Quantifying root water extraction by rangeland plants through soil water modeling

Abstract

We used soil water modeling as a tool to quantify water use of non-cultivated plant communities based on easily measured field data of soil water contents, soil hydraulic properties, and leaf area index. The model was applied in the mixed-grass prairie, considering a dynamic and non-uniform root distribution, the effect of soil water stress on plant water uptake, as well as the compensation effect of root water uptake. The simulation was conducted for the 111 days from mid May to early September of 2009. A good agreement between the model simulated and field measured soil water contents was obtained, with a maximum rooting depth estimated within the depth range of 1.3–1.6 m. The results suggest that a reasonable estimate of soil water retention parameters, and especially the use of the root uptake compensation significantly improved both numerical accuracy in predicted soil water dynamics, and the biological importance in the predicted seasonal root water extraction. In particular, the model gave a reasonable simulation of the seasonal progression of the drying zone in the soil profile in the summer of 2009. The method and analyses used in this paper may be useful in a wider context of soil-plant relationships.

Appendices

A list of main symbols used in this paper

Symbol:

Definition (Unit)

a _g , b _g :

Empirical root growth parameters (-,-)

α(h):

Reduction factor for water uptake as a function of h (-)

ARD :

Average relative discrepancy between simulation and measurement

β, λ:

Shape factor for root density distribution (-)

c :

Soil water capacity (m^-1)

D₁ :

Day of the start of root growth (=0 on April 15)

D₂ :

The number of days required for the maturity of plants

Δt :

Time step of simulation (=100 s)

Δz :

Vertical increment of simulation (=0.025 m)

E _a (t):

Actual soil evaporation at time t (m s^-1)

E _p (t):

Potential soil evaporation at time t (m s^-1)

ET _p (t) :

Potential evapotranspiration at time t (mm day^-1)

γ,m,n :

Parameters for the water retention curves (m^-1,-,-)

F _i :

Fraction of root length in top 10% of the root zone

g :

Acceleration due to gravity (=9.81 m s^-2)

h :

Soil matric potential based on unit weight (m)

h ₁ :

Soil matric potential at anaerobiosis point (m)

h ₂ :

Upper matric potential for optimal uptake (m)

h ₃ , $h_3^1,h_3^2$:

Lower matric potential for optimal uptake (m)

h ₄ :

Soil matric potential at wilting point (m)

h ₍₁₎ :

Soil matric potential at soil surface (m)

K _c :

Average canopy transmission coefficient (=0.4)

K(h):

Hydraulic conductivity as a function of h (m s^-1)

$K_{sat}^s$ :

K _sat at soil surface (m s^-1)

K _sat :

Saturated hydraulic conductivity (m s^-1)

${K_{{z_{\max }}}}$ :

Hydraulic conductivity at soil bottom (m s^-1)

K ₍₁₎ :

Hydraulic conductivity at soil surface (m s^-1)

LAI :

Leaf area index (m² m^-2)

L _nrd :

Normalized root density (-)

L _r (t):

Rooting depth at time t (m)

L _m :

Maximum rooting depth (m)

RMSE :

Root mean square error

M _w :

Molecular weight of water (=0.018 kg g mol^-1)

n′:

Number of depths of soil water measurement (m)

ψ:

Pressure potential at soil-atmosphere interface (m)

R :

Gas constant (kg m² s^-2 K^-1 g mol^-1)

R _ain :

Daily rainfall (mm day^-1)

R _h :

Average daily relative humidity of air (as a fraction)

S(z,t):

Root water uptake at depth z and time t (s^-1)

S _e :

Effective saturation (-)

t :

Time (s, day)

T :

The absolute temperature (K)

T _a :

Average daily air temperature (°C)

T _d :

Average daily dew point temperature (°C)

_θ :

Volumetric soil water content (m³ m^-3)

_θr , _θs :

Residual and saturated water content (m³ m^-3)

_θsi :

Simulated water content in ith depth (m³ m^-3)

_θmi :

Measured water content in ith depth (m³ m^-3)

_θm :

Average of measured water contents (m³ m^-3)

T _p :

Daily potential transpiration (mm day^-1)

z :

Vertical axis pointing downwards from soil surface (m)

z _max :

Vertical coordinate at the bottom of soil profile (m)

z _r (=z/L _r ):

Normalized soil depth containing plant roots (-)

Appendix

According to Lai and Katul (2000) and Liu et al. (2005), the integration of the root distribution function g(z,t) along the root zone must equal to unity, so that the potential transpiration is partitioned along the whole root zone:

$$ \int\limits_0^{{L_r}(t)} {g\left( {z,t} \right)} \,dz = 1. $$

(A1)

Using the root density function of Ojha and Rai (1996), we show that Eq. A1 is satisfied:

$$ \begin{gathered} \int\limits_0^{{L_r}\left( t \right)} {g\left( {z,t} \right)} \,dz = \begin{array}{*{20}{c}} {\int\limits_0^{{L_r}\left( t \right)} {\frac{{\beta + 1}}{{{L_r}\left( t \right)}}{{\left[ {1 - \frac{z}{{{L_r}\left( t \right)}}} \right]}^\beta }\,dz} } \hfill \\ { = \frac{{\beta + 1}}{{{L_r}\left( t \right)}}\int\limits_0^{{L_r}(t)} {{{\left[ {1 - \frac{z}{{{L_r}\left( t \right)}}} \right]}^\beta }dz} } \hfill \\ { = \frac{{\beta + 1}}{{{L_r}\left( t \right)}}\int\limits_1^0 {z{\prime ^\beta }[ - {L_r}\left( t \right)]\,dz\prime } } \hfill \\ { = \frac{{\beta + 1}}{{{L_r}\left( t \right)}}\int\limits_0^1 {z{\prime ^\beta }{L_r}\left( t \right)\,dz\prime } } \hfill \\ { = \left( {\beta + 1} \right)\int\limits_0^1 {z{\prime ^\beta }\,dz\prime } } \hfill \\ { = \frac{{\beta + 1}}{{\beta + 1}}\,z{\prime ^{\left( {\beta + 1} \right)}}\left| {_0^1} \right.} \hfill \\ { = 1,} \hfill \\ \end{array} \hfill \\ \hfill \\ \end{gathered} $$

(A2)

where we defined a new variable $z\prime = 1 - \frac{z}{{{L_r}(t)}}$, with differential $dz\prime = - \frac{1}{{{L_r}(t)}}dz$. When $z = {L_r}(t)$, we have $z\prime = 1 - \frac{{{L_r}(t)}}{{{L_r}(t)}} = 0$; when z = 0, we have z′ = 1. So, the lower and upper limits of the integration need to be changed accordingly, if z is replaced by z′. In deriving Eq. A2, we assumed that both L_r(t) and β are constants, given time t.