Analysis and use of cumulative nutrient uptake formulas in plant nutrition and the temporal-weight-averaged influx

REGINATO, JUAN C.; BLENGINO, JORGE L.; TARZIA, DOMINGO A.

JOURNAL OF PLANT NUTRITION

TAYLOR & FRANCIS INC

Año: 2017 vol. 40 p. 2511 - 2520

0190-4167

A generalized cumulative uptake formula of nutrient uptake by rootsfollowing our previous formula (Reginato-Tarzia, Comm. Soil Sci. and Plant.,33 (2002), 821-830) is developed. Cumulative nutrient uptake obtained bythis formula is compared with the simulated results obtained by the Claassenand Barber (Claassen and Barber, Agronomy J., 68 (1976) 961?964) andCushman (Cushman, Soil Sci. Soc., 43 (1979) 1087?1090) formulas. A massbalance is analyzed for the three formulas of cumulative nutrient uptake inorder to decide which of them is correct. Moreover, the mass balance is alsoverified through a computational algorithm using data obtained fromliterature, and we compute the potassium (K) uptake for maize for low andhigh soil concentrations using the three mentioned formulas. The theoreticalanalysis shows that Claassen and Barber, and Cushman formulas do notverify, in general, the mass balance condition. The Claassen and Barberformula only verifies this condition when the influx is constant and rootgrows linearly. The Cushman formula verifies the mass balance when theinflux is constant regardless of the law of root growth. Reginato and Tarziaformula always verifies the mass balance whatever be the representativefunctions for the influx and the law of root growth. Moreover, we propose aredefinition of the averaged influx from which the Williams formula (Williams,J. Scientific Res., 1 (1948) 333?361) can be deduced. We remark that Williamsformula is a consequence of our definition of temporal-weight-averagedinflux for all root growth law expressions. Also, we present a comparison ofinflux and cumulative uptake of cadmium (Cd) with data extracted fromliterature. Cumulative uptake is obtained through the Barber?Cushmanmodel and our moving boundary model by using the redefinition ofaveraged influx on root surface and the correct cumulative uptake formulapresented in this paper.