C-7 
algorithm is not constrained by prior theoretical assumptions concerning error struc¬ 
ture. It is, therefore, simpler mathematically and can be adapted to interpolation in 
three dimensions (i.e., with depth). Second, due to its simplicity, IDW does not 
require operator decisions at interim steps. Thus, it is conducive to automation— 
running large numbers of interpolation without having to make decisions as part of 
the interpolation process. The algorithm is susceptible to problems with interpo¬ 
lating across land; however, methods exist to prevent such problems for Chesapeake 
Bay application (as described in previous sections and in detail in Appendix D). It 
can be applied at any scale, but is most appropriate for large scales where three- 
dimensional interpolation becomes a necessity and data collection sites may remain 
too dispersed to provide good estimates of error structure no matter which algorithm 
is used. 
In addition to its advantages, IDW also has a major disadvantage: it is not a statis¬ 
tical method. The method is a deterministic approach without any sampling or model 
error assumed or accounted for (STAC 2006). In addition, IDW does not account for 
potential spatial autocorrelation among the observations and, therefore, does not 
fully utilize the information contained within the data. No method exists to estimate 
either source of error associated with a set of predicted values when using IDW and 
it cannot be used as a basis for statistical decision-making using the CFD. Dedicated 
research could determine whether IDW could be made more statistically defensible. 
EVALUATION OF KRIGING AS A SPATIAL 
INTERPOLATION ALGORITHM FOR 
ASSESSING CHESAPEAKE BAY WATER QUALITY 
Kriging has been considered by the Chesapeake Bay Program as a principal alterna¬ 
tive algorithm for spatial interpolation in CFD water quality criteria assessment 
methodology. Kriging is a spatial interpolation technique that arose from geostatis¬ 
tics, a subfield of statistics that analyzes spatial data. Kriging and the field of 
geostatistics have been used in a wide variety of environmental applications and are 
generally accepted methods for statistically optimal spatial interpolations (Cressie 
1991, Schabenberger and Gotway 2004, Diggle and Ribeiro 2006). Kitanidis (1997), 
Wang and Liu (2005), and Ouyang et al. (2006) elaborate on the application of 
kriging in water-related research. References on kriging methodology, geostatistics, 
and their related statistical development can be found in Cressie (1991), Diggle et al. 
(1998), Schabenberger and Gotway (2004), and Diggle and Ribeiro (2006). 
Kriging can be formulated equivalently in terms of a general linear regression 
model: 
Y (s) = /3 0 -h 1 Xi(s) • • • + /? p X p (s) + e(s) Equation C-1 
with s representing a generic spatial location assumed to vary continuously over 
some domain of interest and Y (s) capturing the outcome of interest measured at s, 
X|(s), . . . ,X p (s) potential covariates indexed by location s and their associated 
regression effects /3j./? p . The uncertainty in this regression relationship is 
modeled with the random error term e(s) assumed to have zero mean and constant 
appendix c 
Evaluation of Options for Spatial Interpolation 
