If it is 40 degrees F at 100 miles south of your remote location and 30 degrees 100 F at miles north of your location and then you reason it is 35 degrees at your location, you have used linear interpolation to find the temperature. Interpolation is the main element that makes forecasting challenging. It makes forecasting challenging because it is an estimation of the unknown. However, an educated meteorological guess can be made. Every model, every analysis chart, and every chart with isopleths has the isopleths formed by interpolation.

Interpolation is an educated guess of a meteorological parameter. Computers are best at interpolating since they can make the best educated guess (often in a 3-D field) and are not subjected to human error asumming the data has no human error. Suppose you had a temperature sensor at the exact location an isopleth is located. Will it be the exact temperature of the isopleth? The answer is sometimes yes and sometimes no. This is where the mystery of the atmosphere occurs. Isopleths are educated guesses; they may have some error. In fact, the smaller the number of observations the more likely there is going to be error. If you had to interpolate isotherms with only 1/4th the number of data points, the temperature interpolation would look different. Errors with interpolation grow with time. This is the primary reason forecast model data becomes increasingly inaccurate with time, especially if the initial data is suspect. The phrase "garbage in equals garbage out" applies well to this statement. This is especially true over ocean surfaces and isolated mountain and desert terrain where surface and upper air observations are lacking. This is the reason forecast models have difficulty initializing storms off the West Coast of the U.S. and in Mexico.