appendix 
Equations for the Open-Water, 
Deep-Water and Deep-Channel 
Dissolved Oxygen Criteria 
Summer Biological Reference 
Curves 
A biological reference curve of acceptable violation rates is generated using a cumu¬ 
lative frequency distribution (CFD) of violation rates for “healthy” designated uses. 
The violation rates are sorted in ascending order, ranked in descending order, and 
graphed on a quantile plot: 
• Violation rates are plotted on the x-axis, with plotting position on the y-axis. 
• Plotting position represents the probability, i/n, of being less than or equal to a 
given violation rate, or x, and is plotted on the y-axis as a function of rank, or 
“i”, and sample size, or “n”. 
• The x-axis is labeled “Percentage of Volume” because the violation rate repre¬ 
sents the fraction of volume that is in violation. 
• The y-axis is labeled as “Percentage of Time” because “probability” represents 
the probable amount of time that a given violation rate will be observed. 
• The Chesapeake Bay Program currently uses the Wiebull plotting position to 
plot the cumulative distribution function. The Wiebull equation for calculating 
probability, y, for each violation rate with rank “i” is: y = i/(n+l); i = rank. 
In order to generate a graph of the CFD: 
• X|, x 2 , x 3 ,...x n = violation rates provided herein, sorted in ascending order, 
with rank (i) assigned in descending order. 
• yj = i/(n+l). 
• After plotting the data’s violation rates and probabilities, two additional points 
should be added to the distribution in order to complete the CFD curve: 
Insert (x 0 , yo) = (0,1) before the first data point; and 
Insert (x n+1 , y n+1 ) = (1,0) after the last data point. 
appendix g • Equations for the Summer Biological Reference Curves 
