Water Loss in Horticultural Products - Modelling, Data Analysis and Theoretical Considerations

The water loss of individual fruit (melon, plum and mandarin) was analysed using the traditional diffusion based approach and a kinetic approach. Applying simple non linear regression, both approaches are the same, resulting in a quite acceptable analysis. However, by applying mixed effects non linear regression analysis, explicitly including the variation over the individuals, the kinetic approach was found to reflect the processes occurring during mass loss better than the diffusion approach. All the variation between the individuals in a batch could be attributed to the initial mass or size of the individuals. The fraction of the fruit mass that is available for transpiration is the key item in the water loss process, rather than the skin resistance and fruit area. Obtained explained parts are well over 99%. INTRODUCTION Water loss in horticultural products is still a major problem for growers, wholesalers and retailers (Banks et al., 2000). Research on water loss however, is nowadays very limited. The problem has been solved, hasn’t it? Water diffuses through the skin into the environment which seems to be a simple and straightforward formulation and modelling using Fick’s first law (De Smet et al., 2002; Díaz-Pérez, 1998; Maguire et al., 1999a, b, 2001). However, recently results have been found in the behaviour of water loss in different fruits (melons, plums and mandarins) that suggest a different mechanism is active. Non linear mixed effects regression analysis was applied to mass loss in monitored individual fruit. All the variation between the individuals in a batch could be attributed to the initial mass or size of the individuals. The rate constant of water loss (transpiration) was exactly the same for all individuals, even over different near-isogenic lines of melons with most probably large differences in skin thickness and water vapour resistance. The amount of potential water loss is limited and certainly not equal to the total mass of the fruit. A fraction of the fruit mass is dry matter and will not be involved in water loss. Moreover, water will be less available for transpiration when bound to compounds like pectines, cellulose, sugars, etc., or occluded inside cells (cytosol). That forces us to rethink and remodel water loss. The traditional approach is diffusion based and assumes that the rate of transpiration depends on the fruit area, size and resistance of the skin with respect to gases and water vapour. This approach has been used for several decades, however, to our knowledge never on individually monitored fruit. Since the size or mass vary over the individuals, this traditional approach inherently assumes that the biological variation will be in the overall rate constant of transpiration. In this paper the water loss of melons, plums and mandarins, will be analysed using the same generic model based on a chemical equilibrium reaction as an approximation for the diffusive process of transpiration, assuming that the variation will be present in the amount of water that potentially can be transpired. By statistical analysis using nonlinear mixed effects analysis, better results were obtained than with the traditional approach. All analyses achieved explained parts well over 99%. Proc. III IC Postharvest Unlimited 2008 Ed: W.B. Herppich Acta Hort. 858, ISHS 2010 466 MATERIALS AND METHODS Experimental Setup 1. Melons. In two successive seasons (2005 and 2006) near-isogenic lines (NILs) containing introgressions of different extent from the Korean accession ‘Shongwan Charmi’ PI 161375 (SC) on the linkage group III VII and X into the ‘Piel de Sapo’ (PS) genetic background (Eduardo et al., 2005) were grown in Torre Pacheco (Murcia, Spain) according the commonly used practise for melon cultivation. Fruit were stored covered by plastic liners (Plásticos del Segura, Murcia, Spain) at 21±1oC and 66±6% RH (2005) and at 20.6±1.5oC and 78±13% RH (2006). Fruit were individual labelled and monitored for mass during 22 and 24 d of storage respectively for both seasons. Details of the plant material used and the experimental setup have been reported in Fernández-Trujillo et al. (2008) and Tijskens et al. (2009). 2. Plums. ‘Jubileum’ plums were grown in 2006 and 2007 at the orchard of Planteforsk Ullensvang Research Center in Western Norway and harvested in September at commercial maturity. Plums were stored in storage rooms at 16oC (2006) and 20oC (2007) at about 60-70% RH. In each season, 60 fruit were individually labelled. The mass of these fruit was individually recorded during 5 d of storage. 3. Mandarins. ‘Fortune’ mandarins were grown at a commercial orchard in Cartagena (Spain) during 2007, harvested according commercial criteria and stored for 50 d at 5oC and about 95% RH. During growth, mandarin trees were submitted to four RDI (Regulated Deficit Irrigation) treatments (see Fig. 1). Per water stress treatment 84 fruit were individually labelled and fruit mass was measured regularly during the storage period. Model Development The traditional approach in modelling water loss is based on Fick’s first law of diffusion. Assuming an inner compartment (fruit tissue) separated from an outer compartment (storage room) by some membrane (skin), and assuming the outer volume is large compared to the amount of water loss, i.e., the outer conditions are unchanged by the process, and solving the differential equation for constant external conditions, we arrive at: