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The Shape of the Transpiration Reduction Function under Plant Water Stress

^a Dep. of Environmental Sciences, Wageningen Univ., Droevendaalsesteeg 4, 6708 PB Wageningen, the Netherlands
^b Exact Sciences Dep., Esalq-Univ. of São Paulo, 13418-900 Piracicaba (SP), Brazil, currently at Dep. of Environmental Sciences, Wageningen Univ., the Netherlands

View larger version (20K): [in this window] [in a new window]   Fig. 1. Schematic representation of (a) spatial distribution of roots in root zone and (b) root and axial segments, as used for the simulations (rm is the radius of the root extraction zone, r0 is the root radius, dr is the root segment size, and z is the rooting depth).

View larger version (13K): [in this window] [in a new window]   Fig. 2. Relative matric flux potential M/Ml as a function of distance from the root center at selected times, obtained from numerical simulations with the van Genuchten hydraulic relations for the clay soil at a potential transpiration rate of 6 mm d–1 and low root density (tl = time of first occurrence of limiting hydraulic conditions).

View larger version (18K): [in this window] [in a new window]   Fig. 3. Relative deviation of matric flux potential ratio M/Ml from its value at the outside of the rhizosphere at selected times from time of first occurrence of limiting hydraulic conditions (tl) between tl + 0.16 d and tl + 14 d, as a function of distance from the root center at selected times, obtained from numerical simulations with the van Genuchten hydraulic relations for the clay soil at a potential transpiration rate of 6 mm d–1 and low root density.

View larger version (20K): [in this window] [in a new window]   Fig. 4. Transpiration as a function of mean matric flux potential for combinations of root density, soils, and transpiration rates (Table 2). Cases where the decrease of water content from limiting hydraulic conditions to the permanent wilting point at potential transpiration (tl–w) 1 d were omitted (see Table 3). Filled symbols result from simulations at a potential transpiration rate (Tp) = 3 mm d–1; open symbols are from simulations at Tp = 6 mm d–1; Ml is the mean matric flux potential at the onset of the falling-rate phase.

View larger version (18K): [in this window] [in a new window]   Fig. 5. Relative transpiration Ta/Tp as a function of mean soil water content , obtained from numerical simulations with the van Genuchten hydraulic relations for the three soils (Table 1) at four root densities (RD, Table 2) and low transpiration rate (3 mm d–1).

View larger version (16K): [in this window] [in a new window]   Fig. 6. Relative transpiration Ta/Tp as a function of , obtained from numerical simulations with the van Genuchten hydraulic relations for the three soils (Table 1) at a potential transpiration rate of 3 mm d–1 for four root densities (RD, Table 2).

View larger version (19K): [in this window] [in a new window]   Fig. 7. Relative transpiration Ta/Tp as a function of (Eq. [24]) according to analytical solutions for Green and Ampt, Brooks and Corey, versatile nonlinear, and exponential soils, compared with a constant diffusivity soil. (Root densities [RD] according to Table 2; factor A as defined by Eq. [27].)

View larger version (15K): [in this window] [in a new window]   Fig. 8. Relative transpiration Ta/Tp (a) as a function of volumetric water content and (b) as a function of pressure head h, for three root densities (RD) according to the analytical solution for the Green and Ampt soil, applied to the sand soil at low transpiration rate (3 mm d–1).