Comparison of methodologies for degree-day estimation using numerical methods

Abstract

The development of projects related to the yield of various crops has been greatly eiihaticcd with the incorporation of mathematical models as well as essential and more consistent equations which enable a prediction and greater approximation to their actual behavior, thus reducing error in estimate. Among the operations requiring further investigation are those related to crop growth, characterized by the ideal temperature for addition of dry matter. Due to the wide use of mathematical methods for representing, analyzing and attaining degree-day estimation as well as the great importance of sugarcane in the Brazilian economy, we carried out an evaluation of the mathematical models and numerical integration methods commonly used for estimating the availability of degrees-day for this crop in the region of Botucatu, in Sao Paulo State, Brazil. Integration models with discretization every 6 hours have shown satisfactory results in degree-day estimation. Conventional methodologies have shown satisfactory results when the estimation of degrees-day was based on the time-temperature curve for each day and for groups of 3, 7, 15 and 30 days. Through numerical integration method, the region of Botucatu showed a annual thermal availability average from 1,070.6 degrees-day for the sugarcane. Keywords: vegetative development, heat units, numerical integration methods, sugar cane.RESUMO. Cotnparaçâo de metodologias para estimativa de graus-dia usando métodos numéricos. O desenvolvimento de projetos relacionados ao desempenlio de diversas culturas tem recebido aperfeiçoamento cada vez maior, incorporado a modelos matemáticos sendo indispensável à utilizaçâo de equaçôes cada vez mais consistentes que possibilitem previsâo e maior aproximaçâo do coniportaniento real, diminuindo o erro na obtençâo das estimativas. Entre as operaçôes unitarias que demandam maior estudo estáo aquelas relacionadas com o crescimento da cultura, caracterizadas pela temperatura ideal para o acréscimo de materia seca. Pelo ampio uso dos métodos matemáticos na representaçâo, análise e obtençâo de estimativas de graus-dia, juntamente com a grande importancia que a cultura da cana-de-acúcar tem para a economia brasileira, foi realizada uma avaliaçâo dos modelos matemáticos comumente usados e dos métodos numéricos de integraçâo na estimativa da disponibilidade de graus-dia para essa cultura, na regiáo de Botucatu, Estado de Sao Paulo. Os modelos de integraçâo, com discretizaçâo de 6 em 6 h, apresentaram resultados satisfatórios na estimativa de graus-dia. As metodologias tradicionais apresentaram desempenhos satisfatórios quanto à estimativa de grausdia com base na curva de temperatura horaria para cada dia e para os agrupamentos de tres, sete, 15 e 30 dias. Pelo método numérico de integraçâo, a regiáo de Botucatu, Estado de Sao Paulo, apresentou disponibilidade térmica anual média de 1.070,6 GD para a cultura da cana-de-acúcar.Palavras-chave: desenvolvimento vegetativo, unidades térmicas, métodos de integraçâo numérica, cana-de-acúcar.

Does thermal time for germination vary among populations of a tree legume (Peltophorum dubium)?

“…Souza et al (2011) estimated the annual degree-days availability for cane sugar in Botucatu (SP), and observed that a DD2 similar method using the averages calculated from daily maximum and minimum temperatures produced estimations of degree-days accumulation similar to those obtained from Villa Nova et al (1972) method. Furthermore, when the authors used integration methods from temperatures taken hourly the lowest estimates of degree-days accumulation were obtained, as reported in the present study.…”

Thermal Requirements and Productivity of Squash (Cucurbita moschata Duch.) in the Cerrado-Amazon Transition

“…This behavior is often expected since the degree-days method assumes a linear link between temperature and plant development; however, such connotation is only true into the cardinal temperature range of the plant -minimum base temperature Tb; optimum temperature -Topt; and maximum base temperature TB (Fagundes et al, 2010;Cardoso, 2011;Souza et al, 2011). The coefficient of variation (CV %) could be used to measure the duration variability (days or degree days) on the developmental phases of cultures grown at different times (Cardoso, 2011).…”

“…The minimum (Tb) and maximum (TB) basal temperatures of 12 and 35 °C respectively (Mota et al, 1977), were used to find the thermal sums (accumulated degree days, GDD) for squash. The proposal by Ometto (1981) was adopted due to cases that were seen as possible, depending on the local weather conditions, as it was recommended by Souza et al (2011). The experiment was conducted in randomized blocks with six treatments (sowing epochs with ten-days intervals in winter, on June 05, 15 th , 25 th , and July 05, 15 th , 25 th of 2013) and four repetitions of five plants each.…”

Yield and water use efficiency of cauliflower under irrigation different levels in tropical climate

“…The minimum (Tb) and maximum (TB) basal temperatures of 14 and 36°C (Nowbuth and Pearson, 1998) were applied in order to find the thermal sums (accumulated degree-days) for cauliflower plants. The proposal by Ometto (1981) was applied to cases suitable for it which depends on the local weather conditions, according to Souza et al (2011b).…”