Some Mathematical Considerations in the Predictability of Weather
Abstract
LONG-TERM GOALS. My long term goal is to understand the fundamental limitations on short-term, mesoscale predictability. Of particular interest are the effects of mid-scale turbulence on episodic initiations, or triggering mechanisms, and the sensitivities of the predictions of consequential events to these mechanisms. The issue is to develop techniques by which we can objectively distinguish between hard and impossible prediction problems. We are especially interested in applying these results to provide guidance for the design and interpretation of the ensemble forecast systems. OBJECTIVES. I wish to investigate the concept of a well-posed prediction problem, a prediction problem that has a theoretical solution. The complementary set of ill-posed prediction problems are those for whom no prediction algorithm or model can be developed, which will satisfy the required forecast accuracy or skill. A prediction problem may be well-pose, even though the prediction technology has not yet been developed. Thus the well-posed concept separates the impossible predition problems from those that are just very challanging. Studying well-posed prediction problems includes quantifying the relationship between the prediction goals and the verification results. These investigations also involve considerations of the methodology for quantifying the skill of prediction systems. Since the specification of a well-posed problem includes the selection of an objective verification procedure, it is necessary to have a sound statistical foundation for verification. We examine how this paradigm applies to a simple classical chaotic system and predictions of states on its attractor. Studies of the predictability of the Logistic Mapping from various initial states on its attractor provide insight. The notion of condition entropy is introduced as the skill metric for these studies.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 30, 1999
- Accession Number
- ADA630247
Entities
People
- F. W. Wilson
Organizations
- Massachusetts Institute of Technology