A nonlinear model for crop development as a function of temperature

Abstract

The Beta function, commonly used as a skewed probability density function in statistics, was introduced to describe the effect of temperature on the rate of crop development. The framework is set by three cardinal temperatures, namely the base (Tb), the optimum (T 0 ) and the ceiling (T,) temperature. The model parameters T b and 7;; and three other coefficients JJ., a and {3 can be used to derive the value of T 0 and the maximum developmem rate. Parameter a also characterizes the curvature of the relationship with temperatures between Tb and T 0 , and parameter {3 describes the curvature between T 0 and T..,. The model has one parameter less than the Rice Clock Model (RCM); and in contrast to the RCM, it ensures that the maximum development rate occurs exactly at 7;,. The model accurately described the response to temperature of several developmental processes, and was superior to two widely used thermal time approaches in predicting rice flowering time.

Soma térmica de algumas fases do ciclo de desenvolvimento da escala de COUNCE para cultivares Sul-Brasileiras de arroz irrigado

“…Quando se consideraram as temperaturas cardinais constantes durante o ciclo de desenvolvimento do arroz, o CV foi ligeiramente menor com a soma térmica calculada pelo método 3 (STa 3 ), seguidas por STa 2 , STa 1 e dias após a emergência. Esses resultados confirmam que o efeito da temperatura sobre o desenvolvimento vegetal é mais bem representado levando-se em conta as três temperaturas cardinais (YIN et al, 1995;STRECK, 2002;STRECK et al, 2003), o que é contemplado no método 3, embora a pequena diferença de CV entre os métodos (Figura 3) possa ser motivo para se propor o uso do método mais simples de cálculo (STa 1 ), o qual apenas leva em conta o acúmulo térmico acima da Tb (eq. 1).…”

“…Essa maneira de calcular é outra fonte de críticas, pois não é completamente realística do ponto de vista biológico, haja vista que a resposta dos processos biológicos à temperatura, inclusive desenvolvimento, é mais bem expressa em termos das três temperaturas cardinais, (temperatura mínima, ótima e máxima) (YIN et al, 1995;BONHOMME, 2000;STRECK, 2002). Outra fonte de crítica é com relação às temperaturas cardinais geralmente consideradas constantes ao longo do ciclo da cultura, muitas vezes, também, não é uma pressuposição adequada; essas temperaturas não são constantes durante o ciclo de desenvolvimento vegetal para muitas espécies (STRECK et al, 2003;PAULA et al, 2005).…”

Temperate and boreal forest tree phenology: from organ-scale processes to terrestrial ecosystem models

“…The modeling of fruit maturation or cone development has received even less attention in forest tree species, and most studies (but see Chuine and Beaubien 2001) consider crops and fruit trees (e.g., Yin et al 1995;Garcia de Cortazar-Atauri et al 2009, but see Mutke et al 2003). Fruit maturation models represent the action of temperature from the flowering date, first on fruit cell multiplication and growth and, second, on the rate of carbohydrate accumulation in the fruit.…”

A Model for Phenological Development of Vietnamese Rice Influenced by Transplanting Shock

“…The value of DVI is the integration of the developmental rate (DVR). In this study, we used the beta function to express the DVR response to temperature as proposed by Yin et al (1995),…”

“…Takezawa and Tamura, 1991;Nakagawa and Horie, 1995;Yin et al, 1995;Huang et al, 1998), most models do not cover the infl uence of the transplanting shock because they were not targeted to transplanting cultivation or because of a lack of adequate quantitative data for model development. Only a few models, CERES-Rice (Ritchie et al, 1987), ORYZA1 (Kropff et al, 1994), RIBHAB (Salam et al, 1994) and the transplanting shock sub-model for CERESRice and RIBHAB (Salam et al, 2001), considered the transplanting shock which was estimated from the seedling age expressed as degree days during the nursery period.…”