Table 6.

Formulas used to calculate peak timing from an estimate of phase shift $\mathsf{\psi }$ , harmonic regression estimates of ${\beta }_s$ and ${\beta }_c$, and the length of the annual cycle M.

Quadrant	Peak Timing
${\beta }_s>0$ ${\beta }_c>0$	$\mathsf{\Psi }\times \frac{M}{2\mathsf{\pi }}$
${\beta }_s>0$ ${\beta }_c<0$	$\left(\mathsf{\Psi }+\mathsf{\pi }\right)\times \frac{M}{2\mathsf{\pi }}$
${\beta }_s<0$ ${\beta }_c<0$	$\left(\mathsf{\Psi }+\mathsf{\pi }\right)\times \frac{M}{2\mathsf{\pi }}$
${\beta }_s<0$ ${\beta }_c>0$	$\left(\mathsf{\Psi }+2\mathsf{\pi }\right)\times \frac{M}{2\mathsf{\pi }}$