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Modellering af optagelse af organiske stoffer i grøntsager og frugt

Bilag D
Fruit Tree Model

The tree model considers chemical influx into stem via xylem, outflux after equilibration, dilution by growth and first order metabolism (Trapp 2001). Exchange with air is neglected. The main difference between herbs or vegetables trees is the big wood compartment of trees with a mass of up to several hundred tons per ha. Wood is composed of cellulose, hemicellulose and lignin, which is a giant macromolecule with lipophilic sorption properties. The concentration ratio between wood and water named "K_Wood,W" (mg chemical per g dry wood to mg chemical per ml water) is significantly correlated to the log K_OW, for oak (Trapp et al. 2001):

Mass balance for the stem

Steady-state solution (dC_Stem/dt = 0):

Equation 21

where

The transpiration stream concentration factor (TSCF) is calculated by the correlation of Burken & Schnoor (1998) for poplars (corrected):

The calculated concentration ratio between stem and bulk soil with and without metabolism is shown in Table D.1. Chemicals with a low or medium log K_OW have a potential to accumulate in significant amounts in the stem via xylem from soil. Very lipophilic chemicals have low steady-state concentrations in stem compared to the soil concentration, due to slow uptake and dilution by growth. If chemicals are metabolized in wood, chemicals with slow uptake (high lipophilicity) will decrease in concentration. The half-life of 1 year is given to illustrate that even slow rates can lower steady-state concentrations of the lipophilic compounds in wood significantly.

Table D.1
Calculated steady-state concentration ratio between the concentration in the stem of an oak and bulk soil for different metabolism half-lives. 2% organic carbon in soil assumed.

Concentration in fruit

Transport into fruits can occur both with the phloem sap and with the xylem sap. In fruits, all dry mass arrives via the phloem. Phloem sap has a high dry mass content, about 10%. This dry mass remains in the fruit. Therefore, we can assume that the phloem flow is approximately 10 times the dry mass content. Different to leaves, fruits do not transpire very much, approximately the same amount of water is additionally flowing to the fruit via the xylem, to replace water evaporated from the peels. Table D.2 gives the dry mass content of a number of fruits from trees (Elmadfa et al. 1991), and the calculated water flow per kg fruit (fresh weight).

where

Although phloem loading with sugars occurs in the leaves, phloem concentrations of nonionized chemicals change toward the equilibrium with the stem. Thus the concentration of the chemical in the phloem sap is assumed to be the same concentration as within the xylem sap, which is calculated assuming chemical equilibrium between xylem and xylem sap.

The amount of chemical m transported with this water can then be calculated from the concentration in stem:

The concentration is then obtained by dividing the chemical mass m by the weight of the fruit (1 kg).

Table D.2
Dry weight of popular Danish fruits, and estimated water flow per kg fresh fruit

An example calculation for a fruit tree stand with 100 tons/ha biomass and 300 mm/year transpiration, a metabolisation half-life of one year of the chemical, and the water flux for nuts (19 L water flux per kg fruit) or apples (3.12 L water per kg fruit) is shown in Table D.3.

Calculated concentrations in fruit are rather high for the polar compounds, but probably overestimated. The model can be considered as "conservative", because loss of compound from the stem and the fruit by volatilization into air and by metabolism in the fruit is neglected.

Table D.3
Calculated bioconcentration in fruits (mg/kg fresh fruits : mg/kg wet soil). 2% organic carbon in soil

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