Inclass Laboratory 4: Storm Relative Helicity

 

 

 

Background: Doswell, C.A., 1991:  A review for forecasters on the application of hodographs to forecasting severe thunderstorms.  Nat. Wea. Digest, 10, pp. 2-10.

 

 

The air ingested into thunderstorms often occurs across a layer several 100s of meters deep.  Much research has verified that the source of rotation in thunderstorms lies in the horizontal helicity (horizontal vorticity, horizontal streamwise vorticity) that is tilted into the vertical. 

 

 

       In order to estimate this, the helicity through the ingested (inflow) layer needs to be calculated:

 

                                                       (1)

 

       where 0 is ground level and h is the height at the top of the inflow layer.

 

       Other research shows that the motion of the storm needs to be subtracted out to obtain an estimate of the ingest of horizontal vorticity relative to the storm:

 

                                                (2)

 

       where H is the Storm Relative Helicity (SREH or SRH) and c is the storm motion vector.

 

 

 

 

 

1. Assignment Tasks

 

A. Expand out equation (2).


B.
The best way to accomplish the computation is to use the expanded equation (2) by using Excel or other spreadsheet program to compute the derivatives. You will do this to calculate the 0-3 km SRH for the case shown in the sounding/hodograph for KOAK for 18 UTC 6 October 2011
To compute ∂V/∂z use a finite difference with the value of this derivative evaluated from the ground to 1 km  using a Ęz of 1 km, and applying to the wind and storm motion at 1 km etc.


C.
Once you have your answer, print out the Excel spreadsheet.

 

 

2. Data and Procedure


A. Storm motion

The actual thunderstorm motion on 6 October (from radar) was 345o, 12.4 m s-1. 

B. Wind Data

The winds (as shown on the sounding and hodograph) are as follows AGL:

  • 0 km, 195o, 3 m s-1;
  • 1 km, 265o, 8 m s-1;
  • 2 km, 310o, 11 m s-1;
  • 3km, 315o, 13 m s-1;

C. Things you will need to do

  1. expand out equation (2) (we did this in class);
  2. break the storm motion into its components;
  3. break the wind at each level into its components

Step 1 is easy. But you will need to include the expansion in what you turn in. Review the Helicity handout from earlier in the semester.

Step 2 is something you can have Excel do for you or you can do it with a calculator. To do it, you will need to convert the storm motion angle into radians. The u and v components of motion can be obtained by using sin and cos, but I am not going to tell you which.

Step 3 is done exactly the same as in Step 2, except for the winds instead of the storm motion.

I've tried to simply this by having you just complete the process for ONLY three layers: 0-1 km, 0-2 km and 0-3 km, which you will then add to get the total SRH. You'll need the mean wind for each layer, which you can get by adding the wind at the top and bottom of the layer and dividing by 2.

You can set up your Excel spreadsheet to complete all of the computations. You can then use it as a template to insert future storm motions or hodograph points to calculate SRH for other cases.

D. Sources of error

  1. we are estimating integrals and derivatives by using a very coarse finite difference grid;
  2. we are estimating the mean wind very crudely by assuming that it is the average of the wind at only two layers that are actually 1000 meters apart.