PHU requirements and phenological development

The simulation of crop phenological development from emergence through anthesis to maturity was controlled by temperature and modified by vernalization requirements. Spatially explicit accumulated thermal units—here PHU (in °C day)—are based on daily weather data averaged for the 1980–2010 period, individually derived from the three observational climate datasets mentioned above. For each climate dataset, crop, growing season (see above), and grid cell (i), we determined heat units required to reach maturity (PHUreq,i) by calculating the sum of daily (j) average temperature Embedded Image above a crop- and location-specific base temperature (Tb,i), weighted by a vernalization factor Vi,j from sowing (j = 0) to the harvest day (J)Embedded Image(1)where base temperatures Tb,i are calculated asEmbedded Image(2)with minimum temperatures Embedded Image = 5°C for maize and 0°C for wheat, maximum base temperatures Embedded Image = 15°C for maize and 0°C for wheat (33, 34), and annual average temperatures Embedded Image.

For maize, we assume no vernalization requirement (V = 1). Winter wheat is assumed to require exposure to low temperatures to reach anthesis (54, 55). It is distinguished from spring wheat if sowing takes place between the 243rd and 365th day of the calendar year on the Northern Hemisphere and between the 59th and 181st day of the calendar year on the Southern Hemisphere and if the mean temperature of the three coldest months within the growing season is below 10°C. Heat unit accumulation is down-regulated by V < 1 as long as the vernalization requirement Vreq is not yet fulfilled. Vreq is derived from cell-specific average winter temperatures of the five coldest months within the growing season.

For winter wheat, we assume a maximum vernalization requirement of 70 days. That being said, fewer vernalization days are required if monthly average temperatures of the coldest months i1,..., i5 are above 3°CEmbedded Image(3)where Embedded Image if monthly average temperature is below 3°C and linearly decreases to zero at a monthly temperature of 10°C.

To reach the vernalization requirement, each day in the growing season is weighted according to their vernalization effectiveness and successively added up. Here, we assume that vernalization effectiveness is highest (=1) if daily temperature is between 3° and 10°C. Below 3°C, it linearly decreases and reaches 0 at −4°C, and above 10°C, it also decreases linearly to 0 at 17°C (55). As soon as Vreq is reached, the vernalization factor for daily heat sum accumulation V is set to 1. Before a minimum vernalization requirement of Vreq/5 is reached, V is set to 0. In between, it increases linearly from 0 to 1 with accumulated weighted vernalization days (29).

In the default phenology model (referred to as semistatic), LPJmL–Ref (and also LPJmL–WaterLimIrr and LPJmL–NoWaterStress), heat requirements are not derived from reported growing seasons, and sowing dates are internally derived on the basis of climate conditions. For maize, the harvest date is not based on local observations but on a global constant Embedded Image, while only the base temperature (Tb,i) is assumed to vary geographically (same as Eq. 2). For spring wheat, heat requirements are defined as a multiple of the mean annual temperature (Embedded Image, 1980–2010 mean) Embedded Image or a maximum value of Embedded Image and a minimum value of Embedded Image. For winter wheat, Embedded Image is calculated asEmbedded Image(4)where Ds is the sowing date and Dk is 365 (Northern Hemisphere) or 181 (Southern Hemisphere). The default model also uses a simplified approach to the effect of vernalization with geographically constant vernalization requirements.

Phenological development is a function of daily accumulation of weighted heat sum increments over the growing season (PHUsum,j, calculated as in Eq. 1). Anthesis is assumed to occur as soon as PHUsum,j reaches 0.5*PHUreq for maize and 0.45*PHUreq for wheat (33). Physiological maturity is assumed to be reached as soon as PHUsum,j reaches either PHUreq or a crop-specific age limit of 240 days for maize, 334 days for spring wheat, and 364 days for winter wheat, which represents the maximum growing season length in the MIRCA2000 crop calendar. We further assume time requirements between crop maturity (green leaf area index reaches zero) and harvest, as suggested by Elliott et al. (30), that is, 21 days for maize and 7 days for wheat. As phenological development of specific crops can also be influenced by day length, PHU accumulation in LPJmL can be weighted by photoperiodism, as described in Schaphoff et al. (33), but results were outperformed by the simpler model without photosensitivity, which was thus presented herein. Additional physiological stresses were not considered to directly affect phenological development but explicitly influence the simulation of photosynthesis and carbon allocation (see next section).

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