METR 6613
Project #3
Brett Roberts
2011-11-28
Part (1)
A hydrometeor classification algorithm was applied to the 0.5° elevation scan of one volume from
KOUN. For bins identified as rain, DSD retrieval was performed. Both exponential (Eq. 1) and constraintgamma (Eq. 2) parameters were retrieved.
𝑁(𝐷) = 𝑁0 𝑒 −Λ𝐷
(1)
𝑁(𝐷) = 𝑁0 𝐷 𝜇 𝑒 −Λ𝐷
(2)
The retrieval procedure was as follows:
1. The slope parameter Λ was inferred from the value of ZDR. To facilitate this, a table of ZDR  Λ
values was created in advance of the retrieval. This table specifies ZDR on the Λ interval [0.1,
30.0] mm-1 at increments of 0.1 mm-1, and the resulting ZDR values were used for interpolation to
the ZDR observed by KOUN.
2. For the Constraint-Gamma model, the shape parameter µ was determined as a function of Λ
only, as in Zhang et al. (2001).
3. The intercept parameter N0 was calculated from Zh and the inferred Λ. Unlike the slope
parameter, N0 differs between the two DSD models at any given gate. This is necessary in order
to account for the influence of µ in the constraint-gamma model.
The slope parameter Λ was plotted over the volume (Fig. 1). It is notable that relatively low values
appear in the squall line east of the radar, due to the relatively large drops in that regime. Large drops
are typically associated with lower (less steep) slope parameters.
The intercept parameter N0 was plotted over the volume for the exponential (Fig. 2a) and constraintgamma (Fig. 2b) DSD models.
Following DSD retrieval, rain rate (Fig. 3) and mean drop diameter (Fig. 4) were calculated and plotted at
each gate. Because both quantities are functions of DSD moments (R ~ M3, Dm ~ M4/M3), this
computation was trivial, given the DSD parameters. The calculations for rain rate showed relatively good
agreement between the two DSD models. Mean drop diameter, however, showed some significant
differences. Most notable is that the exponential DSD tended toward extremes more frequently than
the constraint-gamma DSD, with the former showing far more gates with Dm < 1.5 mm. This illustrates
the utility of the constraint-gamma model, as the exponential distribution is known to overestimate the
concentration of very small and very large drops.
Part (2)
A timeseries of Zh and ZDR from KOUN at one gate was used as the basis for retrieval of the DSD
parameters described above. In this case, only the constraint-gamma model was used. After retrieval,
rain rate (Fig. 5), mean diameter (Fig. 6), and total number concentration (Fig. 7) were calculated from
the DSD model. In addition, observed DSD data from a 2DVD was used to calculate and plot these same
quantities.
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METR 6613
Project #3
Brett Roberts
2011-11-28
Agreement between the constraint-gamma values and 2DVD-derived values is excellent for rain rate,
and still quite good for number concentration and mean diameter. The number concentration is not
expected to be highly accurate, since it represents the zero moment, and we are inferring from the sixth
moment (Zh and Zv).
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METR 6613
Project #3
Brett Roberts
2011-11-28
Figure 1. Slope parameter for DSD models.
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METR 6613
Project #3
Brett Roberts
2011-11-28
Figure 2a. Intercept parameter for exponential DSD model.
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METR 6613
Project #3
Brett Roberts
2011-11-28
Figure 2b. Intercept parameter for constraint-gamma DSD model.
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METR 6613
Project #3
Brett Roberts
2011-11-28
Figure 3. Rain rate for exponential (top) and constraint-gamma (bottom) DSD models.
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METR 6613
Project #3
Brett Roberts
2011-11-28
Figure 4. Mean diameter for exponential (top) and constraint-gamma (bottom) DSD models.
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METR 6613
Project #3
Brett Roberts
2011-11-28
Figure 5. Rain rate for observed and constraint-gamma DSDs.
Figure 6. Mean diameter for observed and constraint-gamma DSDs.
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METR 6613
Project #3
Brett Roberts
2011-11-28
Figure 7. Total number concentration for observed and constraint-gamma DSDs.
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