Shows the soil temperature gradient (warmer top, cooler bottom) together with root growth and above-ground emergence advancing with days after sowing. Color reflects cumulative germination.
$$f_T = \exp\!\left(-\left(\frac{T_s-25}{8}\right)^{2}\right),\qquad f_W = 1-\frac{|W-27.5|}{20}$$
Temperature factor f_T (Gaussian, valid 10-35 °C) and moisture factor f_W (= 1.0 inside 20-35%, linear decay outside).
$$G_{day} = 95\,f_T\,f_W\,f_d\,f_c\,s_s,\qquad \Sigma T = d\cdot\max(0,\,T_s-6)$$
Single-day germination G_day (%, capped at 98) and effective thermal time ΣT (base 6 °C). f_d depth factor, f_c compaction factor, s_s soil suitability.
$$G_{cum} = G_{day}\left(1-\exp\!\left(-\frac{\Sigma T}{100}\right)\right),\qquad Y \approx \frac{G_{day}}{100}\cdot 3.0$$
Cumulative germination G_cum and projected yield Y (t/ha). First-order emergence model with 100 °C·day characteristic thermal time.