Second, there is an underlying assumption to the calculations conducted as defined in the U.S. 
EPA 2007a and 2008 chlorophyll a criteria assessments that Chesapeake Bay chlorophyll data 
show log-normal tendencies. Based on this assumption, analyses depend on log-transforming of 
chlorophyll a data to provide a reasonable approximation of the normal distribution and support 
the use of normal distributional inference procedures. There is use of log-transformation 
chlorophyll a data in the Chesapeake Bay criteria literature cited in U.S. EPA 2007b, and there is 
a suggestion for positive skewness for chlorophyll a data shown with a hypothetical chlorophyll 
a data distribution (U.S. EPA 2007b). However, there is little background documenting the 
statistical distributional characteristics of Chesapeake Bay chlorophyll a data within the Ambient 
Water Quality Criteria for Dissolved Oxygen , Water Clarity and Chlorophyll a for Chesapeake 
Bay and its Tidal Tributaries publication series (U.S. EPA 2003, 2007a, 2007b, 2008). 
The following sections address: 1) peer-reviewed supporting literature regarding skewness and 
non-normality issues of chlorophyll a data; 2) log-normal transformation applications during 
analyses of Chesapeake Bay and other chlorophyll a data; and 3) recommended refinements to 
the published criteria assessment procedures. All these sections are directed towards providing 
consistency in computing the season mean of the 3-year assessments in logarithmic-space, 
thereby providing a sound estimate of central tendency for the final chlorophyll a assessment 
measures with the seasonal mean criteria. 
CHLOROPHYLL A: DATA SKEWNESS, LOG TRANFORMATION AND THE 
SEASONAL MEAN CALCULATION 
Log-normal Character of Chlorophyll a Data 
Support for the log-normal characteristics of chlorophyll a data have been published in the peer- 
reviewed scientific literature across a diversity of ecosystems. Harris (1986, Figure 9.7) 
illustrates seasonally dependent log-normal chlorophyll results for Hamilton Harbor (Lake 
Ontario). Vollenweider and Krekes (1980), as cited in Harris (1986), noted that algal biomass 
data from lakes was log-normally distributed. Recent work on Colorado lakes (n = 20) showed 
19 of 20 lakes chlorophyll measurements were well fit with log-normal transformations to 
approximate the normal distribution 4 . 
Within Chesapeake Bay, Jordan et al. (1991) describe correlations between watershed discharges 
and chlorophyll concentrations as complicated by non-normal distributions. Jordan et al. (1991) 
used the Box-Cox method (Sokal and Rohlf 1981) to identify the best power transformation for 
normalizing the data which was a log transformation. Harding (1994) showed that frequency 
distributions of chlorophyll and nutrient concentrations in Chesapeake Bay data were skewed; 
logarithmic transformations of the data produced normal distributions. 
4 http://\vAvw.chatfieldwatershedauthoritv.org / pdf/Characterizing%20Chlorophyll%20Distributions%2Qin%20Colora 
do.pdf 
Log-transforming Chesapeake Bay water quality indicator data (including chlorophyll) was 
integral to improvements of the Relative Status Indicator during its evolution (Olson 2009). 
Initially, Olson (2009) reports that positive skewed data led to unequal data distributions 
34 
