A-25 
Table 3.1. A short list of recent articles comparing the precision of IDW to a subset of 
other possible interpolation methods. 
Authors 
Methods Compared 
Variables 
Manipulated 
Conclusions 
Kravchenko(2003) 
Inverse Distance 
Weighting (IDW), 
Ordinary Knging 
(OK) 
spatial structure and 
sample grid spacing 
IDW better than OK 
unless sample sizes 
were fairly large 
Dille. et al. (2002) 
IDW. OK, Minimum 
Surface Curvature 
(MC). Multiquadric 
Radial Basis Function 
(MUL) 
neighborhood size, 
spatial structure, 
power coefficient in 
IDW, sample grid 
spacing, quadrat size 
No interpolator 
appears to be more 
precise than another. 
Sample grid spacing 
and quadrat size were 
deemed more 
important. 
Valley, et al. (2005) 
IDW, OK. Non- 
parametric Detrend + 
Splines 
spatial structure, 
sample size, quadrat 
size 
OK tended to be more 
precise but IDW was 
very similar 
Lloyd (2005) 
moving windovs- 
Regression (MWR), 
IDW, OK. simple 
kriging with locally 
varying mean (SKlm). 
kriging with external 
drift (KED) 
spatial structure, 
sample size 
KED and OK best 
Remstorf, et al. 
(2005) 
IDW, OK, KED + 
deterministic 
chemical transport 
models 
single dataset was 
analyzed 
OK best 
Zimmerman, et al. 
(1999) 
2 types of IDW, UK. 
OK 
spatial structure, 
sampling pattern, 
population variance 
UK and OK better 
than IDW 
One final and important issue with IDW is that, as currently used, IDW is a deter¬ 
ministic method which makes no assumptions as to the probability distribution of the 
data being interpolated. Hence, it does not allow for estimating prediction errors, i.e. 
it does not allow for the possibility of random variation at interpolation sites. A 
simple question is whether IDW can be recast in the knging framework given the 
similarity in prediction method (weighted average) and hence can a method be found 
to estimate prediction errors? The short answer is no - the distance function used by 
IDW. which is an implicit assumption about the autocorrelation function in the 
spatial field, does not meet the assumptions required for development of a valid vari¬ 
ance-covariance matrix describing the spatial covariance. As a result. IDW cannot be 
modified to take advantage of the statistical knowledge that has been developed for 
geostatistical analyses such as kriging. This does not imply that other approaches to 
estimating prediction error are also not possible. 
A non-parametric approach for estimating variance was proposed (Tomczak, 1998) 
in which jack-knifing was used to provide error estimates. 95% confidence intervals 
for the mean were calculated and then compared to the actual observed values. Not 
surprisingly, only 65% of the data were captured within their associated confidence 
interval. The method appears to have been misapplied—the jackknifing method as 
appendix a 
"he Cumulative Frequency Diagram Method for Determining Water Quality Attainment 
