The use of gamma distributions to quantify the dependence of cloud particle size distributions in hurricanes on cloud and environmental conditions

Mascio, Jeana

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https://hdl.handle.net/2142/46624 Copy

Description

Title

The use of gamma distributions to quantify the dependence of cloud particle size distributions in hurricanes on cloud and environmental conditions

Author(s)

Mascio, Jeana

Issue Date

2014-01-16T17:56:34Z

Director of Research (if dissertation) or Advisor (if thesis)

McFarquhar, Greg M.

Department of Study

Atmospheric Sciences

Discipline

Atmospheric Sciences

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

M.S.

Degree Level

Thesis

Keyword(s)

• tropical cyclones
• cloud microphysics
• gamma distribution
• incomplete gamma fit
• hurricane intensity
• North American Maritime Ministry Association (NAMMA)
• in-situ observations
• National Aeronautics and Space Administration (NASA) DC-8
• Two Dimensional Stereo probe
• Precipitation Imaging Probe
• Cloud Imaging Probe
• gamma distribution parameters
• ice parameterization scheme
• mesoscale model
• Atlantic hurricane intensity forecast

Abstract

Mesoscale models that predict the temporal evolution of tropical cyclones (TCs) are sensitive to the representation of cloud microphysical processes through their effect on modeled latent heat release. The cloud parameterizations used in such models make assumptions about the size distributions (SDs) of different ice species, such as cloud ice, graupel, and snow, which have typically not been based on observations obtained in TCs. The representativeness of these parameterizations for TCs is not well known. In this study, observations acquired in tropical storms, depressions and waves during the NASA African Monsoon Multidisciplinary Analyses project with in-situ cloud probes installed on the NASA DC-8 are used to identify snow and graupel particles through measures of particle morphology, and then to define SDs of snow and graupel, and of all ice hydrometeors combined. These SDs are then fit to gamma functions to determine how the intercept (No), shape (μ), and slope (λ) parameters vary with cloud and environmental conditions such as the ice water content (IWC), vertical velocity (w), temperature (T), and TC stage of development. The No, μ, λ solution representing the best fit is determined using a non-linear Levenberg-Marquardt algorithm by forcing three moments of the fit distributions to match as closely as possible the corresponding moments computed from the observed SDs that are truncated between the minimum and maximum dimension detected in the in-situ probes. A volume of equally plausible solutions in No-μ-λ phase space is defined as all solutions whose \chi^2 difference from the observed moments is within some Δ\chi^2 of the minimum \chi^2 for each SD, where Δ\chi^2 is determined as the largest of the minimum \chi^2 for the best fit and the uncertainty in the measured SD due to statistical sampling. Families of SDs are determined for different cloud and environmental conditions (e.g. SDs found in updrafts, downdrafts and stratiform regions for w, for different ranges of IWC and T, and for the differing stages of TC development). There are minor differences in the range of No-μ-λ that characterize the SDs for environmental and cloud conditions, which are visualized by representing the range of possible values as an ellipsoid of equally realizable solutions. The largest differences in ellipsoid volume are found between w families where the calculated volumes vary by an order of magnitude. It is hypothesized that the much smaller sample size of SDs in downdraft and updraft regions compared to stratiform regions caused the differences in volumes. Variation in IWC had the smallest impact on ellipsoid volume, with volumes varying by only 494 cm-4-μμm-1, which is only about an 8.5% difference between the largest and smallest ellipsoids in the IWC families. In the relationship between the most likely μ and No values, for all cloud and environmental conditions, μ increases with No linearly. However, as T decreases, μ decreases for the same No, and as IWC increases, μ increases for the same No. For all cloud and environmental conditions, the most likely value of λ increases with the most likely value of μ until about μ = 6, and thereafter decreases. For the λ-No relation, λ increases with No linearly for all environmental and cloud conditions. The largest difference between elements of families was found for the T families, where when T decreases, λ increases for equal No. There is a wider range of plausible No, μ, and λ values for graupel SDs than for snow SDs because fewer graupel than snow were detected in the NAMMA clouds, leading to greater uncertainty in the graupel SDs, and hence larger Δ\chi^2. The snow SDs and their characterizations are very similar to those for the SDs for all particles because of the small contributions of graupel to the total. To test the impact of the variability in fit parameters characterizing both single SDs and families of SDs, frequency distributions of mass-weighted terminal fall velocities (VT) were derived. Given the uncertainty in the fit parameters for a single SD, VT varied by about 13%. The differences between the ranges of VT determined for the different cloud and environmental conditions were minimal with all having a range between 0.2 and 1 m s-1. The largest difference in averaged VT between families of a specific environmental condition of 0.18 m s-1 (about 42% of the smallest family average VT) was found for variations in T. The average VT for families decreased with decreasing T, which could be from the decrease of particle size with decreasing T.

Graduation Semester

2013-12

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http://hdl.handle.net/2142/46624

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Copyright 2013 Jeana Mascio

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