Convective Cell Bounds

Since most convectively active days had several cells occurring at the same time,

the LDAR data for a given day usually contained VHF source point information for a

number of cells. Thus, if a cell met the required criteria, it was necessary to separate the

VHF sources associated with the cell of interest from the plethora of VHF sources that

occurred from all cells within range of the LDAR network. This was performed by

constructing a cylinder around each cell such that VHF sources that fell outside the

bounds of the cylinder would not be associated with the cell of interest (Fig. 17). The

center and radius of each cylinder were constructed based on the ice-ice collisional (or

non-inductive) charging mechanism (Takahashi, 1978). The presence of a sufficient

Fig. 17. 3-D depiction of radar reflectivity, dBZ shown. a) Vertical cross section taken through a cell occurring on 27 June 2001 during peak intensity at 1457 UTC (t = 35 minutes). Shaded cylinder constructed around cell shows bounds of the cell. Cross-section grid box spacing is 4km in the vertical plane and 5km in the horizontal plane. (b) Same as (a), but for cell 1 with vertical cross section taken during peak intensity at 1825 UTC (t = 40) minutes).

typically associated with radar echoes approaching 30-40 dBZ between the -10º C and -

20º C isotherm level (e.g. Dye et al. 1986). Previous studies have also shown that the

main negative charge region typically resides around the level of the -10º C isotherm (e.g.

Krehbiel 1986).

Therefore, the center and radius of each cylinder were based on reflectivity values

at the height of the -10º C isotherm with the center of the cylinder being placed at an

approximate center point of the cell. The radius of each cylinder extended out to the

furthest 20 dBZ contour from the cell’s center in effort to capture the most electrically

active portion of each cell. Fig. 17a shows one of the few cases in which the bounds of

the cell came in close proximity to another cell. However, measures were taken to reduce

the likelihood of VHF sources from neighboring cells from entering the bounds of

another. One such measure incorporated flash origin information from the flash

algorithm to exclude any VHF sources of a flash that did not originate within the

specified bounds of the cell. In addition, the main negative charge regions of both cells

(as inferred by the 20 dBZ echo above the -10° C isotherm) remained at distances greater

than 10 km from one another. Thus, given that flash origins typically occur in close

proximity to the main negative charge region (Proctor 1991), it is unlikely that flashes

from one cell could be associated as a flash from another. However, cells that came

within close proximity of another did so during at least one cell’s dissipating stage, when

no VHF sources were being recorded for the dissipating cell.

Latitude and longitude information for the center of each cylinder were recorded

using the active readout display from WDSS-II, which allows for a mouse-over

(18)

(19) from the NASA flash algorithm such that only those flashes that had origins within the

bounds of the cell were associated with the cell. Since it is possible that some flashes

could originate outside the bounds of each cell, we selected three cases, all of which were

isolated from other convective cells, and performed sensitivity tests with the cell bounds.

In each case, the cell radii were expanded by 100% to test the possibility of flashes

occurring outside the range of the former bounds. All cases maintained the same number

of flashes with the newly expanded radii suggesting the radii for all cells examined

captured all the detected lightning activity associated with each cell.

Comparisons were made between radar reflectivity values and total lightning data

(i.e. LDAR source points and CG data) by converting radar data from a polar to a

Cartesian grid space using REORDER software (Oye and Case 1995) and overlaying

both data sets. Horizontal and vertical grid spacing for the reflectivity data were set at 2.0

km and 1.0 km, respectively. The x, y, and z radii of influence were set to 2.0, 2.0, and

1.1 km respectively, and a three-dimensional Cressman weighting scheme (Cressman,

1959) was used to derive Cartesian grid points from polar radar data.

The Cressman weighting scheme is a function of the grid spacing and the radii of

influence. The radius of influence, R, is defined as:

The weighting function, W, for a given gate is value is defined as:

! R = dX2 + dY2+ dZ2 ! W = R 2 " r2 R2+ r2

Where r2 is the square of the distance between the gate and the grid point such that grid points located closer to a particular gate with have more weight than grid points further

away.

The reflectivity data associated with each cell were interpolated over 1 km

altitude bins. Despite coarse vertical interpolation and occasional gaps in the radar data,

the smoothing performed creates a general idea of the vertical distribution of reflectivity

values such that the two datasets (total lightning activity and radar reflectivity) can be

overlaid.

Once the reflectivity, VII, and flash rates were obtained, several datasets were

created to provide a general sense of the correlations between total flash rates and the

kinematic and microphysics of each cell. The parameters examined include the 95th and 75th percentile of flash heights, the median and mean of flash heights, and the total and CG flash rates. We then used this lightning information to conduct regression analysis

between LDAR total (or NLDN CG) and radar derived VII using the r2 value as a measure of the goodness of fit.