Barber—Cushman model

The classic Barber-Cushman model treats the root surface as a smooth solid cylinder. Yet many experimental studies have shown that root hairs are important for the uptake of some nutrients, e.g., P (25,26). Various mathematical models for root hairs have been used (5,27,28), which all differ slightly in the way in which root hairs are modeled. Most authors conclude that root hairs make a substantial contribution to uptake, particularly for relatively immobile nutrients. 

While most authors have used the finite-difference method, the finite element method has also been used—e.g., a two-dimensional finite element model incorporating shrinkable subdomains was used to de.scribe interroot competition to simulate the uptake of N from the rhizosphere (36). It included a nitrification submodel and found good agreement between ob.served and predicted uptake by onion on a range of soil types. However, while a different method of solution was used, the assumptions and the equations solved were still based on the Barber-Cushman model. 

Figure 7 Comparison of experimental and modeled potassium depletion in the soil close to a planar mat of rape roots for three soil levels. The modeled lines were calculated using the Barber-Cushman model. (From Ref. 104.)...

Figure 14 The predicted uptake of phosphorus by maize over a 22 day period. The Barber-Cushman model (F, ), u.ses an average root radius calculated at the end of the simulation period, while the F, model uses a population of roots of different radius. Identical parameter values were used by both simulation models with the exception of root radius.

Figure 7.2. Predicted as a function of measured Cd uptake by maize after 24 days of cultivation time, according to the Barber-Cushman model. The numbers enclosed in circles stand for the level of Cd added to the soil (expressed as mg kg ). The model adequately predicts the uptake for Cd contamination levels up to 3 mg kg (level of Cd added to the soil) but clearly overestimates the actual uptake of Cd for greater levels of soil contamination, which were thus discarded for the regression analysis. (Adapted from Sterckeman et al., 2004.)...

Reginato, J.C., Palumbo, M.C., Moreno, I.S., Bernando, I.Ch., Tarzia, D.A., 2000. Modeling nutrient uptake using a moving boundary approach. Comparison with the Barber-Cushman model. Soil Sci. Soc. Am. J. 64, 1363-1367. 

Marschner H. Mineral Nutrition of Higher Plants, Academic Press, London, 1995. S. A. Barber and J. H. Cushman, Nitrogen uptake model for agricultural crops, Moiieling Waste Water Renovation—Land Treatment (I. Iskander, ed.), Wiley In-terScience, New York, 1981. pp. 382-404. 

Barber, S.A., t995. Soil Nutrient Bioavailabitity A Mechanistic Approach. Wiley, New York. Barber, S.A., Cushman, J.H., 1981. Nitrogen uptake model for agronomic crops. In Inskandar, I.K. (Ed.), Modeling Wastewater Renovation-Land Treatment. Wiley-lnterscience, New York, pp. 382-A09. 

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