Common Errors in Statistics (and How to Avoid Them), 4th Edition

DYNAMIC MODELS

Dynamic models are the basis of weather forecasts, long-range models of climate change, and galactic movement. According to Nielsen-Gammon [2003], the following are the chief sources of error in dynamic models:

1. Measurement errors. These tend to be larger at the extremes of each variable.

2. Nonrepresentative measurements (may result when measurements are taken too far apart in time or in space).

3. Attempting to interpolate between grid points. Here is one example: Suppose that after a particularly strong cold front there is a strong wind from the north across Texas, with cloudy skies and very cold temperatures, say 30°F. As the cold air gets blown across the Gulf, it gets heated by the warm Gulf waters. So a grid point 25 km onshore would have a temperature of 30°F and a grid point 25 km offshore might have a temperature of 46°F. Interpolating the model output to the coastline, halfway between the two grid points, gives a temperature of 38°F. But until the air passes over the warm water, it will not start heating up. So the air will stay 30°F all the way to the coastline. Simply using interpolated model output (38°F) would have given an 8°F error.

To improve a model:

• Do not merely copy computer output but temper it with your other knowledge of the phenomena you are modeling.
• Refine the model on the basis of the errors observed when it is applied to a test dataset. Note that errors may be either of position (in space or in time) or of magnitude.