A-28 
propagate this interpolation uncertainty through the CFD process for gener¬ 
ating confidence intervals for estimates of attainment. 
• Kriging can be applied in situations where the data are sparse, as in CBP fixed 
station data, or densely sampled, as in CBP shallow water monitoring. Kriged 
and IDW spatial interpolations may very well produce near identical results for 
these two extreme scenarios. However it is the kriging approach that provides 
a statistical model, the uncertainty of which is influenced by the quantity and 
quality of data. Knowledge of interpolation uncertainty is crucial for discrimi¬ 
nating the improved water quality assessment obtained from densely sampled 
networks relative to sparsely sampled networks. 
As alluded to earlier kriging is an advanced statistical technique and like all such 
techniques should be carried out by well trained statistician(s) with experience in 
spatial or geostatistical methodology and experience analyzing water quality data. 
Assessing model fits (of the variogram and regression model) and kriging accuracy 
via cross validation and/or likelihood based criteria should be employed routinely. 
To further exemplify this point consider kriging the densely sampled shallow water 
monitoring data which is generated by the DATAFLOW sampling. In addition to the 
other technical complexities mentioned within, this spatial sampling design may 
raise other issues not immediately recognized by untrained users (Deutsch 1984). 
For kriging in CBP applications one potential methodological drawback is the issue 
of non-Euclidean distance (Curriero 2006). Current kriging methodology only 
allows the use of the straight line Euclidean distance as the measure of proximity. 
However, the irregular waterways in the Chesapeake Bay system may very well 
suggest other non- standard measures of distance. For example, the spatial design of 
the fixed station data including those in the Bay mainstem and tidal tributaries. The 
straight line Euclidean distance may very well intersect land particularly in regions 
containing convoluted shorelines. There has been research initiated on this topic 
(Curriero 2006, Jensen et al. 2006, Ver Hoef et al. 2007), however, results are not yet 
ready for universal use. 
Three dimensional interpolations (including depth as the third dimension) are poten¬ 
tially required for CBP applications. The IDW and kriging methodologies, 
mathematically speaking, certainly extend to three dimensions. However the rapid 
change of water quality over depth would lead to significant anisotropies in the 
application three dimensional kriging that would complicate this approach far more 
than the application of IDW. On the other hand, a simplistic implementation of IDW 
that does not recognize the rapid decay of covariance over depth would inappropri¬ 
ately reach across the pycnocline when choosing nearest neighbors. Clearly the 
special properties of water quality in a highly stratified bay require innovation for 3- 
dimensional interpolations. Another approach would be to apply universal kriging 
where a third dimension (depth) is used as a covariate. The use of depth as an inde¬ 
pendent variable is motivated by the observation that often water quality exhibits a 
predictable trend over depth as for example the trend of DO decreasing with 
increasing depth. To include depth as a covariate, model (1) would be written as 
Y (s) = fio + /J]Depth(s) + y (s): 
appendix a 
The Cumulative Frequency Diagram Method for Determining Water Quality Attainment 
