An analogic model of water extraction by grass roots

An Analogic Model of Water Extraction by Grass Roots

Clóvis Angeli Sansigolo

Epaminondas S. Barros Ferraz

DMA, CPTEC, Instituto Nacional de Pesquisas Espaciais

São José dos Campos, São Paulo, Brazil

The water extraction by plant roots is the main water balance component in vegetated soils. The basic one dimensional differential equation for the soil water flux and root extraction is ¶q/¶t = ¶q/¶z [k (¶x/¶z) - k] - qr . The single root model is the analytical solution of ¶q/¶t =1/n¶/¶n(n k ¶ys /¶n) i.e. q¢r = - [2 p k (yr - ys)] / ln (n2 /n1), which can be extended for an uniform root system by qr = q¢r zr lr . Root water extraction can also be expressed analogically to Ohm's law by qr = - (yr - ys) / rs =- (yp - yr) / rr = - (yp - ys) / (rr + rs), where the soil resistence rs = b/k, and b = ln (n2 /n1) / 2 p lr zr. A simulation model was developed from the first equation combined with an analogic macroscopic root extraction function: ¶q/¶t = ¶/¶z [k (¶x/¶z) - k] + [yp - ys(z)] / [rr(z) + rs(z)]. Supposing an exponential variation of b(z) and rr(z), due to the exponential decreasing in mass of the root system, w(z) = w(0)exp(-az): b(z) = b(0)exp(az) and rr(z) = rr(0)exp(az), we have - [ys(z)/qr] exp(-az) = yp/qr(z) exp(-az) - b(0)/k(z) - rr(0). Applying this equation to 3 or more layers at depths z we have the solutions for yp, b(0), and rr(0). The average rates of water extraction by roots, from 20 cm soil layer, were obtained from q profiles, measured with a neutron probe during 3 dry months (Sept-Nov), at 3 days interval, in a 2m depth soil covered by short grass. The soil matric potential, hydraulic conductivity, and mass distribution of the root system was fitted to field data. The fitted model coefficients were b(0) = 2 ± 0.4 cm, and rr (0) = 15000 ± 6600 days.The average root resistance predominates until soil water potential x < -5000 cm. It was also observed that the plant water potential is constant until x = -5000 cm, increasing abruptally after this point. The model reproduced very well the field root extraction rates used in the model calibration and may be used to study the dynamics of the complexes interactions among soil, plant and atmosphere.