## 2.20.3. Seasonal-Deciduous Phenology[¶](#seasonal-deciduous-phenology "Permalink to this headline")
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The seasonal-deciduous phenology algorithm derives directly from the treatment used in the offline model Biome-BGC v. 4.1.2, (Thornton et al., 2002), which in turn is based on the parameterizations for leaf onset and offset for temperate deciduous broadleaf forest from White et al. (1997). Initiation of leaf onset is triggered when a common degree-day summation exceeds a critical value, and leaf litterfall is initiated when daylength is shorter than a critical value. Because of the dependence on daylength, the seasonal deciduous phenology algorithm is only valid for latitudes outside of the tropical zone, defined here as \\(\\left|{\\rm latitude}\\right|>19.5{\\rm {}^\\circ }\\). Neither the background onset nor background litterfall mechanism is invoked for the seasonal-deciduous phenology algorithm. The algorithm allows a maximum of one onset period and one offset period each year.

The algorithms for initiation of onset and offset periods use the winter and summer solstices as coordination signals. The period between winter and summer solstice is identified as \\({dayl}\_{n} > {dayl}\_{n-1}\\), and the period between summer and winter solstice is identified as \\({dayl}\_{n} < {dayl}\_{n-1}\\), where \\({dayl}\_{n}\\) and \\({dayl}\_{n-1}\\) are the day length(s) calculated for the current and previous timesteps, respectively, using

(2.20.45)[¶](#equation-20-45 "Permalink to this equation")\\\[dayl=2\\cdot 13750.9871\\cdot acos\\left(\\frac{-\\sin (lat)\\sin (decl)}{\\cos (lat)\\cos (decl)} \\right),\\\]

where _lat_ and _decl_ are the latitude and solar declination (radians), respectively, and the factor 13750.9871 is the number of seconds per radian of hour-angle.

