Modeling fruit growth of apple

Abstract

Fruit growth of an individual apples starts after petal and is affected by different environmental factors and orchard and tree management. Prediction of fruit size is critical for management and to prepare for postharvest processing and the logistics. The objective of this study was to develop a model to predict growth of an individual apple fruit as a function of the physiological time using cumulative degree days (GDD). The cultivars 'Cripps Pink', 'Gala', and 'Red Delicious' were monitored twice weekly during four growing seasons for eleven different locations in the main apple growing regions of eastern Washington. Thirty fruits were selected and the equatorial diameter was monitored and registered weekly. Daily temperature data came from the closest automated weather station of AgWeatherNet to the orchard where the samples were collected. The model was based on the accumulation of GDD starting after the stage of full bloom. To determine GDD, the base temperature, i.e. 7.22°C, was subtracted from the average temperature for 'Cripps Pink', 5.55°C for 'Gala' and 6.11°C for 'Red Delicious' respectively. The Bon Verthalanfy statistical model was used to determine the base temperature and other model parameters and to derive growth rate of the apple using the equation δD/δt, where D is the adjusted function and t is time in days. To determine the diameter of an apple on a daily basis, the Euler integration method was used. The observed data showed differences in fruit size among years and locations. The cultivar 'Gala' was harvested earlier than the cultivars 'Cripps Pink' and 'Red Delicious' resulting in differences in base temperatures. The relative error between predicted and observed fruit diameter was in general less than 3%, but varied due to the location and year. The model will be implemented as a prototype on the AgWeatherNet portal (www.weather.wsu.edu) to help predict fruit size as a function of local temperature for locations where an automated weather station is available.