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  • View in gallery

    Term A(D) from the 2DCs during (a) ISDAC and (b) IDEAS-2011. Subscript s (m) denotes the use of standard (modified) tips, and superscript a (na) when algorithms were (were not) applied as indicated in legend. Mean Ac distribution is indicated in the legend. The Asna(D = 500 μm) is 0.1 mm2 L−2 (0.05 mm2 L−2) higher than Asa(D = 500 μm) for ISDAC (IDEAS-2011).

  • View in gallery

    Scatterplot of βsna, βsa, and βmna as a function of βma. Solid lines are the best fit of quantity on the y axis to quantity on the x axis, with coefficients of fit and regression coefficient indicated in legend. The black line is 1:1. In general, βsna > βmna > βma > βsa.

  • View in gallery

    (a) As in Fig. 2, but for IWCsna, IWCsa, and IWCmna as a function of IWCma. BL06 method was used to calculate IWC. (b) Scatterplot of IWCma and IWCsa calculated using the CPI-mD method as a function of IWCma and IWCsa, respectively, calculated using the BL06 method. The black line is 1:1. In general, IWCsna > IWCmna > IWCma > IWCsa.

  • View in gallery

    As in Fig. 2, but for Dm-mna, Dm-sa, and Dm-sna as a function of Dm-ma. Solid lines are the best fit of quantity on the y axis to quantity on the x axis. The black line is 1:1. In general, Dm-sna > Dm-sa > Dm-mna > Dm-ma.

  • View in gallery

    (a) As in Fig. 2, but for Dmm-sna, Dmm-sa, and Dmm-mna as a function of Dmm-ma. BL06 method was used to calculate Dmm. (b) Scatterplot of Dmm-ma and Dmm-sa calculated using the CPI-mD method as a function of Dmm-ma and Dmm-sa, respectively, calculated using the BL06 method. The black line is 1:1. Dmm-sna, Dmm-sa, Dmm-mna, and Dmm-ma differ by less than 5%.

  • View in gallery

    (a) As in Fig. 2, but for υm-sna, υm-sa, and υm-mna as a function of υm-ma. BL06 method was used to calculate υm. (b) Scatterplot of υm-ma and υm-sa calculated using the CPI-mD method as a function of υm-ma and υm-sast, respectively, calculated using the BL06 method. The black line is 1:1. Terms υm-sna, υm-sa, υm-mna, and υm-ma differ by less than 5%.

  • View in gallery

    (a) As in Fig. 2, but for re-sna, re-sa, and re-mna as a function of re-ma. BL06 method was used to calculate re. (b) Scatterplot of re-ma and re-sa calculated using the CPI-mD method as a function of re-ma and re-sa, respectively, calculated using the BL06 method. The black line is 1:1. Terms re-sna, re-sa, re-mna, and re-ma differ by less than 5%.

  • View in gallery

    (a) Mean narrowband ω0sa, ω0sna, ω0ma, and ω0mna as a function of wavelength λ for (b) gsa, gsna, gma, and gmna as a function of λ. Error bars denote one standard deviation about the mean. The difference between the four different versions of ω0 and g is less than 0.01.

  • View in gallery

    (a) Mean narrowband ω0sa, ω0sna, ω0ma, and ω0mna as a function of wavenumber υ for infrared wavelength. (b) Terms gsa, gsna, gma, and gmna as a function of υ. Error bars denote one standard deviation about the mean. The difference between the four different versions of ω0 and g is less than 0.01.

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An Assessment of the Impact of Antishattering Tips and Artifact Removal Techniques on Bulk Cloud Ice Microphysical and Optical Properties Measured by the 2D Cloud Probe

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  • 1 Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, Urbana, Illinois
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Abstract

A recent study showed that the ratio of the number of distribution functions derived from 2D cloud probes (2DCs) with standard tips to those with antishatter tips used during the 2008 Indirect and Semidirect Aerosol Campaign (ISDAC) and Instrumentation Development and Education in Airborne Science 2011 (IDEAS-2011) was greater than 1 for ice crystals with maximum dimension D < 500 μm. To assess the applicability of 2DC data obtained without antishatter tips previously used in parameterization schemes for numerical models and remote sensing retrievals, the impacts of artifacts on bulk microphysical and scattering properties were examined by quantifying differences between such properties derived from 2DCs with standard and antishatter tips, and with and without the use of shatter detection algorithms using the ISDAC and IDEAS-2011 data. Using either modified tips or algorithms changed the quantities dominated by higher-order moments, such as ice water content, bulk extinction, effective radius, mass-weighted terminal velocity, median mass diameter, asymmetry parameter, and single-scatter albedo, at wavenumbers from 5 to 100 cm−1 and wavelengths of 0.5–5 μm by less than 20%. This is significantly less than the fractional changes quantities dominated by lower-order moments, such as number concentration. The results suggest that model parameterizations and remote sensing techniques based on higher-order moments of ice particle size distributions obtained in conditions similar to those sampled during IDEAS-2011 and ISDAC derived from 2DCs are not substantially biased by shattered remnants.

Corresponding author address: Robert Jackson, Dept. of Atmospheric Sciences, University of Illinois at Urbana–Champaign, 105 S. Gregory St., Urbana, IL 61801. E-mail: rjackso2@illinois.edu

Abstract

A recent study showed that the ratio of the number of distribution functions derived from 2D cloud probes (2DCs) with standard tips to those with antishatter tips used during the 2008 Indirect and Semidirect Aerosol Campaign (ISDAC) and Instrumentation Development and Education in Airborne Science 2011 (IDEAS-2011) was greater than 1 for ice crystals with maximum dimension D < 500 μm. To assess the applicability of 2DC data obtained without antishatter tips previously used in parameterization schemes for numerical models and remote sensing retrievals, the impacts of artifacts on bulk microphysical and scattering properties were examined by quantifying differences between such properties derived from 2DCs with standard and antishatter tips, and with and without the use of shatter detection algorithms using the ISDAC and IDEAS-2011 data. Using either modified tips or algorithms changed the quantities dominated by higher-order moments, such as ice water content, bulk extinction, effective radius, mass-weighted terminal velocity, median mass diameter, asymmetry parameter, and single-scatter albedo, at wavenumbers from 5 to 100 cm−1 and wavelengths of 0.5–5 μm by less than 20%. This is significantly less than the fractional changes quantities dominated by lower-order moments, such as number concentration. The results suggest that model parameterizations and remote sensing techniques based on higher-order moments of ice particle size distributions obtained in conditions similar to those sampled during IDEAS-2011 and ISDAC derived from 2DCs are not substantially biased by shattered remnants.

Corresponding author address: Robert Jackson, Dept. of Atmospheric Sciences, University of Illinois at Urbana–Champaign, 105 S. Gregory St., Urbana, IL 61801. E-mail: rjackso2@illinois.edu

1. Introduction

In situ aircraft observations of the ice crystal number distribution function N(D) as a function of maximum dimension D are conventionally derived from in situ aircraft probes. However, as shown by Gardiner and Hallett (1985), Gayet et al. (1996), Field et al. (2003, 2006), Korolev and Isaac (2005), Heymsfield (2007), McFarquhar et al. (2007b, 2011), Jensen et al. (2009), Zhao et al. (2011), Lawson (2011), Febvre et al. (2012), Korolev et al. (2011, 2013a,b), and Jackson et al. (2014), the shattering of large ice crystals on the tips or inlets of such probes can cause significant overestimates in N(D). The impact of the shattering on N(D) is especially problematic for crystals with D < 500 μm and in estimates of the total number concentration NT. Thus, any parameterization or use of such data requiring accurate estimates of NT may provide biased or misleading results. However, many schemes also make use of estimates of quantities that are derived from higher-order moments of N(D), and the degree to which these quantities are biased by shattering is not well established. Examples of such quantities include the ice water content (IWC), ice crystal effective radius (re), visible extinction (β), mass-weighted terminal velocity (υm), and median diameter weighed by number (Dm) and mass (Dmm). Wavelength-dependent properties such as single-scatter albedo ωo and asymmetry parameter g may also be biased by shattering. All of these properties can be derived or estimated from in situ aircraft observations of N(D).

These quantities are necessary for the development of model parameterizations of sedimentation and radiative effects, for the development and evaluation of remote sensing retrieval schemes of bulk microphysical parameters, and for understanding processes occurring in ice and mixed-phase clouds. For example, ωo and g used in satellite retrieval algorithms are parameterized in terms of re derived from in situ observations (Baum et al. 2005a,b, 2007, 2011). In situ estimates of IWC, Dmm, and υm are used to evaluate the Doppler radar retrievals of ice clouds (i.e., Deng and Mace 2006) and to determine ice mass flux. The representation of scattering and absorption of solar and infrared radiation used in general circulation models depends on knowledge of β, ωo, and g as a function re (i.e., Fu 1996), which is again based on measurements of N(D). Table 1 summarizes a list of applications for which estimates of bulk parameters based on in situ observations have been used and provides references for previous studies using bulk properties derived from in situ measurements of N(D).

Table 1.

Examples of products developed using in situ aircraft observations of ice clouds.

Table 1.

Uncertainties in N(D) can translate into uncertainties in representations of sedimentation and single-scattering properties in models, which in turn affects model evolution. For example, Mitchell et al.’s (2008) global model simulations showed that increasing the number of ice crystals with D < 150 μm induced an upper-tropospheric warming of 3 K and a total cloud forcing of −5 W m2 in the tropics through an increase of cirrus cloud coverage compared to a control simulation. On the other hand, Boudala et al.’s (2007) simulation, including contributions of crystals with D < 150 μm, had a net radiative forcing of 2.4 W m−2 greater than that of a simulation where such contributions were excluded. Further, McFarquhar et al. (2003) showed that decreasing re in a parameterization scheme affected the vertical profile of radiative forcing, which in turn impacted low cloud cover, changing the shortwave radiative forcing by up to 25 W m−2. Similar studies need to be conducted where the assumed uncertainties in bulk parameters are more closely tied to uncertainties associated with observations.

The impact of ice crystal shattering on IWC, β, υm, re, Dm, Dmm, ω0, and g is investigated in this paper. Following Korolev et al. (2013b) and Jackson et al. (2014) the impact of two different methodologies used to reduce the role of shattered artifacts on the calculated bulk parameters is examined:

  1. algorithms based on the time between which particles are detected in the sample volume (Field et al. 2003, 2006) and based on the numbers, sizes, and gaps between fragments in a single image recorded by probes (Korolev and Isaac 2005) that identify shattered artifacts
  2. two-dimensional cloud probes (2DCs) tips modified to deflect most artifacts generated by the shattering of large ice crystals away from the sample volume (Korolev and Isaac 2005; Korolev et al. 2011; Lawson 2011).

Although previous studies have investigated the relative importance of algorithms and modified tips on N(D) and NT, they have not thoroughly examined the effects of algorithms or modified tips on the derivation of υm, re, Dm, Dmm, ω0, and g. In this study, data from flights in which 2DCs with both standard and modified tips were installed on the same aircraft are used to determine the contributions of particles identified as shattered artifacts to the IWC, β, υm, re, Dm, Dmm, ω0, and g derived from 2DC data. This is investigated using measurements of particles with 125 μm < D < 3.2 mm acquired by 2DCs installed on the National Research Council’s (NRC) Convair-580 during the 2008 Indirect and Semidirect Aerosol Campaign (ISDAC) and the National Science Foundation (NSF)/National Center for Atmospheric Research’s (NCAR) C-130 during IDEAS-2011. As described by Jackson et al. (2014), three sorties were conducted in two deep precipitating storms during IDEAS-2011, and in a multilayer mixed-phase stratocumulus during ISDAC. Further details on the meteorology and aircraft maneuvers used are given in section 2 of Jackson et al. (2014).

The remainder of the paper is organized as follows. Section 2 highlights the instrumentation used and describes how IWC, β, υm, re, Dm, Dmm, ω0, and g were derived from N(D). The effect of the modified tips and shattering removal algorithms on the derivation of IWC, β, υm, re, Dm, Dmm, ω0, and g is discussed in section 3. The principal findings of the study are summarized in section 4.

2. Instrumentation, data processing, and derivation of bulk properties

Instrumentation and data processing

Details of the instrumentation on the NRC Convair-580 and NSF/NCAR C-130 and the methods used to derive N(D) are given in Jackson et al. (2014). Only the most important details are summarized here. On all three sorties, a 2DC with standard tips was mounted immediately adjacent to a 2DC with modified tips in order to minimize any effect of cloud inhomogeneities over larger spatial scales on the probe intercomparisons. As in Jackson et al. (2014) and following Cober et al. (2001), McFarquhar and Cober (2004), McFarquhar et al. (2007c), and Jackson et al. (2012), cloud phase was determined using the change in voltage from the Rosemount icing probe, the standard deviation of the forward scattering spectrometer probe/cloud droplet probe size distribution (SD), and manual inspection of 2DC/cloud imaging probe/cloud particle imager (CPI) images. Only data from ice phase clouds were used in this study.

The 2DC data were processed using the University of Illinois algorithm outlined in section 2 of Jackson et al. (2014). Shattered artifacts were subsequently removed by fitting the normalized frequency distribution of the particle interarrival time Δt to a bimodal Poisson probability density function :
e1
where τ1, τ2 represent the Δt for the natural and shattered particle modes, respectively; and S represents the relative contribution of the shattered particle mode to . Particles with Δts < 2τ2 were classified as shattered artifacts. The initial particle arriving before a shattered artifact, which frequently has Δts > 2, was also classified as a shattered artifact. To account for natural particles that may be removed by excluding particles with Δts < 2τ2, the N(D) is multiplied by (Field et al. 2006). Details are given in section 3 of Jackson et al. (2014).
A number of different bulk parameters were computed from N(D). The area ratio is the cross-sectional area of a particle divided by the area of a circle with the same D (McFarquhar and Heymsfield 1996). It was used in the calculation of β given by
e2
where is the extinction efficiency, and is the ice crystal number distribution function for bin j with maximum dimension midpoint , width , and area ratio midpoint . For particles with D > 125 μm at visible wavelengths, ≈ 2, since geometric optics applies (Um and McFarquhar 2007). Thus, β = 2Ac, where Ac is the total cross-sectional area estimated from the two-dimensional images of particles measured by the probe.
To estimate IWC, information about the relationship between crystal mass m and D, which depends on ice crystal habit, is required. Following Jackson et al. (2012), two different techniques were used for estimating IWC. One method, CPI-mD, is derived from IWCCPI-mD using
e3
where fk(Dj) is the fraction of crystals in the bin centered at Dj having crystal habit k; αk and βk are habit-dependent coefficients (listed in Table A1) that define the mass of an individual crystal m = αkDj βk; and N(Dj) is the number distribution function for bin j with midpoint Dj and width ΔDj. Only contributions from crystals with > 0.2 were included. For 30 April 2008 and 1 November 2011, the 2.3-μm-resolution CPI images were used to determine fk(Dj) using the habit classification scheme of Um and McFarquhar (2011). Because the CPI has a smaller sample volume than the 2DC or CIP, the averaging period of 60 s required to obtain a statistically significant sample was larger than the 10-s period required for the 2DC, and hence the habit distributions were applied to each of the 2DC/CIP size distributions occurring within the CPI averaging period. The three-view CPI (3V-CPI) was not installed on the NSF/NCAR C-130 on 25 October 2011, so fk(Dj) were derived from the 2DC data using the Holroyd (1987) technique for that day.
A second method for computing IWC used the cross-sectional mass–area relation of Baker and Lawson (2006, hereinafter BL06) to determine the mass of each particle from the area measured by the optical array probes. If the mass calculated by this method was greater than that of an ice sphere with the same maximum dimension, then the ice sphere mass was used instead. IWCBL06 is given by
e4
where a = 0.115 mg mm−2.436.

Terms Dm and Dmm are defined as the median number and median mass dimension, respectively. Because of the uncertainty in the concentrations of particles with D > 1.6 mm during ISDAC from the use of the 32 photodiode 2DC, particles with 1.6 < D < 3.2 mm were not considered in the calculation of Dmm and IWC for ISDAC but were for IDEAS-2011. Since particle mass scales approximately with the square of D (e.g., Brown and Francis 1995), Dmm and IWC were somewhat affected by the absence of large particles in the ISDAC calculations.

There are multiple definitions of re for distributions of ice crystals (McFarquhar and Heymsfield 1998). Fu’s (1996) definition of re,
e5
was used here because the scattering properties of ice crystals are closely linked to the ratio of mass to cross-sectional area (McFarquhar and Heymsfield 1998). Following McFarquhar and Black (2004) and others, the mass-weighted fall speed υm was determined as
e6
where γk and δk are habit-dependent coefficients from empirical fits of ice crystal fall speed υ to Dj as υ = αkDj βk from Locatelli and Hobbs (1974) and Mitchell (1996).
The narrowband single-scatter albedo ω0 and asymmetry parameter g were derived following McFarquhar et al. (2002) and Baum et al. (2005a,b) as
e7
and
e8
where gik is the asymmetry parameter, is the single-scatter albedo, and is the scattering cross section of a particle with habit k and maximum dimension Dj at wavelength . Libraries of gk, , and for eight idealized shapes (droxtals, hexagonal plate, hollow and solid columns, four- and six-bullet rosettes, and smooth and rough aggregates) from Yang et al. (2000, 2003) were used to calculate these properties for 56 solar wavelengths. For infrared wavelengths, gik, , and were taken from Yang et al.’s (2005) libraries for seven idealized shapes (aggregates, bullet rosettes, droxtals, hollow and solid columns, plate, and spheroid) and 49 wavenumbers from 100 to 3250 cm−1. The Yang et al. (2000, 2005) libraries did not always include the same habits used in the CPI and 2DC habit classification schemes. In this case, idealized habits whose shapes were closest to the morphological features of observed crystals were used. Table 2 lists the mapping between the CPI/Holroyd shapes and the corresponding Yang et al. (2000, 2005) shapes.
Table 2.

List of m–D, υ–D relationships, and assumed ice crystal model used in Eqs. (3), (5), (6), (7), and (8).

Table 2.

3. Contributions of shattered particles to bulk parameters

In this section, the differences in bulk microphysical parameters derived from 2DCs with standard and modified tips and processed with and without shattered artifact removal algorithms are compared. Data from both IDEAS-2011 and ISDAC are used. Subscript s (m) is used to denote when standard (modified) tips were used, and superscript a (na) denotes when algorithms were (were not) used to derive β, IWC, υm, re, Dm, and Dmm from the 2DC probes. For example, βsa is the visible extinction from the 2DC with standard tips calculated using shattered artifact removal algorithms. A list of symbols, subscripts, and superscripts used is provided in Table A1 in the appendix.

Figure 1 shows the mean cumulative area distribution from the 2DC Asa(D), Asna(D), Ama(D), and Amna(D) for ISDAC and IDEAS-2011. Jackson et al. (2014) showed that on average shattered artifacts contributed 71% to N(D) for particles with 125 < D < 300 μm and 63% for particles 300 < D < 500 μm during ISDAC and IDEAS-2011, and that their contribution was higher in the presence of graupel. In Figs. 1a and 1b, Asna(D = 500 μm) is 0.1 mm2 L−1 (0.05 mm2 L−1) higher than Asa(D = 500 μm) for ISDAC (IDEAS-2011). Even though this means shattered artifacts contributed at least 15% (5%) to the cumulative area distribution at 500 μm, the fractional amount of shattered artifacts contributed to Ac is much less than to NT. In fact, particles with D < 500 μm contributed only 25% (10%) to Ac, whereas they contributed 79% (59%) to NT during ISDAC (IDEAS-2011). In the remainder of this section, it is shown that shattered artifacts make smaller contributions to bulk cloud and single-scattering properties that are dominated by the higher moments.

Fig. 1.
Fig. 1.

Term A(D) from the 2DCs during (a) ISDAC and (b) IDEAS-2011. Subscript s (m) denotes the use of standard (modified) tips, and superscript a (na) when algorithms were (were not) applied as indicated in legend. Mean Ac distribution is indicated in the legend. The Asna(D = 500 μm) is 0.1 mm2 L−2 (0.05 mm2 L−2) higher than Asa(D = 500 μm) for ISDAC (IDEAS-2011).

Citation: Journal of Atmospheric and Oceanic Technology 31, 10; 10.1175/JTECH-D-14-00018.1

It should also be noted that Asa(D) < Ama(D) for D > 1.2 mm in Fig. 1b. At first this seems counterintuitive. But, the sampling of different particle populations by the two distinct probes could easily cause this difference. For a 10-s average, the error due to statistical sampling, proportional to the square root of the actual number of particles measured, was 15.9% on average compared to the 7.5% difference between Asa(D = 3.2 mm) and Ama(D = 3.2 mm) in Fig. 1a. For particles with D < 500 μm, Asa(D = 500 μm) is 0.05 mm2 L−1 higher than Amna(D = 500 μm) for ISDAC and equal to Amna(D = 500 μm) for IDEAS-2011, which is consistent with the modified tips removing at least as many particles as the algorithms. It is also possible that the accidental removal of large, real particles by the shattered artifact removal algorithm is causing this difference.

Figure 2 shows βsa, βsna, and βmna as functions of βma. There is a strong (R = 0.99) correlation between all variables. Term βsna is 1.14 times higher than βmna, while βsna is 1.27 times higher than βsa, and βsna is 1.22 times higher than βma. These differences indicate that β was lower on average when derived from SDs measured by the standard tips and processed using the shatter-detecting algorithms than for SDs measured by the probe with modified tips. However, as explained above, this result is not inconsistent with Jackson et al.’s (2014) claim that the tips are more effective than the algorithms at removing artifacts because the contribution of the artifacts to β are smaller than the differences associated with statistical samples of particles from the same population.

Fig. 2.
Fig. 2.

Scatterplot of βsna, βsa, and βmna as a function of βma. Solid lines are the best fit of quantity on the y axis to quantity on the x axis, with coefficients of fit and regression coefficient indicated in legend. The black line is 1:1. In general, βsna > βmna > βma > βsa.

Citation: Journal of Atmospheric and Oceanic Technology 31, 10; 10.1175/JTECH-D-14-00018.1

Figure 3a shows scatterplots of IWCsa, IWCsna, and IWCmna as functions of IWCma derived using the BL06 method. There is a strong (R = 0.99) correlation between all variables. Term IWCsna is 25.7% higher than IWCsa, while IWCsna is 1.12 times higher than IWCmna. Term IWCsna is 1.22 times higher than IWCma. As for the trends in β noted in Fig. 2, the comparisons of IWC at first glance seem surprising in that IWC is lower for SDs measured by the standard probes with the artifact algorithms applied than for the SDs measured by the modified probes without algorithms. However, as explained above, the differences between IWCs is mainly associated with varying numbers of large crystals with D > 1.2 mm measured by the two probes, since the concentrations of these large particles have the greatest uncertainty because of counting statistics (McFarquhar et al. 2007a,c). Since crystals with D > 500 μm are not likely shattered artifacts, the trends in Fig. 3a are not inconsistent with Jackson et al.’s (2014) finding that modified tips are more effective than algorithms at removing shattered artifacts.

Fig. 3.
Fig. 3.

(a) As in Fig. 2, but for IWCsna, IWCsa, and IWCmna as a function of IWCma. BL06 method was used to calculate IWC. (b) Scatterplot of IWCma and IWCsa calculated using the CPI-mD method as a function of IWCma and IWCsa, respectively, calculated using the BL06 method. The black line is 1:1. In general, IWCsna > IWCmna > IWCma > IWCsa.

Citation: Journal of Atmospheric and Oceanic Technology 31, 10; 10.1175/JTECH-D-14-00018.1

Another uncertainty in calculating IWC is the poorly known relationship between particle mass and D. Figure 3b shows a scatterplot of IWCma, derived using the “CPI-mD” method as a function of IWCma, derived using the BL06 method. Term IWCsa, derived using the CPI-mD method as a function of IWCsa, derived using the BL06 method, is also shown. The slope of the best fit of IWCma, derived using the CPI-mD method to IWCma, derived using the BL06 method, is 0.47 and the R is only 0.78. Thus, there is a greater amount of scatter and more discrepancy in the values in Fig. 3b than in Fig. 3a. Thus, the contribution of particles identified as shattered artifacts to IWC is less than the uncertainty in IWC associated with the use of varying mD relations for the conditions sampled during ISDAC and IDEAS-2011, showing shattered artifacts are not the largest source of uncertainty in determining IWC.

Figure 4 shows scatterplots of Dm-mna, Dm-sna, and Dm-sa as functions of Dm-ma. On average, Dm-sna is 53% of Dm-mna. Meanwhile, Dm-sna is 71% of Dm-sa, and Dm-sna is 43% of Dm-sa, on average. This shows that the use of modified tips changes Dm more than the use of shattered artifact removal algorithms. The lack of correlation (R = 0.16) and up to a factor of 5 difference between Dm-sa and Dm-ma in Fig. 4 show that it is critical that both modified tips and shattered artifact algorithms are used when deriving Dm from 2DCs. Thus, parameterizations of Dm derived from 2DC data in ice phase conditions, such as those of Kristjánsson et al. (2000) and Ivanova et al. (2001), may need to be revised using data from 2DCs with modified tips and shattered artifact removal algorithms. It is not surprising that Dm is more sensitive to shattered artifacts and less sensitive to larger particles than β or IWC, as it is weighted more toward lower moments of N(D) and, consequently, by smaller particles.

Fig. 4.
Fig. 4.

As in Fig. 2, but for Dm-mna, Dm-sa, and Dm-sna as a function of Dm-ma. Solid lines are the best fit of quantity on the y axis to quantity on the x axis. The black line is 1:1. In general, Dm-sna > Dm-sa > Dm-mna > Dm-ma.

Citation: Journal of Atmospheric and Oceanic Technology 31, 10; 10.1175/JTECH-D-14-00018.1

Figures 5a shows Dmm-sa, Dmm-sna, and Dmm-mna as functions of Dmm-ma, calculated using mass derived from the BL06 method. Term Dmm-sna is 99% of Dmm-sa, while Dmm-sna is 98% of Dmm-mna on average. To test the sensitivity of Dmm to the mD relationship, Fig. 5b shows a scatterplot of Dmm-ma derived using the CPI-mD method as a function of Dmm-ma derived using the BL06 method. The slopes of the best fit of Dmm-ma calculated using the CPI-mD method to Dmm-ma using the BL06 method of 0.75 is lower than 0.95 for the fit of Dmm-sa to Dmm-ma shown in Fig. 5a. The R values of 0.83 for this best fit are lower than all of the R values of 0.89 or greater for the fits in Fig. 5a, indicating a greater amount of scatter in Fig. 5b than in Fig. 5a. Therefore, changing the mass calculation techniques impacts Dmm more than does applying shattered artifact algorithms or using modified tips. Thus, for conditions sampled during ISDAC and IDEAS-2011, the impact of shattering is not the largest uncertainty for the calculation of Dmm.

Fig. 5.
Fig. 5.

(a) As in Fig. 2, but for Dmm-sna, Dmm-sa, and Dmm-mna as a function of Dmm-ma. BL06 method was used to calculate Dmm. (b) Scatterplot of Dmm-ma and Dmm-sa calculated using the CPI-mD method as a function of Dmm-ma and Dmm-sa, respectively, calculated using the BL06 method. The black line is 1:1. Dmm-sna, Dmm-sa, Dmm-mna, and Dmm-ma differ by less than 5%.

Citation: Journal of Atmospheric and Oceanic Technology 31, 10; 10.1175/JTECH-D-14-00018.1

Figure 6a shows υm-sa, υm-sna, and υm-mna as functions of υm-ma, calculated using mass derived from the BL06 method. Term υm-sna is 96% of υm-sa, while υm-sna is 94% of υm-mna on average. To test the sensitivity of υm on the m–D relationship, Fig. 6b shows a scatterplot of υm-ma derived using the CPI-mD method as a function of υm-ma derived using the BL06 method. The υm-ma derived using the BL06 method is 97% of υm-ma derived using the CPI-mD method on average. The υm-sa derived using the BL06 method is 100% of υm-sa derived using the CPI-mD method on average. Therefore, the use of modified tips, algorithms, and a different m–D relationship all change υm by similar amounts for the ISDAC and IDEAS-2011 data, with none of the changes invoking more than a 5% difference in υm on average.

Fig. 6.
Fig. 6.

(a) As in Fig. 2, but for υm-sna, υm-sa, and υm-mna as a function of υm-ma. BL06 method was used to calculate υm. (b) Scatterplot of υm-ma and υm-sa calculated using the CPI-mD method as a function of υm-ma and υm-sast, respectively, calculated using the BL06 method. The black line is 1:1. Terms υm-sna, υm-sa, υm-mna, and υm-ma differ by less than 5%.

Citation: Journal of Atmospheric and Oceanic Technology 31, 10; 10.1175/JTECH-D-14-00018.1

Figure 7a shows re-sa, re-sna, and re-mna, as functions of re-ma, calculated using mass derived from the BL06 method. Term re-sna is 98% of re-sa and re-sna is 97% of re-mna on average. Therefore, modified tips and algorithms change re by less than 5% for the ISDAC and IDEAS-2011 data. Figure 7b shows a scatterplot of re-ma derived using the CPI-mD method as a function of re-ma derived using the BL06 method. The re-ma derived using the BL06 method is 74% of re-ma derived using the CPI-mD method on average. In addition, R for the best fit of re-ma derived using the BL06 method to re-ma derived using the CPI-mD method is equal to 0.10, suggesting there is essentially no correlation between the two calculations of re-ma. Because re is proportional to IWC/β, the scatter in Fig. 7b is related to the scatter in IWC in Fig. 3b caused by uncertainties in the conversion of two-dimensional particle images into three-dimension volumes and mass. Therefore, changing mass calculation techniques has more of an impact on re than does the application of shattered artifact algorithms or the use of modified tips. Finally, it should be noted that although no true values of Dm, Dmm, re, or υm are known because shattered artifacts may still make contributions even with the use of algorithms and modified tips, the preceding analysis gives some indication of the expected uncertainties on these quantities due to shattering.

Fig. 7.
Fig. 7.

(a) As in Fig. 2, but for re-sna, re-sa, and re-mna as a function of re-ma. BL06 method was used to calculate re. (b) Scatterplot of re-ma and re-sa calculated using the CPI-mD method as a function of re-ma and re-sa, respectively, calculated using the BL06 method. The black line is 1:1. Terms re-sna, re-sa, re-mna, and re-ma differ by less than 5%.

Citation: Journal of Atmospheric and Oceanic Technology 31, 10; 10.1175/JTECH-D-14-00018.1

Figures 8 and 9 show the mean and standard deviation of ω0sna, ω0sna, ω0ma, ω0mna, gsa, gsna, gma, and gmna as functions of wavelength and wavenumber. Figures 8a and 9a show that ω0sa, ω0sna, and ω0mna are all greater than ω0ma by at most 0.005. In addition, gsa, gsna, and gma are all greater than gma by at most 0.01 in Fig. 8b and less than gma by at most 0.01 in Fig. 9b. In Eqs. (7) and (8), ω0 and g are weighted by the scattering cross section, which is related to the particle cross-sectional area. Therefore, ω0 and g are weighted toward higher-order moments of N(D) and larger particles, so it is not surprising that shattered artifacts contribute fractionally less to ω0 and g, on the order of 1%, than they do to number concentration and Dm. These differences are much less than the uncertainties associated with dominant crystal habits or the choice of size distribution (Macke et al. 1998; McFarquhar et al. 1999; Um and McFarquhar 2007) or the presence of surface roughness (Yang et al. 2013). Further, the uncertainties in these single-scattering quantities derived for the cloud conditions sampled on these three sorties during ISDAC and IDEAS-2011 are less than the certainty with which they need to be known from a climate perspective (Vogelmann and Ackermann 1995; McFarquhar et al. 2002).

Fig. 8.
Fig. 8.

(a) Mean narrowband ω0sa, ω0sna, ω0ma, and ω0mna as a function of wavelength λ for (b) gsa, gsna, gma, and gmna as a function of λ. Error bars denote one standard deviation about the mean. The difference between the four different versions of ω0 and g is less than 0.01.

Citation: Journal of Atmospheric and Oceanic Technology 31, 10; 10.1175/JTECH-D-14-00018.1

Fig. 9.
Fig. 9.

(a) Mean narrowband ω0sa, ω0sna, ω0ma, and ω0mna as a function of wavenumber υ for infrared wavelength. (b) Terms gsa, gsna, gma, and gmna as a function of υ. Error bars denote one standard deviation about the mean. The difference between the four different versions of ω0 and g is less than 0.01.

Citation: Journal of Atmospheric and Oceanic Technology 31, 10; 10.1175/JTECH-D-14-00018.1

4. Discussion and conclusions

In situ aircraft measurements of ice crystal number distribution function N(D) were acquired by a 2DC with standard tips immediately adjacent to a 2DC with tips modified to reduce the number of shattered fragments entering the sample volume on the NRC Convair-580 during ISDAC and on the NSF/NCAR C-130 during IDEAS-2011. Extending the study of Jackson et al. (2014), the impact of the tips and artifact removal algorithms (Korolev and Isaac 2005; Field et al. 2006) on a number of bulk cloud properties, such as bulk extinction β, ice water content IWC, asymmetry parameter g, single-scatter albedo ω0, median diameter Dm, median mass diameter Dmm, effective radius re, and mass weighted fall speed υm, derived from the number distribution function N(D) was examined. The principal conclusions of this study are as follows:

  1. The use of modified tips reduced β from 2DC data by 15%, while the use of shattered artifact removal algorithms reduced β by 25%. Shattered artifacts contributed up to 15% to the total cross-sectional area. The β derived from the 2DC with standard tips with the use of shattered artifact removal algorithms was lower than that from modified tips with the use of shattered artifact removal algorithms, most likely due to differences in statistical sampling of particles with D > 1.2 mm by the different probes.
  2. The IWC, re, and Dmm changed by less than 20% when either shattered artifact removal algorithms or modified tips were used. These changes were less than the up to 60% change in IWC, re, and Dmm when changing the assumed relationship between mass and D. The large amount of scatter in the relationship between IWC, re, and Dmm calculated from mass derived from habit-dependent m–D relationships versus those calculated from mass from the BL06 method shows that the error in IWC, re, and Dmm induced by shattering is not the primary uncertainty in deriving these quantities.
  3. Term υm, changed by less than 20% when either shattered artifact removal algorithms or modified tips were used and when changing the assumed relationship between mass and D.
  4. Term Dm increased by an average of 43% when modified tips were used in place of standard tips. When only shattered artifact removal algorithms were used, the increase was 30%. There was also a large amount of scatter in the relationship between Dm from the standard tips and Dm from the modified tips whether algorithms were used, indicating that both the algorithms and modified tips must be used in deriving Dm for the conditions encountered during ISDAC and IDEAS-2011.
  5. The use of modified tips and shattered artifact removal algorithms changed g and ω0 by at most 0.01 and 0.005, respectively—less than how well they currently need to be known for climate parameterizations.

The comparisons made in this paper can be used as an estimate of the bias due to shattered artifacts in bulk parameters derived from 2DCs in the cloud conditions sampled during one sortie of ISDAC and two sorties of IDEAS-2011. Despite the differences in the electronics of the 2DCs used and the sampling conditions encountered during IDEAS-2011 and ISDAC, there are common trends between both projects. Therefore, the determined differences between quantities calculated between probes with standard and modified tips, and those processed with and without artifact removal algorithms provides some guidance on the bias that shattering induces on various bulk cloud properties. However, the results of this study cannot necessarily be generalized to determine the contribution of shattered artifact on bulk parameters any 2DC used in any cloud condition.

The results of this study provide guidance on interpreting biases in data collected prior to the development of the modified tips and processed before the development of shatter-detecting algorithms. In general, biases induced by shattering on quantities dominated by higher-order moments (e.g., β, IWC, Dmm, υm) are less than those in quantities dominated by lower-order moments (e.g., N and Dm). This implies that historical observations of and parameterizations using β, g, IWC, Dmm, and υm derived from particle size distributions with N(D > 125 μm) from 2DCs with standard tips might still be acceptable for use, provided the differences noted here are less than the accuracy at which this quantities need to be known. However, historical observations and parameterizations of N and Dm derived from 2DCs with standard tips are likely to be contaminated by the large amounts of shattered artifacts indicated here and in Jackson et al. (2014), and therefore caution is advised in the use of these parameters. Future studies should concentrate on conducting similar comparisons with data acquired in ice clouds at colder temperatures (e.g., <−40°C), in a wider range of aircraft-operating parameters (e.g., higher true air speeds), in a wider range of crystal habits (e.g., more rimed particles and graupel) with a wider variety of probes (e.g., 2D stereo probe), and with different designs of probe tips for deflecting shattered particles from the probe sample volume (e.g., Korolev et al. 2013a).

Acknowledgments

This work was supported by the Office of Biological and Environmental Research (BER) of the U.S. Department of Energy (DOE) Grants DE-SC00001279 and DE-SC0008500, as well as the National Science Foundation (NSF) Grant AS-1213311 and the NCAR Advanced Study Program. NCAR is supported by the NSF. Data were obtained from the Atmospheric Radiation Measurement Program archive, sponsored by the U.S. DOE Office of Science, BER Environmental Science Division. We would like to acknowledge the operational, technical, and scientific support provided by NCAR’s Earth Observing Laboratory, sponsored by NSF. We are grateful for the comments of three anonymous reviewers, which considerably improved the quality of this manuscript.

APPENDIX

Table A1 provides a list of symbols, superscripts, and subscripts used in this manuscript.

Table A1.

List of symbols, superscripts, and subscripts used in this paper.

Table A1.

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