are certain that the particles are ice, and (d)–(f) as in KWAJEX, but for MC3E. (top) The ratio of the estimated snowfall rate to the PSD intercept parameter. (middle) The PSD slope as a function of the difference between the calculated radar reflectivity at 13 and 35 GHz. (bottom) The temperature dependence of the PSD intercept parameter. Fits to the observations are shown as solid curves.

The value of N0 should depend primarily on temperature, and we see this tendency, with a factor of 2 or so variability at a given temperature (Figs. 20c,f). Fits of the relationship between N0 and temperature are shown in Figs. 20c and 20f. Using the temperature and the relationships developed in Fig. 20, we therefore can find a method to derive S that is relatively insensitive to the error in our forward modeling of the radar reflectivity.

5. Summary and conclusions

The objective of this study was to characterize the melting of a population of ice particles as they descended through the melting layer and gradually melted into rain. This study draws on data collected during four field programs, one conducted in the equatorial Pacific, one over southern Florida, one in the continental United States, and one in Canada. The in situ aircraft flight patterns included slow, Lagrangian spiral descents and Eulerian descents and ascents through the melting layer. Snow precipitation rates entering the melting layer ranged from 0.1 to 10 mm h−1, and the relative humidities ranged from 70% to 100%.

Exponential size distributions were fitted to the concentration versus size data acquired from two-dimensional imaging probes sizing in the range from about 100 μm to above 2 cm. The following trends were noted:

  1. With decreasing temperatures from −4° to +1°C and with relative humidities with respect to water of 90% or above, the PSD slope and intercept parameters uniformly decreased downward, while the maximum particle size of the largest particle continued to increase. Aggregation is responsible for these trends. Melting proceeded from the smallest to the largest particles, beginning between +0.5° and +1°C and ending at about +2°C. The aggregation process appears to be enhanced beginning at the top of the melting layer, possibly because the aggregates become stickier on their bottom side and exterior surfaces as they melt, and since these are their collecting surfaces, this could enhance the aggregation process.

  2. For highly subsaturated conditions and for temperatures from about −4° to +2°C, the PSD slope and intercept parameters continued to decrease downward, whereas the size of the largest particles either remained about the same or increased. There was relatively little melting until a temperature of +2°C or above was reached. There is no apparent increase in the total concentrations of the ice particles or the particles larger than about 1 mm, suggesting that breakup of the particles during the melting process is not significant.

Previously McFarquhar et al. (2007) demonstrated the effects of subsaturated conditions on the ice PSDs in the melting layer of clouds associated with bow echoes and we show them very clearly here; nonetheless, it is often assumed that the relative humidity in the melting layer is at water saturation. What is really important to the melting process is the ice-bulb temperature, which controls whether the ice particles are sublimating, growing, or melting. Although it is possible that melting does not begin until a temperature of +4°C with extremely dry conditions, the trade-off is whether the ice particles sublimate before that point, in which case melting will not occur.

Slow, Lagrangian-type spirals through the melting layer are most suited to studying the melting process, and more such studies are clearly needed. Also, more collocations of in situ aircraft with overflying or ground-based, dual-wavelength radar will improve the algorithm that we have developed to estimate the snowfall rate from dual-wavelength radar.

Acknowledgments

The authors wish to thank Sergey Matrosov and Simone Tanelli for their help on the radar-related components of this work. This work was supported by NASA through NASA GPM/PMM Grant NNX13AH73G, DOE ASR Grant DE-SC0008648, and through funding from JPL through Deb Vane of the CloudSat Project Office.

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Footnotes

*

The National Center for Atmospheric Research is sponsored by the National Science Foundation.