Table IV-2. Previously published Chesapeake Bay chlorophyll a criteria assessment methods 
and recommended modifications. 
U.S. EPA 2008 Addendum 
U.S. EPA 2010 Addendum 
1. Chlorophyll a data used for scenario assessments 
comprise all chlorophyll a values in the C1MS 
water quality database with layer flagged “S” for 
surface. 
No modification recommended. 
2. Data are organized into individual ‘‘cruise” files for 
interpolation. 
No modification recommended. 
3. Individual cruise files are interpolated using the 
Chesapeake Bay Interpolator (version 4.61), with 
the "ln-transform” and the “2-D Inverse-Distance 
Squared” options selected. The Interpolator 
automatically back-transforms chlorophyll a 
values in its output files. 
No modification recommended. 
4. Interpolated chlorophyll a surfaces are averaged 
for an entire season (on a cell-by-cell basis). The 
current methodology calculates an arithmetic 
mean on the back-transformed chlorophyll a 
values 
4a. Interpolated chlorophyll a surfaces are In-transformed 
4b. Seasonal means are calculated on ln-transformed 
chlorophyll a values. 
5. Seasonal arithmetic means are assessed (cell-by¬ 
cell) against the criterion for the relevant river 
segment-season. 
5. Ln-transformed seasonal means are assessed (cell-by¬ 
cell) against the ln-transformed criterion for the 
relevant river segment-season. 
Source: U.S. EPA 2008. 
IMPLICATIONS OF THE REVISED ASSESSMENT PROTOCOL 
Conducting the spatial and temporal analyses in log-space produces geometric means. Geometric 
means will be less than the arithmetic means of the raw data, i.e. bias low for the estimator of the 
arithmetic mean, for all data sets with at least one pair of nonequal values (Bland and Altman 
1996). When all values in the data set are the same value and only then will the arithmetic mean 
equal the geometric mean. However, while geometric means may be less than arithmetic means, 
the values will always be above the minimum observed value and below the observed maximum 
value in both approaches. For log-normally distributed data such as the chlorophyll a data, the 
geometric mean is further a more efficient measure of central tendency, efficiently estimating the 
median which might be considered more typical of observations from the sampled population (E. 
Perry, 2010, Pers. Comm.). 
Given the very small number of data points in the tidal James River data analyses that influence 
the statistical measure of departure from normality, then this departure occurs in a small 
percentile of the distribution. Overall, the data align very well with the expected up through the 
10th percentile (see Appendix D). Because the CFD assessment method is defining the upper 
bound chlorophyll a criteria somewhere around the 10th percentile, it is fair to conclude that the 
log-normal is adequate for that purpose. While there may be another distribution that matches the 
data better than the normal distribution, one would, however, have to weigh the benefits of 
improved estimation against the costs of developing a suite of estimation procedures for this 
other distribution. One clear advantage of working with the log-normal is that the log 
transformation provides for a normal metric where one has many choices of well developed and 
well tested statistical methods (E. Perry 2010, Pers. Comm.). 
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