# 3.2.3  Calculating water depletion around roots

Figure 3.8 Calculated distributions of volumetric soil water content (left) and pressure in water-filled pores (right) as functions of distance from a model root. Pressures become more negative over time, indicating increasing suction. Horizontal lines denote water status on each of six successive days (day 1 is uppermost). The steepening of curves at later times reflects how transport of water from bulk soil to the root surface becomes increasingly difficult as the soil dries. r = distance from central axis of root

Water removed by transpiration results in drier soil around roots compared with bulk soil, with profound consequences for rhizosphere biology, chemistry and nutrient fluxes. As soil dries near the root surface, water flows radially from bulk soil to replenish it. Calculated distributions of water content and pore water pressure with radial distance from an absorbing root (Figure 3.8) show a pronounced increase in suction adjacent to absorbing surfaces.

Roots are cylindrical sinks for water. A radial flow of water from the bulk soil towards roots of transpiring plants is maintained by suction at the root surface. However, because K falls away with falling water content, there is a limit to how fast roots can extract water from soil. Once this limit has been reached, increasing suction by roots simply steepens the gradient in P to match the fall in K close to root surfaces so that the product of the two (Equation 3.1) remains the same.

Although soil water is driven by gradients of pressure, it is more convenient when water content is changing to describe this flow in terms of gradients in volumetric water content, θ (m3 m–3). The coefﬁcient relating flow rate to the gradient in water content is known as diffusivity, D (m2 s–1), and the appropriate equation is formally analogous to Fick’s First Law of diffusion:

This equation can be elaborated to allow for cylindrical flow, and then solved to derive a simple expression to quantify the gradient in soil water content around roots as follows:

where ∆θ is the difference in volumetric water content between bulk soil and the root surface (m3 m–3), Q is the flow rate of water through the soil (m3 m–3 s–1) and L is the average length of absorbing root per unit volume of soil (root length density — m m–3).

Like K, D varies with soil water content, although not so widely. Laboratory measurements of D, which are so far the only ones made with any accuracy, show a decrease of at least 50-fold as soil dries, for example in sandy loam from about 10–7 to about 10–9 m2 s–1.

The decrease in soil moisture near absorbing roots can be calculated by substituting values into this equation. In a damp (not wet) soil (water potential, Ψ = –100 kPa), D might be 10–8 m2 s–1 and L a modest 104 m m–3 (1 cm cm–3). If Q, the transpiration rate, is 5 × 10–7 m3 m–3 s–1 (about 10 mm of water lost from the surface 200 mm of soil each day), then θ at the root surface will be only 0.0015 m3 m–3 less than in the bulk soil. This corresponds to less than a 1% decrease in water content close to the root of a transpiring plant.

Now imagine a sparser root system with undiminished transpiration; L drops to 5 × 102 m m–3 and D to 7.5 × 10–9 m2 s–1 as soil around the roots dries. To sustain transpiration, θ would have to be 0.04 m3 m–3 lower at the root surface or about 25% drier than bulk soil. Shoot water potential must then decrease as the soil around roots dries if water transport is to be maintained. A point will be reached where resistance to water flow through soil is so great that a plant’s ability to generate water potential gradients is insufﬁcient to sustain transpiration. Drought ensues (Chapter 15).

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