C-9 
reflected in these inferences. Kriging, however, is a less-than-routine type of analysis 
and requires statistical expertise to execute. The short description on variogram esti¬ 
mation above merely introduces this involved and often complicated step. 
Further issues regarding kriging and Chesapeake Bay Program applications are 
listed below. 
• Kriging is flexible; it is based on an estimate of the strength of spatial dependence 
in the data (variogram). Kriging can consider direction-dependent weighted inter¬ 
polations (anisotropy) and can include covariates (universal kriging) to influence 
interpolations—either simple trends in easting and northing coordinates or water- 
related measures such as salinity. 
• A key feature of kriging is that a measure of uncertainty (called the kriged 
prediction variance) is generated along with kriged interpolations. Research 
has started to propagate this interpolation uncertainty through the CFD. 
• Kriging can be applied in situations for which the data remain sparse (such as 
the Chesapeake Bay Water Quality Monitoring Program's fixed station data) or 
dense (such as the Chesapeake Bay Shallow-water Monitoring Program). 
Kriged and IDW spatial interpolations may very well produce near identical 
results for these two extreme scenarios. The kriging approach, however, 
provides a statistical model, the uncertainty of which is influenced by the quan¬ 
tity and quality of data. Interpolation uncertainty information is crucial for both 
sparsely and densely sampled networks. 
In comparison to IDW, kriging is more sophisticated, but requires greater expertise 
in implementation. Kriging is available in commercial statistical software and also 
in free open-source applications, such at the R Statistical Computing Environment. 
Use of the technique requires geostatistical expertise programming skills for these 
two software packages. Segment-by-segment variogram estimation and subsequent 
procedures would require substantial expert supervision and decision-making. 
Chesapeake Bay Program managers may very well view this as a limitation in using 
kriging for certain Chesapeake Bay Program activities, such as criteria assessments, 
applications that need automated spatial interpolations. Furthermore, for some 
Chesapeake Bay Program applications, the decision on criteria attainment is clearly 
not influenced to any substantial degree by the method of spatial interpolation 
because the water quality conditions remain far out of attainment. One possible 
strategy is using a mix of IDW and kriging in situations for which attainment was 
grossly exceeded or clearly met (IDW) versus borderline cases (kriging). Table C-l 
provides a comparison of the capabilities of assessments based on lumping data, 
spatial interpolation based on IDW, and spatial interpolation based on kriging. 
appendix c 
Evaluation of Options for Spatial Interpolation 
