Computation of vertical velocities

David O. Blanchard
National Severe Storms Laboratory, Boulder, Colorado
Cooperative Institute for Mesoscale Meteorological Studies, Norman, Oklahoma
and
Jerry Straka
School of Meteorology, University of Oklahoma, Norman, Oklahoma

The goal of this exercise is to determine the optimal configuration(s) of the CEDRIC software package for computing vertical velocities using pseudo-Doppler derived horizontal winds from a supercell in a strongly sheared environment.

To simplify the analysis, we make the assumption that there are no errors or biases in the radial velocities, and that these radial velocity terms have been "perfectly" converted into horizontal components (u, v) of the wind. This is easily accomplished by substituting cloud-model generated winds for measured winds.

Starting with the horizontal components (u, v) of the cloud-model winds, we use CEDRIC to compute the horizontal divergence at each level, then integrate to get the vertical velocity. CEDRIC has multiple options for lower and upper boundary conditions (b.c.), as well as variable methods of integration. The preponderance of options and methodologies means that you can get a variety of solutions for the vertical velocity. Some are better suited to specific data collection strategies; others are best for situations where boundary conditions are unknown. Similar conclusions have been reached by Matejka and Bartels in a paper that appeared in the January 1998 issue of Monthly Weather Review.

Getting reasonable vertical velocities out of any Doppler radar processing software requires that the user be acutely aware of these issues.


Vertical velocities for Supercell Simulation

Maximum upward and downward vertical velocities at 1.0 km grid levels for each of the eight analysis configurations.
______________________________________________________________________________
\EXP|   1a      1b      1c      1d      2a      2b      3a      3b      Model
Z\  |
__\_|_________________________________________________________________________
 1.0|   0/0     6/-1    0/0     6/-2    0/0     7/-2    9/-3    9/-2    4/-3
____|_________________________________________________________________________
 2.0|   7/-1    12/-2   5/-1    12/-2   7/-1    12/-3   15/-2   14/-2   10/-4
____|_________________________________________________________________________
 3.0|   12/-3   17/-3   11/-3   16/-4   11/-3   17/-4   17/-4   18/-3   15/-4
____|_________________________________________________________________________
 4.0|   14/-4   21/-3   15/-5   20/-5   14/-4   21/-5   16/-4   21/-3   19/-5
____|_________________________________________________________________________
 5.0|   16/-3   22/-6   16/-8   22/-9   16/-3   22/-6   16/-2   23/-2   22/-6
____|_________________________________________________________________________
 6.0|   15/-2   22/-6   14/-14  20/-12  14/-3   22/-5   15/-1   23/-3   23/-4
____|_________________________________________________________________________
 7.0|   9/-2    18/-5   8/-18   16/-16  9/-2    17/-6   9/-1    18/-4   21/-6
____|_________________________________________________________________________
 8.0|   0/0     10/-3   0/-20   8/-19   0/0     10/-1   0/0     10/-3   15/-5
____|_________________________________________________________________________

Maximum upward/downward vertical velocities on a grid level.

Exp 1a:  Variational integration with const b.c. = 0.0
Exp 1b:  Variational integration with fract b.c. = 1.0

Exp 1c:  Upward integration with const b.c. = 0.0
Exp 1d:  Upward integration with fract b.c. = 1.0

Exp 2a:  Relaxed u,v,w (1a) variational integration with const b.c. = 0.0
Exp 2b:  Relaxed u,v,w (1b) variational integration with fract b.c. = 1.0

Exp 3a:  Downward integration with const b.c. = 0.0
Exp 3b:  Downward integration with fract b.c. = 1.0

Model:   Actual vertical velocities from the model

Note:    Vertical velocities rounded to the nearest m/s.

Details

Want more details? Here are some statistics for the supercell thunderstorm vertical velocities.

For those who prefer plots -- vertical velocities (m/s) at 5.0 km for

| Exp 1a | Exp 1b | Exp 1c | Exp 1d | Exp 2a | Exp 2b | Exp 3a | Exp 3b | Model |

Even more details? Okay! Here are the vertical profiles of the vertical velocities for each of the experiments with the maximum downdraft, mean vertical velocity, and maximum updraft plotted.

| Exp 1a | Exp 1b | Exp 1c | Exp 1d | Exp 2a | Exp 2b | Exp 3a | Exp 3b | Model |


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Updated December 5, 1997.