Hi, I'd like to help you with your question.
Yes, systematic desensitization could help you. But what you want to find out first is whether or not you are experiencing anxiety and phobic disorder, or PTSD.
The difference in the anxiety you have from the anxiety someone else has is that your anxiety is based on a real event. Most people with anxiety are fearful of something that most others are not afraid of such as bridges, snakes or cats. Although their fear is very real and quite distressing, your fear is based on a real events and most people are afraid of tornado's.
Therefore what you describe could be PTSD, similar to what veterans of wars describe. To be sure, it would be a good idea for you to get an evaluation with a therapist to determine the nature of your problem. To find a therapist, talk with your doctor for a referral. Or you can contact your local community mental health center. You can also search on line at http://therapists.psychologytoday.com/rms/.
Here are some of the symptoms of PTSD:
Avoiding any reminders of the event
Intense feelings and anxiety about the event or reminders of the event
Physical reactions such as rapid heart beats, sweating, muscle tension and fast breathing.
To treat PTSD or anxiety, cognitive based therapy (CBT) is the best option. This type of therapy helps you retrain your thought patterns so you can respond to the stress in a better way. It gives you more control and helps you learn ways to cope when you begin to feel fearful.
Systematic Desensitization does help, but it requires exposure to the object of fear. You could start with pictures of tornado's then move up to hearing news reports then to video of tornado's, but to be exposed to one in real life is not possible. So it can help you to a point.
Here are some resources to help you work on this issue at home as well:
The PTSD Workbook: Simple, Effective Techniques for Overcoming Traumatic Stress Symptoms by Mary Beth Williams and Soili Poijula
The Post-Traumatic Stress Disorder Sourcebook: A Guide to Healing, Recovery, and Growth by Glenn R. Schiraldi
Mind-body Workbook for PTSD: A 10 Week Program for Healing After Trauma by Stanley Block and Carolyn B. Block
You can find these books on Amazon.com or your local library may have them for you.
Let me know if I can help in any other way,