Determining the Tier I Lake Michigan Basin Acute Aquatic Life Toxicity Criterion (LMAATC): Dependent on Water Chemistry

Section 302 Section 302.560  Determining the Tier I Lake Michigan Basin Acute Aquatic Life Toxicity Criterion (LMAATC):  Dependent on Water Chemistry If data are available to show that a relationship exists between a water quality characteristic (WQC) and acute toxicity to two or more species, a Tier I LMAATC must be calculated using procedures in this Section.  Although the relationship between hardness and acute toxicity is typically non-linear, it can be linearized by a logarithmic transformation (i.e., for any variable, K, f(K) = logarithm of K) of the variables and plotting the logarithm of hardness against the logarithm of acute toxicity.  Similarly, relationships between acute toxicity and other water quality characteristics, such as pH or temperature, may require a transformation, including no transformation (i.e., for any variable, K, f(K) = K), for one or both variables to obtain a least squares linear regression of the transformed acute toxicity values on the transformed values of the water quality characteristic.  An LMAATC is calculated using the following procedures. a)         For each species for which acute toxicity values are available at two or more different values of the water quality characteristic, a least squares linear regression of the transformed acute toxicity (TAT) values on the transformed water quality characteristic (TWQC) values is performed to obtain the slope of the line describing the relationship. b)         Each of the slopes determined under subsection (a) is evaluated as to whether it is statistically valid, considering the range and number of tested values of the water quality characteristic and the degree of agreement within and between species.  If slopes are not available for at least one fish and one invertebrate species, the available slopes are too dissimilar, or too few data are available to define the relationship between acute toxicity and the water quality characteristic, then the LMAATC must be calculated using the procedures in Section 302.555. c)         Normalize the TAT values for each species, by subtracting W, the arithmetic mean of the TAT values of a species, from each of the TAT values used in the determination of the mean, such that the arithmetic mean of the normalized TAT values for each species individually or for any combination of species is zero (0.0). d)         Normalize the TWQC values for each species using X, the arithmetic mean of the TWQC values of a species, in the same manner as in subsection (c). e)         Group all the normalized data by treating them as if they were from a single species and perform a least squares linear regression of all the normalized TAT values on the corresponding normalized TWQC values to obtain the pooled acute slope, V. f)         For each species, the graphical intercept representing the species TAT intercept, f(Y), at a specific selected value, Z, of the WQC is calculated using the equation: f(Y) = W - V(X – g(Z)) Where: f() is the transformation used to convert acute toxicity values to TAT values Y is the species acute toxicity intercept or species acute intercept W is the arithmetic mean of the TAT values as specified in subsection (c) V is the pooled acute slope as specified in subsection (e) X is the arithmetic mean of the TWQC values as specified in subsection (c) g() is the transformation used to convert the WQC values to TWQC values Z is a selected value of the WQC g)         For each species, determine the species acute intercept, Y, by carrying out an inverse transformation of the species TAT value, f(Y).  For example, in the case of a logarithmic transformation, Y = antilogarithm of (f(Y)); or in the case where no transformation is used, Y = f(Y). h)         The Final Acute Intercept (FAI) is derived by using the species acute intercepts, obtained from subsection (f), in compliance with the procedures described in Section 302.555(b) through (g), with the word "value" replaced by the word "intercept".  Note that in this procedure, geometric means and natural logarithms are always used. i)          The Aquatic Acute Intercept (AAI) is obtained by dividing the FAI by two.  If, for a commercially or recreationally important species, the geometric mean of the acute values at Z is lower than the FAV at Z, then the geometric mean of that species must be used as the FAV. j)          The LMAATC at any value of the WQC, denoted by WQCx, is calculated using the terms defined in subsection (f) and the equation: LMAATC = exp[V(g(WQCx) – g(Z)) + f(AAI)]