A-27 
0 10 20 30 40 50 60 70 80 90 
X 
Figure 3.1. Bivariate fit of Y By X. Straight line is a linear large-scale trend fit (R 2 = 0.19); 
the moderately wavy line around the straight line is a 6th-order polynomial fit (X enters 
the model as X, X 2 , X 3 , and X 6 ; R 2 = 0.25); and the jagged line is a spline fit with a 
very small bandwidth (neighborhood used in local estimation at each X; R 2 = 0.90). 
3.3 COMPARISON OF METHODS 
The following describes some of the benefits and potential limitations of kriging in 
regards to CBP application with some comparisons to the IDW approach towards 
spatial interpolation outlined in the previous section. Nonparametric methods are not 
sufficiently developed to include in this comparison. A primary benefit of the kriging 
methodology compared to IDW is that it is a statistical technique. As such the field 
of statistics (including kriging) is designed to make inference from sampled data in 
the presence of uncertainty and the quantity and quality of the sample data are 
reflected in those inferences. However, kriging is a less than routine type of statis¬ 
tical analysis and requires a certain level of statistical expertise to carry out the 
process. The short description on variogram estimation provided above merely intro¬ 
duces this involved and often complicated step. This requirement for informed 
decision making limits the degree to which kriging can be automated and still main¬ 
tain its flexibility and optimal properties. 
Further issues regarding kriging and CBP applications are listed below. 
• Kriging is flexible in that it is based on an estimate of the strength of spatial 
dependence in the data (variogram). Kriging can consider direction dependent 
weighted interpolations (anisotropy) and can include covariates (universal 
kriging) to potentially influence interpolations, either simple trends in easting 
and northing coordinates or water related measures such as sea surface temper¬ 
ature measured by satellite. 
• A key feature of a statistical technique like kriging is that a measure of uncer¬ 
tainty (called the kriged prediction variance) is generated along with kriged 
interpolations. Research has been initiated (i.e., conditional simulation) to 
appendix a • The Cumulative Frequency Diagram Method for Determining Water Quality Attainment 
