Richards equation has been widely used to simulate rice grain filling rates, but the lack of capability to relate environmental factors in its simulation impedes the application of Richards' equation in evaluating the impact of adverse climate on grain filling process. Therefore, a mathematical modeling method, together with two-year filed-seeding experiment(2012–2013) data, was used in this paper to examine the feasibility of an extended Richards' equation on this issue. The two-year experiment was carried out in Nanjing with two indica two-line hybrid rice cultivars, Lingliangyou 268 and Liangyoupeijiu. On the basis of the observations, Richards equation was first used to estimate rice grain filling parameters and calculate mean grain filling rate in each effective grain filling period. Subsequently, a radiation and temperature correction function was introduced into the Richards' equation to form an extended equation by linking the mean grain filling rates to daily radiation and mean temperature observations. A set of radiation and temperature characteristic parameters were included in the correction function, which theoretically reflect the response of mean grain filling rates to the change of temperature and radiation conditions and form response curves for the two tested varieties. To estimate these parameters, we applied the Shuffled Complex Evolution(SCE-UA) global optimization algorithm in this paper, since the extended equation was highly nonlinear. Statistical methods were also applied to analyze the relations between retrieved rice grain filling parameters and climatic factors. The results showed that insufficient sun radiation had an indirect and negative effect on mean grain filling rate by imposing an adverse influence on CO2 assimilation. Daily mean temperature mainly showed an evident effect on mean grain filling rate which could be accelerated under high temperatures or slow down at adverse low temperatures, but it also had a great influence on CO2 assimilation as well as the accumulation of assimilation products in grains. The estimated critical radiation and critical temperatures for Lingliangyou 268 were 18.94 MJ m–2 d–1, 6.81℃, 33.29℃, 30.28℃, respectively, and 21.71 MJ m–2 d–1, 6.10℃, 33.74℃, and 24.16℃ for Liangyoupeijiu, which demonstrate an evident difference between the two varieties. Quantitative analyses based on the temperature and radiation response curves showed that the correction coefficients for rice seeding dates in May in 2012 for both rice varieties were generally higher than that of other seeding dates, which implies that the time of seeding is critical to grain filling and yield formation. In addition, Lingliangyou 268 exhibited stronger temperature sensitivity in grain filling period, which means that the mean grain filling rate is more sensitive to the temperature change than to the radiation variation. In comparison, Liangyoupeijiu represented greater radiation sensitivity in grain filling, which indicates that this cultivar can be greatly influenced by insufficient radiation during the grain filling stage. On the whole, the mathematical model presented successfully retrieved the critical parameters representing the effects of daily mean temperature and radiation on mean grain filling rates from field observations. Although more validations are expected to examine the reliability and effectiveness of the proposed method, it can be an important reference for developing agro-meteorological indexes for monitoring and evaluating the effects of meteorological factors on rice grain filling as well as on yield formation.
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