This formula is based on the Richards formula, which includes well-kno
wn growth formulae, and is invariant for allometry. It is expanded by
exchanging the independent variable from time to its function, in othe
r words the cumulative water temperature. This standard formula includ
es the method of substituting values for the cumulative water temperat
ure into the time term, the mathematical model of adding sine function
s to the time term, and switched growth rate models. This standard mod
el is given by general theory, which makes the character of parameters
clear and helps to analyze the growth formula statistically.