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Supplementary material
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Applicability of the method to various datasets
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To show the applicability of our method to various datasets, we applied the same method
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to the Hiaper Pole-to-Pole Observations (HIPPO) Global campaign deployments #1-5 [Wofsy et
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al., 2011]. HIPPO Global campaign covers from 87°N to 67°S, sampling both North America
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continent and the central Pacific Ocean. The HIPPO Global campaign provided ~400 hr flight
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time and ~600 vertical transects from the surface to the tropical UT or the extratropical UT/LS.
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Ice crystals were measured by the 2DC ice probe [Korolev et al., 2011] onboard the NSF
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Gulfstream-V aircraft during the HIPPO Global campaign (no ice data were available in
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HIPPO#1). 2DC ice probe has a measurement range of 25–800 µm, which reports ice crystal
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number density (Nc in #/L) and number-weighted mean diameter (Dc in micron). Water vapor
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was measured by the VCSEL hygrometer [Zondlo et al., 2010]. In HIPPO Global campaign, our
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analyses of ISS and ICR are also restricted to T ≤ -40°C, which range from ~4.5 to 14.9 km. The
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ISS and ICR observations are ~8.5 and 4.9 hr, respectively. The overlap between ISS and ICR is
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~3.0 hr.
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The evolution of RHi is illustrated in Supplementary Figure 1. The trend of RHi
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evolution for each phase in Figure S1 agrees well with the trend shown in the main text Figure 2,
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that is, increasing RHi with increasing clear-sky ISSR length during Phase 1, decreasing RHi
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with evolution during ice crystal formation and growth in Phases 2 to 4, and decreasing RHi as
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ICR length decreases during Phase 5. Similarly, the evolution of Nc is illustrated in
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Supplementary Figure 2, where the Nc in Phases 2 to 4 increases with the time evolution as ICRs
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take over the space of ISSRs. Because the 2DC probe measurement range is 25–800 µm, the
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evolution of Dc does not show Dc < 10 µm in the nucleation stage as Figure 3 showed in the
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main text. However, for the later phases, i.e., ice crystal growth stage in Phases 2 to 4, the mean
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value of Dc is relatively constant, which agrees with the converging Dc value in Figure 3. All ice
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crystal evolution trends of HIPPO campaign show that the method is applicable to different
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datasets even though the ice measurements and geographical locations are both different.
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The probability of the five phases is show in Supplementary Figure 3. The probability of
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each phase are comparable with Figure 4 in the main text, which further illustrate the
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applicability of the method in analyzing the time evolution of cirrus clouds using Eulerian
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observations.
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Supplementary references
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Korolev, A. V., E. F. Emery, J. W. Strapp, S. G. Cober, G. A. Isaac, M. Wasey, and D. Marcotte
(2011), Small Ice Particles in Tropospheric Clouds: Fact or Artifact? Airborne Icing
Instrumentation Evaluation Experiment, Bulletin of the American Meteorological Society,
92(8), 967–973, doi:10.1175/2010BAMS3141.1.
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Wofsy, S. C. et al. (2011), HIAPER Pole-to-Pole Observations (HIPPO): fine-grained, globalscale measurements of climatically important atmospheric gases and aerosols.,
Philosophical transactions. A, Mathematical, physical, and engineering sciences,
369(1943), 2073–86, doi:10.1098/rsta.2010.0313.
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Zondlo, M. A., M. E. Paige, S. M. Massick, and J. A. Silver (2010), Vertical cavity laser
hygrometer for the National Science Foundation Gulfstream-V aircraft, Journal of
Geophysical Research, 115(D20), D20309, doi:10.1029/2010JD014445.
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Supplementary Figure 1. Similar to Figure 2 in main text: RHi evolution for the five evolution
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phases. (a) Phase 1; (b) Phases 2, 3 and 4; (c) Phase 5; (d) All five phases. All binning of length
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scale and spatial ratios used the 2i to 2i+1 bins (i = 1, 2 ,3…). All error bars in this study show ±
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one standard deviation.
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Supplementary Figure 2. Similar to Figures 3a and b. Evolution of ice crystal number density
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(Nc) and mean diameter (Dc). The marker colors of yellow, green and blue stand for Phases 2, 3,
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and 4, respectively. The color bar and marker shape are the same as supplementary Figure 1.
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Supplementary Figure 3. Similar to Figure 4 in the main text: (a) the probability of each
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evolution phases and (b) the probability of each bin of spatial ratio Q (Q = ICR/ISSR), both
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normalized by the total 1168 samples.
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