A 3D model for simulating the spatial and temporal distribution of temperature within ellipsoidal fruit Marc Saudreau a, * , Herve ´ Sinoquet a , Olivier Santin b , Andre ´ Marquier a , Boris Adam a , Jean-Jacques Longuenesse c , Lydie Guilioni d , Michae ¨l Chelle b a UMR547, PIAF, INRA, UNIV BLAISE PASCAL, F-63100 Clermont-ferrand, France b UMR1091, Environnement et grandes cultures, INRA, F-78850 Thiverval-Grignon, France c UR1115, PSH, INRA Domaine Saint-Paul – Site Agroparc, F-84914 Avignon, France d Montpellier SupAgro, UMR 759, LEPSE, 2 Place Viala, F-34060 Montpellier, France Received 21 December 2006; received in revised form 31 May 2007; accepted 7 June 2007 Abstract A physical model simulating the spatio-temporal distribution of temperature in an ellipsoidal fruit has been developed. It is based on the numerical resolution of the three-dimensional (3D) unsteady heat conduction equation with unsteady and non-homogeneous heat fluxes as boundary conditions. The numerical scheme and the physical models have been tested by comparing with an analytical solution for simple configurations. The model quality has been assessed by comparing model outputs to temperature measured with thermocouples at several locations in isolated peach and apple fruits. The root mean square error (RMSE) for temperature simulated at a 1 min time step was about 0.8 8C. A sensitivity analysis showed that accurate estimations of the surface conductance to water vapor diffusion and of the thermal conductivity are necessary. The model has also been used for identifying the main microclimate variables governing temperature dynamics within fruits. # 2007 Elsevier B.V. All rights reserved. Keywords: Fruit; Temperature; Dynamics; Three-dimensional; Microclimate; Modeling 1. Introduction Numerous biological processes involved in the development of fruits depend on temperature. Tempera- ture influences the early growth and gas exchange of peach fruit (Lescourret et al., 2000; Pavel and Dejong, 1993). Temperature impacts ripening, sugar and acid content of apples (Yamada et al., 1994), mandarins (Marsh et al., 1999) and tomatoes (Tomes, 1963). The color of the skin may also be a consequence of local surface temperature gradients (Lakso, 1980). Conse- quences on fruit quality such as size, taste and appearance are straightforward and well established (Ge ´nard and Bruchou, 1992). Also, temperatures within fruits are of economic significance because of sunburn injury (Glenn et al., 2002; Piskolczi et al., 2004) and of larval development (Ku ¨hrt et al., 2005) with loss of yield. The temperature of an organ generally differs from air temperature since an organ can gain or lose energy from radiation, evaporation, convection, conduction processes or from metabolism activity (Monteith and Unsworth, 1990; Cellier et al., 1993). However, air or soil temperature are usually used as relevant parameters in models (e.g. Ritchie and NeSmith, 1991; Gastal et al., 1992) as well as in experimental studies on the rela- tionship between temperature and organ physiology (Landsberg, 1974). But the use of such parameters can lead to erroneous conclusions as shown by Jamieson www.elsevier.com/locate/agrformet Agricultural and Forest Meteorology 147 (2007) 1–15 * Corresponding author. Tel.: +33 4 73 62 46 33; fax: +33 4 73 62 44 54. E-mail address: marc.saudreau@clermont.inra.fr (M. Saudreau). 0168-1923/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.agrformet.2007.06.006