12.2.2 Empirical linear interpolation  12.2.1 Surface fitting  12.2.1.3 OTHER METHODS OF

12.2.1.4 ADVANTAGES AND DISADVANTAGES OF SURFACE FITTING

Surface fitting is an attractive method for small numbers of observations, especially when the observing network is fixed. No background (first guess) field is required. It is possible to account for observational error. There are several disadvantages:

• No incorporation of information from a background field is possible. Thus, the meteorological knowledge about the situation is ignored, except when variational constraints are imposed.
• One must be wary of underfitting, overfitting, or using the wrong set of functions. If the data are underfit (not enough functions in the polynomial expansion), important details resolved by the data may be lost in the analysis. If the data are overfit (too many functions), variability in the analysis may have no meteorological significance. Gradients between observing sites may be completely unrealistic.
• In data sparse areas or outside the domain of observations, surface fitting can lead to implausible functional values.
• Surface fitting is computationally expensive when large numbers of observations are considered. In some cases, the problem is ill-conditioned (numerically unstable).

   
 12.2.2 Empirical linear interpolation  12.2.1 Surface fitting  12.2.1.3 OTHER METHODS