Supplementary Materials
Equations:The ETS impacts on the harvest index.
Table S1Characteristics of the studied regions in China.
Table S2 Prior intervals, mean estimates, standard deviations of the optimal 30 parameter sets in each grid for model calibration in the single-rice cultivation provinces.
Table S2 Continued for the early-rice cultivation provinces.
Table S2 Continued for the late-rice cultivation provinces.
Fig.S1 Spatial distribution of temporal trends (% year-1) (a-c) and decadal-change types (d-f) of three ETS indicators for single and early rice in China during 1981–2010.
Fig.S1 Continued for late rice in China during 1981–2010.
Equations: the ETS impacts on the harvest index.
In the MCWLA-Rice model,the effects of high- and low-temperature stresses on yield formation are simulatedthrough their effects on the daily harvest index, which is calculated by the followingequations (Tao and Zhang, 2013).
(Eq.S1)
Where HIi is the daily harvest index, hci and hhi are the harvest index under low- and high-temperature stress, respectively.
(Eq.S2)
(Eq.S3)
(Eq.S4)
Where HImaxis the maximum harvest index underoptimum climatic conditions, Khis an empirical constant (day),γcis the percent ofsterile spikelet due to low temperature,γ0and Kqare empiricalconstants,Ccool is the curvature factor of spikelet sterility due to lowtemperature, Q is the cooling degree-days, T* is the base temperature for calculating coolingdegree-days. The summation of cooling degree-days isfor the period in which the rice panicle is sensitive to lowtemperature. The period is defined by the developmentindex as 0.75≤DVI≤1.20.
(Eq.S5)
(Eq.S6)
Whereγhis the spikelet sterility due to high temperature, is the average daily maximum temperature overthe flowering period, defined by 0.96≤DVI≤1.20, andChotis the curvature factor of spikelet sterility due tohigh temperature. The empirical constants To, TcandTbrepresent the optimum temperature, critical upper limitand critical bottom limit for crop growth, respectively.
Table S1Characteristics of the studied regions in China.
Table S2 Prior intervals, mean estimates, standard deviations of the optimal 30 parameter sets in each grid for model calibration in the single-rice cultivation provinces. For the listed parameters: AT, the sensitivity ofthe developmental rate to air temperature; This the air temperature at which DVR is half the maximum rate at theoptimum temperature; DVI* is the value of DVI atwhich the crop becomes sensitive to photoperiod; Gv is the minimum number of days required fromtransplanting to heading; Lcis the critical daylength; Kl, Kf and Tcr is empirical constants; Rmis the maximum relative growth rate of LAIunder an optimum condition; Ygpis the yield gap parameter representingthe ratio of actual yield to theoretical yield; Rr:l, relative growth rate of the root depth and LAI; Sle, scaling factor forabsorbed photosynthetically active radiation at ecosystem vs leaf scale;TTmax, maximum transpiration rate; gm, empirical parameter incalculating atmospheric demand water; R m25, maintenance respiration at 25℃; mr, empirical parameters in calculating maintenancerespiration; ag, growth respiration parameter.Ccoolis the curvature factor of spikelet sterility due to lowtemperature; Chotis the curvature factor of spikelet sterility due tohigh temperature. Please refer to Tao et al. (2009) for more details.
Table S2Continued for the early-rice cultivation provinces.
Table S2Continued for the late-rice cultivation provinces.
Fig.S1 Spatial distribution of temporal trends (% year-1) (a-c) and decadal-change types (d-f) of three ETS indicators for single and early rice in China during 1981–2010.
Fig.S1 Continued for late rice in China during 1981–2010.