Relationship between root water uptake and soil respiration: A ...

Journal of Geophysical Research: Biogeosciences RESEARCH ARTICLE 10.1002/2017JG003831 Key Points: • A comparison of three root water uptake (RWU) models accounting for root water compensation and hydraulic redistribution was performed • RWU models drive the vertical distribution of soil moisture affecting modeled soil CO2 dynamics and CO2 efflux from the soil surface • Differences between models for the studied scenario were up to 20% for total transpiration and 14% for the soil CO2 efflux in 50 days

Supporting Information: • Supporting Information S1

Correspondence to: E. Daly, [email protected]

Citation: Teodosio, B., V. R. N. Pauwels, S. P. Loheide II, and E. Daly (2017), Relationship between root water uptake and soil respiration: A modeling perspective, J. Geophys. Res. Biogeosci., 122, 1954–1968, doi:10.1002/2017JG003831.

Received 2 MAR 2017 Accepted 12 JUL 2017 Accepted article online 17 JUL 2017 Published online 10 AUG 2017

Relationship between root water uptake and soil respiration: A modeling perspective Bertrand Teodosio1

, Valentijn R. N. Pauwels1

, Steven P. Loheide II2

, and Edoardo Daly1

1 Department of Civil Engineering, Monash University, Clayton, Victoria, Australia, 2 Department of Civil Engineering,

University of Wisconsin–Madison, Madison, Wisconsin, USA

Abstract

Soil moisture affects and is affected by root water uptake and at the same time drives soil CO2 dynamics. Selecting root water uptake formulations in models is important since this affects the estimation of actual transpiration and soil CO2 efflux. This study aims to compare different models combining the Richards equation for soil water flow to equations describing heat transfer and air-phase CO2 production and flow. A root water uptake model (RWC), accounting only for root water compensation by rescaling water uptake rates across the vertical profile, was compared to a model (XWP) estimating water uptake as a function of the difference between soil and root xylem water potential; the latter model can account for both compensation (XWPRWC ) and hydraulic redistribution (XWPHR ). Models were compared in a scenario with a shallow water table, where the formulation of root water uptake plays an important role in modeling daily patterns and magnitudes of transpiration rates and CO2 efflux. Model simulations for this scenario indicated up to 20% difference in the estimated water that transpired over 50 days and up to 14% difference in carbon emitted from the soil. The models showed reduction of transpiration rates associated with water stress affecting soil CO2 efflux, with magnitudes of soil CO2 efflux being larger for the XWPHR model in wet conditions and for the RWC model as the soil dried down. The study shows the importance of choosing root water uptake models not only for estimating transpiration but also for other processes controlled by soil water content.

1. Introduction Soil water extracted by plant roots for transpiration not only constitutes a significant portion of the hydrological cycle but also has an important role in the CO2 and energy exchange between the land and the atmosphere [Bonan, 2015]. Thus, key mechanisms regulating root water uptake, such as root water compensation and hydraulic redistribution, are essential for inclusion in models for ecohydrological applications. Root water compensation refers to the ability of vegetation to adjust root water uptake as a function of soil water content, while hydraulic redistribution refers to the movement of soil water from wetter to drier layers through the root system [Aroca et al., 2012]. These mechanisms have been observed to be significant in modulating actual transpiration (Tac ) [Caldwell et al., 1998; Da Rocha et al., 2004; Domec et al., 2010; Howard et al., 2009; Neumann and Cardon, 2012; Prieto et al., 2010], enhancing nutrient uptake [Caldwell et al., 1998; Neumann and Cardon, 2012; Prieto et al., 2012], prolonging root life span [Caldwell et al., 1998; Domec et al., 2006; Neumann and Cardon, 2012; Prieto and Ryel, 2014], and preventing evaporation through hydraulic descent in extremely dry conditions [Neumann and Cardon, 2012]. Accordingly, root water compensation and hydraulic redistribution have been incorporated in mathematical models to provide a more realistic description of root water uptake.

©2017. American Geophysical Union. All Rights Reserved.

TEODOSIO ET AL.

Many mathematical models for ecohydrological applications use the Richards equation with a sink term to describe soil water dynamics. When using a macroscopic approach, the soil water extraction rate from different soil layers is assumed to depend on the soil water content, root density, and potential transpiration [Molz, 1981; Skaggs et al., 2006]. As a first approximation, root water uptake is often considered proportional to root density, but root water compensation is often included by adjusting the distribution of root water uptake from different soil layers [Jarvis, 1989; Simunek and Hopmans, 2009; Jarvis, 2011]. Other models describe root water uptake as a function of water potential gradients between soil and root xylem [Molz, 1981; Mendel et al., 2002; Siqueira et al., 2008; Amenu and Kumar, 2007; Verma et al., 2014], thereby accounting for compensatory mechanisms in a process-based way. Some of these latter models have been extended to include a ROOT WATER UPTAKE MODEL COMPARISON

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detailed description of the root architecture [Couvreur et al., 2012; Javaux et al., 2013]. Although providing a three-dimensional detailed description of soil water dynamics, these models of root architecture are computationally expensive and involve a large number of parameters often difficult to quantify. The sink term introduced by De Jong Van Lier et al. [2013] models root water uptake as a function of the difference between the matric flux potential in the soil and a constant value of matric flux potential characterizing the root surface. This model functions equivalently to the model introduced by Jarvis [1989], as discussed in Jarvis [2010]. Comparisons between models of soil water fluxes using these different expressions for root water uptake have been presented by De Willigen et al. [2012] and Camargo and Kemanian [2016] in some virtual experiments. On the other hand, Santos et al. [2017] evaluated the capability of some empirical models to imitate the water extraction distribution under varying environmental conditions from numerical simulations of a detailed physical model. Since soil water content is one of the key variables regulating soil CO2 production and efflux [Hanson et al., 1993; Davidson et al., 1998; Almagro et al., 2009; Liu et al., 2009; Carbone et al., 2011; Suseela et al., 2012; Balogh et al., 2015; Reynolds et al., 2015; Lellei-Kovács et al., 2016], root water uptake mechanisms might play an important role in controlling CO2 fluxes. Mechanistic models have been developed for CO2 production and transport to adequately describe vertical gaseous diffusion and dispersion as a function of soil water content and temperature [Patwardhan et al., 1988; Simunek and Suarez, 1993; Fang and Moncrieff , 1999]. These models have been calibrated and validated against experimental data [Suarez and Simunek, 1993; Moncrieff and Fang, 1999; Goffin et al., 2015], have been coupled to soil water and temperature models at catchment scale [Welsch and Hornberger, 2004; Riveros-Iregui et al., 2011], and have been combined with experimental data of soil moisture, soil temperature, and air-phase soil CO2 concentrations to estimate soil CO2 production and surface efflux [Hirano et al., 2003; Chen et al., 2005; Jassal et al., 2008; Daly et al., 2009; Liang et al., 2010; Latimer and Risk, 2016]. Given the links between soil water and air phase CO2 dynamics, the inclusion of root water compensation and hydraulic redistribution in models of soil water dynamics will also affect the modeling of soil CO2 dynamics. Since different models of root water uptake are available, the aim of this study is to investigate the effect that different formulations of root water uptake have on the modeling of soil moisture and actual transpiration as well as CO2 dynamics, focusing on soil CO2 efflux. In this study, a model for root water uptake (RWC), accounting for root water compensation by rescaling water uptake rates across the vertical profile, is compared to a model (XWP) estimating water uptake as a function of the difference between soil and root xylem water potential; this second model is used in two modes: one to account for only root water compensation (XWPRWC ) and another to account for both root water compensation and hydraulic redistribution (XWPHR ).

2. Methodology 2.1. Model Description A one-dimensional model based on Simunek and Suarez [1993] is used to describe the soil water flow, heat transfer, and CO2 production and transport. As the equations used here are already available in the literature, we report in this section only the key features of the model with more details provided in Appendix A. The water flow in variably saturated soil is described using the Richards equation with a sink term for root water uptake (S (s−1 )), which reads [ )] ( 𝜕hs 𝜕𝜃 𝜕 𝜕 𝜕𝜃 + qw = − k(hs ) +1 = −S, (1) 𝜕t 𝜕z 𝜕t 𝜕z 𝜕z where 𝜃 (m3 m−3 ) is the volumetric water content, qw (m s−1 ) is the water flux, hs (m) is the soil water pressure head, k (m s−1 ) is the soil hydraulic conductivity, and z (m) is the vertical coordinate (positive upward). The unsaturated hydraulic properties of the soil are expressed by the soil water retention, 𝜃(hs ), and hydraulic conductivity, k(hs ), curves (Appendix A). Soil temperature is driven by C(𝜃)

[ ] 𝜕T 𝜕Ts 𝜕 = 𝜆(𝜃) s , 𝜕t 𝜕z 𝜕z

(2)

where Ts (K) is the soil temperature, 𝜆 (W m−1 K−1 ) is the apparent thermal conductivity, and C is the volumetric heat capacity of the bulk soil. TEODOSIO ET AL.

ROOT WATER UPTAKE MODEL COMPARISON

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The CO2 production and transport are modeled as [ ] ) ] 𝜕c 𝜕 [( 𝜕 𝜕 (𝜃s − 𝜃) + KH RTs 𝜃 ca = DE (𝜃, Ts ) a − qE ca − SKH RTs ca + Π, 𝜕t 𝜕z 𝜕z 𝜕z

(3)

where ca (m3 m−3 ) is the air phase CO2 concentration in the soil, 𝜃s is soil porosity, KH (mol s2 kg−1 m2 ) is the Henry’s Law coefficient, R (kg m2 mol−1 s−2 K−1 ) is the universal gas constant, DE (m2 s−1 ) is the effective dispersion coefficient, qE (m s−1 ) is the effective velocity of CO2 flux, and Π (m3 m−3 s−1 ) is the CO2 production rate. In equation (3), the CO2 dissolved in water, cw , is assumed to be related to ca as cw = KH RTs ca [Simunek and Suarez, 1993]. The CO2 production, Π, is assumed to be the sum of plant root and soil microorganism respiration. Other possible sources and sinks, such as chemical reactions, are neglected. The term Π is thus defined as Π = 𝛾s + 𝛾p ,

(4)

with the CO2 production of soil microorganisms, 𝛾s (m3 m−3 s−1 ), and plant roots, 𝛾p (m3 m−3 s−1 ), calculated as 𝛾s = 𝛾s0 fs (z)fs (hs )f (Ts )fs (ca ),

(5)

𝛾p = 𝛾p0 r(z)fp (hs )f (Ts )fp (ca ),

(6)

and

where 𝛾s0 (m3 m−3 s−1 ) and 𝛾p0 (m3 m−3 s−1 ) represent the optimal CO2 production by soil microorganisms and plant roots. The optimal CO2 production is reduced by functions (fs and fp ) dependent on depth, soil water pressure head, temperature, and CO2 concentration; r(z) in equation (6) is the root distribution (Appendix A). 2.2. Root Water Uptake Models Two models for the term S in equation (1) will be compared. The first model accounts for root water compensation, and it will be referred to as RWC. The second model includes changes in the xylem water potential (XWP) and describes root water compensation and hydraulic redistribution. This second model will be used with root water compensation only (XWPRWC ) and with both root water compensation and hydraulic redistribution (XWPHR ). 2.2.1. Root Water Compensation Model The sink term in equation (1) is commonly modeled as S = Tp fp (hs )r(z),

(7)

where Tp (m s−1 ) is the potential transpiration, and fp (hs ) and r(z) are in equations (A4) and (A12); they account for local water stress and describe the root distribution, respectively. To account for root water compensation, Jarvis [1989] modified equation (7) as S=

[

Tp

max 𝜔(t), 𝜔c

] fp (hs )r(z),

(8)

where 𝜔(t) is the water stress index, given by 0

𝜔=

∫−d

fp (hs )r(z)dz,

(9)

d being the root depth, and 𝜔c is the critical value of the water stress index also known as the root adaptability factor. When 𝜔c is equal to 1, equations (7) and (8) coincide. On the other hand, a value of 𝜔c equal to zero triggers a fully compensated root water uptake. This root water compensation model maintains the total transpiration equal to Tp as long as 𝜔 ≥ 𝜔c . This is achieved by rescaling the root water uptake using the value of 𝜔, meaning that roots experiencing water stress increase their water uptake as well.

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2.2.2. Root Xylem Water Potential Model In the XWP models, S is assumed to depend on the water potential difference between soil and roots [Herkelrath et al., 1977; Molz, 1981; Amenu and Kumar, 2007; Verma et al., 2014] as S = 𝛼S ksr (z)fp (hs )(hs − hx ),

(10)

where hx (m) is the water pressure head in the xylem, and 𝛼S is a factor that regulates hydraulic redistribution; 𝛼S = 1 when hs ≥hx and 0 ≤ 𝛼S ≤ 1 when hs < hx . The parameter ksr (m−1 s−1 ) is the soil-root radial conductance expressed as [Verma et al., 2014] (11)

ksr (z) = ksrt r(z),

where ksrt (s−1 ) is the total soil-to-root radial conductance. The function fp (hs ) in equation (10) accounts for the reduction of root water uptake due to different soil moisture conditions. This function reads as equation (A4) but the values of hs3 and hs4 are different from RWC; these will be indicated as h′s and h′s . The function fp (hs ) 3 4 accounts for the resistance due to the formation of air gaps between the soil and the roots when the soil is dry, as in the model by Herkelrath et al. [1977] [see also Molz, 1981]. The same function also accounts for the stress induced by the reduction of oxygen when the soil approaches full saturation. The use of fp (hs ) thus mirrors the same sources of stress included in RWC. Other formulations of root water uptake as a function of the difference between soil and xylem water potentials, not including the Feddes reduction function, are available [Nimah and Hanks, 1973; Russo et al., 2004], but were not implemented here. Since S depends on hx , a model for water flow in the root xylem is required. The model defines the xylem as a porous medium, and Darcy’s law is used to describe the water flow through the xylem as [Amenu and Kumar, 2007; Verma et al., 2014] 𝜌gSs

[ )] ( 𝜕hx 𝜕hx 𝜕 − kp (hx ) +1 = S = 𝛼S ksr (z)fp (hs )(hs − hx ), 𝜕t 𝜕z 𝜕z

(12)

where Ss (Pa−1 ) is the storage within the xylem and kp (m s−1 ) is the axial hydraulic conductivity of the xylem. The parameter kp is a function of the xylem water potential and is defined as [e.g., Verma et al., 2014] ( kp = kpmax

) 1 1− )) ( ( 1 + exp ap 𝜌ghx − bp

,

(13)

where ap (Pa−1 ) and bp (Pa) are xylem cavitation parameters. Due to the water potential gradient in equations (10) and (12), the roots can both take water from the soil and release water to the soil. XWP thus automatically accounts for both root water compensation and hydraulic redistribution. XWP is used with root water compensation only, XWPRWC , by imposing no flow of water from roots to soil (i.e., 𝛼S = 0 when hs < hx ). This allows for a comparison between RWC and XWPRWC . When XWP accounts for both root water compensation and hydraulic redistribution (i.e., XWPHR ), the flow of water from roots to the soil is assumed to occur with higher resistance [Caldwell et al., 1998; Mendel et al., 2002; Neumann and Cardon, 2012; Prieto et al., 2012]; accordingly, 𝛼S = 0.5 was assumed when hs < hx . The root water uptake in equation (12) is driven by Tp by imposing a boundary condition at the surface that defines the actual transpiration as [ Tac = Tp f (hx ) = Tp 1 +

(

hx hx50

)nl ]−1 ,

(14)

where hx50 (m) represents the pressure head at which the root water extraction is reduced by half; hx50 and nl are both empirical constants. The reduction of Tp , which captures stomatal regulation, is here assumed to depend only on the xylem water potential at the surface. Other sources of stress, such as vapor pressure deficit, solar radiation, and air temperature, could be included; however, a simplified form is used here for the sake of comparing the different models. TEODOSIO ET AL.


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Table 1. List of Parameters of the Richards Equation and Plant Water Transport Functions Parameter

Units

Value

Description

Reference

Retention curve ks

m s−1

2.89 ⋅ 10−6

Saturated hydraulic conductivity of the soil

Simunek and Hopmans [2009]

𝜃s

−

0.43

Saturated volumetric soil moisture content


𝜃r

−

0.078

Residual volumetric soil moisture content


𝛼

m−1

3.6

Soil hydraulic parameter


n

−

1.56

Soil hydraulic parameter


qz

−

10

Root distribution parameter

Verma et al. [2014]

ksrt

s−1

7.2 ⋅ 10−10

Total soil-to-root conductance

Verma et al. [2014]

Ss

Pa−1

1 ⋅ 10−14

Xylem storage

Estimated

kpmax

m s−1

1 ⋅ 10−5

Xylem hydraulic conductivity

Verma et al. [2014]

ap

Pa−1

2 ⋅ 10−6

Xylem cavitation parameter

Estimated

bp

Pa

−3.5 ⋅ 106

Xylem cavitation parameter

Estimated

hx50

m

−350

Jarvis leaf water potential parameter

Estimated

nl

−

8

Jarvis leaf water potential parameter

Estimated

Xylem flow

Water-stress 𝜔c

−

hs1 hs2 hs3 hs4 hs′ hs′

3 4

0.5

Critical water index of RWC


m

−0.1

Feddes parameter


m

−0.25

Feddes parameter


m

−5

Feddes parameter


m

−80

Feddes parameter


m

−25

Adjusted Feddes parameter

Estimated

m

−400

Adjusted Feddes parameter

Estimated

2.3. Numerical Simulations The system of equations (1)–(3), and (12) was solved using COMSOL Multiphysics (Ver. 5.1; http://www. comsol.com/). To compare models, a case similar to one of the examples in Simunek and Hopmans [2009] was selected to define the parameters of the different models. This virtual experiment assumed a loamy soil with a depth of 1.2 m and hydraulic properties as in Table 1. The root depth was 0.9 m; differently from Simunek and Hopmans [2009], the root distribution here was described by equation (A12) with the values of the parameters listed in Table 1. The geometry, soil type, and root distribution were the same for all simulations. A shallow water table was used to generate a strong difference in water content between the soil near the surface and at the bottom of the soil column. The contrast in soil moisture that results is expected to highlight differences between models. With a deep water table, the observed differences among the models are likely to diminish. 2.3.1. Selection of Parameters The parameters in the heat transfer and CO2 equations in the individual models were kept the same with the exception of those related to water stress, which are associated with water flow. The parameters of the water flow equations for the XWP model needed to be selected based on the RWC model in order to compare the results from different models. RWC synthesizes the water stress in one single function (i.e., the Feddes water stress response function, fp (hs )) and implements root water compensation through the critical water stress index (𝜔c = 0.5). Contrarily, XWP has three different forms of water stress (i.e., the Feddes function, fp (hs ), the xylem vulnerability curve, kp (hx ), and the stomatal conductance response curve, f (hx )). To compare the different models, the parameters of RWC were selected similarly to Simunek and Hopmans [2009] (including those appearing in the stress function). Several combinations of parameters of the stress functions in XWPRWC were selected; the set of parameters that resulted in minimal differences (according to the values of the coefficient of determination, R2 , and the root-mean-square error, RMSE) between Tac calculated with RWC and XWPRWC was used in the simulations. The combination of these parameters are listed as estimated in Table 1. The same values of parameters were then used in XWPHR . TEODOSIO ET AL.


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Figure 1. (a) Potential transpiration, Tp , used in equations (8) and (14), and (b) ground heat flux used as boundary condition at the surface in equation (2).

The initial condition of RWC was a hydrostatic pressure head equal to −1.2 m at the soil surface and decreased linearly to zero at the bottom of the soil profile. The boundary conditions were no flux at the ground surface and a pressure head equal to zero at depth of −1.2 m, thereby assuming that the water table was at that depth. The value of Tp in equation (8) was assumed to be constant and equal to 0.44 mm h−1 ; this value, larger than that used by Simunek and Hopmans [2009], was selected to capture large Tp demands in dry areas. XWPRWC needs conditions for both the soil and the root. The Richards equation (equation (1)) of XWPRWC had the same initial and boundary conditions as RWC. The initial condition of the xylem water potential of XWPRWC was the same as the initial soil water potential, so that no root water uptake occurred at the beginning of the simulation. The boundary conditions at the bottom of the root was no flux and at the top was as in equation (14). Simulations were run for 50 days. 2.3.2. Scenarios After the parameters were estimated for XWP models, numerical simulations with boundary conditions at the surface changing in time were generated. These simulations investigated the effect of changes in forcing variables and the impact of different formulations of S on Tac and soil CO2 dynamics. For the water flow equation, the initial condition was similar to that of the simulations used to estimate hydraulic parameters for all models. The boundary conditions for the Richards equation of both RWC and XWP models were a pressure head equal to zero at the bottom of the soil column and no flow at the surface, with the exception of a precipitation event of 3.6 mm, which was represented as infiltration, uniformly distributed on the 25th day of the simulation. Since the focus is on root water compensation, this small rainfall event was selected to generate vertical differences in the water profile to contrast root water uptake mechanisms of the different models. If a large event were used, as, e.g., in De Willigen et al. [2012], the whole soil column would be replenished returning the system to conditions similar to the initial one. The boundary conditions for Darcy’s equation (equation (12)) of the XWP models (XWPRWC and XWPHR ) were no flow at the bottom of the root depth and Tac at the ground surface given by equation (14), with Tp changing in time based on values common to semiarid ecosystems in southeastern Australia (Figure 1a). Transpiration was assumed to stop during the night and was repeated periodically for the entire 50 day simulation. The parameters associated with Richards equation are presented in Table 1. Table 2. Initial Condition of Soil Temperature Depth (m)

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Soil Temperature (∘ C)

−0.05

23.85

−0.15

23.70

−0.30

22.82

−0.50

22.24

−0.70

21.69

−1.20

19.85

For the heat transport simulation, the initial soil temperature profile was based on experimental data shown in Table 2. A constant soil temperature (19.85∘ C) and a periodic soil heat flux (Figure 1b) were imposed as boundary conditions at the bottom and at the top of the soil profile, respectively. The prescribed soil heat flux input was based on a diurnal soil heat flux pattern common to semiarid ecosystems in southeastern Australia. The parameters associated with the heat transfer equation are in Table 3.


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Table 3. List of Parameters of the Heat Equation [Suarez and Simunek, 1993] Parameter

Units

Value

Description

Cs

J m−3 K−1

1.92 ⋅ 106

Volumetric heat capacity for solid

Cw

J m−3 K−1

4.18 ⋅ 106

Volumetric heat capacity for water

Ca

J m−3 K−1

1.20 ⋅ 103

Volumetric heat capacity for air

b1

W m−1 K−1

−0.197

Coefficient of 𝜆(𝜃)

b2

W m−1

−0.962


b3

W m−1 K−1

2.521


K−1

For the CO2 production and transport, the initial CO2 concentration was assumed to decrease linearly from 400 ppm (i.e., atmospheric CO2 concentration) at the top to 6 ⋅ 104 ppm at the bottom of the soil column. These gradients in CO2 concentrations are common in soils [e.g., Daly et al., 2009; Jassal et al., 2008]. The boundary conditions for top and bottom of the soil were 400 ppm and 6 ⋅ 104 ppm, respectively. The parameters associated with CO2 production and transport are listed in Table 4. Fluxes of CO2 are reported as fluxes of carbon (C) equivalent.

3. Results and Discussion Since soil temperature of all the models had negligible differences, the focus will be on the selection of parameters of XWP models and the role of different formulations of S in determining water fluxes, and CO2 production and efflux. The mass balance errors of water in the numerical simulations were deemed reasonable, being up to 1.8 mm over 50 days (0.6% of the mean water content in the soil column). 3.1. Selection of Parameters Parameters of XWPRWC were selected to match Tac with the RWC model. The values of Tac of both RWC and XWP models were very close through time (Figure 2; R2 = 0.9975 and RMSE = 2.05 ⋅ 10−5 mm h−1 ) when the values of XWP water flow parameters were as in Table 1. 3.2. Root Water Uptake When different formulations of the sink term were implemented with a periodic Tp and G, the models generated different Tac dynamics. Initially, for the first 8 days, all the models performed similarly, since the parameters had been calibrated with the same potential transpiration rate and water stress was not yet manifested (Figure 3a). Then, the RWC and XWPRWC models experienced water stress earlier than XWPHR (Figure 3b) and RWC had the largest increase of Tac associated with the rainfall event on day 25. As the soil water stress started to play a role, the RWC model resulted in a slower increase of Tac in the morning and a faster decrease in the evening, even when the peak of Tac was larger than the XWP models (Figure 3). Table 4. List of Parameters of the CO2 Production and Transport Equation Parameter

TEODOSIO ET AL.

Units

Value

Description

Reference

KH

mol s2 kg−1 m−2

5.64 ⋅ 10−4

Henry’s Law constant

Suarez and Simunek [1993]

R

J mol−1 K−1

8.314 ⋅ 10−4

Universal gas constant


Das

m2 s−1

1.57 ⋅ 10−5

Molecular gas phase diffusion at 293 K

Yiqi and Zhou [2006]

Dws

m2 s−1

2.24 ⋅ 10−9

Molecular liquid phase diffusion at 298 K


𝜆w

m

0.1

Dispersivity of CO2 in water


𝛾s0

m s−1

4.8611 ⋅ 10−8

Optimal CO2 production for microbes


𝛾p0

m s−1

3.2407 ⋅ 10−8

Optimal CO2 production for root


a

m−1

10

Empirical constant for CO2 production


h1

m

−1.0

Carbon stress parameter for moisture


h2

m

−1700

Carbon stress parameter for moisture

Manzoni et al. [2012]

Ea

J mol−1

55

Activation energy of a reaction


KMs

−

0.19

Michaelis constant for soil microbes


KMp

−

0.14

Michaelis constant for plant roots


Topt

K

293.15

Optimum temperature for C production

Richardson et al. [2012]


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Figure 2. (a) Actual transpiration plot of XWP and RWC within the simulation period and (b) comparison of the actual transpiration of XWP and RWC to obtain the parameters in Table 1 (dashed line is the 1:1 line and the continuous line is a linear regression fit).

Since Tac temporal patterns differed due to the formulations of S, the total amounts of water that transpired were also different. The total Tac during the simulation period of the XWPRWC model was 13% larger than that of the RWC model (Figure 4). This difference might be partly due to the slight differences in transpiration rates between the two models associated with the estimation of parameters. As shown in Figure 2b, the transpiration rates of XWPRWC are slightly larger than RWC in the range of 0.2–0.3 mm h−1 . The XWPHR model resulted in higher transpiration, with about 0.10–0.30 mm d−1 of water lifted during the nights and released into the shallow soil layers providing an additional water source for the roots near the surface. The magnitude of the lifted soil water was in agreement with the reviewed values by Neumann and Cardon [2012]. The prolonged transpiration due to soil water lifted increased Tac of the XWPHR model by an additional 6% within 50 days; this is comparable to the 4% difference over the period of 100 days in the study by Ryel et al. [2002]. Because of the constant head at the bottom of the soil column, groundwater supplied about 23, 25, and 27 mm to the unsaturated column in 50 days for RWC, XWPRWC , and XWPHR , respectively. The larger values of these upward fluxes for the XWP models are related to the larger root water uptake at deeper soil layers and suggest that the shallow water table helps in sustaining transpiration rates when root water compensation and hydraulic lift are accounted for. However, the differences in total transpiration between the models were much larger than the differences between the fluxes from groundwater.

Figure 3. Comparison of Tac rates between the three models over (a) the length of the simulation period, (b) the period of incipient water stress, and (c) the driest part of the simulation period.

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The soil water extraction profile differed across models. Overall, almost 70% of the root water uptake occurred within 0.40 m below the ground in all models (Figure 5), reflecting the shape of the root distribution. The RWC model took soil water near the surface when possible. Applying hydraulic redistribution led to a wetter soil at shallow depths in the morning, such that the root water uptake of the XWPHR model was higher at these depths. The behavior of soil water extraction affected the soil water pressure head and volumetric soil water content. The minimum value of hs of the RWC and XWP models was governed by the parameters h4 Figure 4. Cumulative actual transpiration for the three models and h′4 equal to −80 m and −400 m, respectively over the length of the simulation period. (Figure 6). Soil moisture in the RWC model did not approach 𝜃r due to the root water uptake limitation of hs at −80 m, which was associated with a value of 𝜃 slightly larger than 𝜃r . The soil layers of the XWPRWC and XWPHR models were drier compared to that of the RWC model, since the XWP models generated larger Tac . 3.3. CO2 Production and Efflux The models generated dissimilar CO2 efflux dynamics due to the different formulations of root water uptake. Although the CO2 dynamics depend on soil moisture and temperature, the CO2 production and efflux were mainly driven by soil moisture, since Ts from all models had negligible differences. Initially, all the models resulted in similar CO2 efflux patterns until the fifth day when the efflux of the RWC model decreased faster than that of the XWP models (Figure 7a). This coincided with incipient water stress, which also led to different transpiration rates as shown in Figure 3. After the start of water stress, the XWPHR model experienced hydraulic redistribution that changed the CO2 efflux; the efflux calculated with the XWPHR model experienced lower daily fluctuations than the RWC and XWPRWC models (Figures 7b and 7c). In addition, the diurnal average CO2 efflux of the XWPHR model had a time lag of almost an hour compared to the RWC and XWPRWC models. The magnitude of CO2 production and CO2 efflux was affected as well due to the different implementations of the term S in the RWC and XWP models. Initially, CO2 efflux of the RWC model was lower than that of the XWPRWC model; however, around the 18th day of the simulation period, the cumulative CO2 efflux of the RWC model became greater than XWPRWC and then greater than XWPHR after about 40 days (Figure 8). The difference in the implementation of root water compensation between the RWC and XWPRWC models resulted in a 13% difference of the calculated CO2 efflux; furthermore, the difference between the XWPRWC and XWPHR models resulted in an 11% difference within the simulation period. The flux of CO2 from the bottom boundary (less than 1 g m−2 over 50 days for all the models), where a constant concentration was imposed, did not largely affect the efflux from the surface, which was mainly related to root and microbial respiration.

Figure 5. Root water uptake (S) profile for (a) RWC, (b) XWPRWC , and (c) XWPHR in different days.

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Figure 6. (a–c) Soil water pressure head and (d–f ) volumetric soil moisture (𝜃 ) profiles in different days for RWC (Figures 6a and 6d), XWPRWC (Figures 6b and 6e), and XWPHR (Figures 6c and 6f ).

The CO2 efflux of RWC was initially lower than that of the XWPRWC model due to the faster decline of the root C production associated with autotrophic respiration; on the contrary, the XWPHR model was larger due to the sustained root C production through hydraulic redistribution (Figure 9). These dynamics are due to the different forms of water stress for root and microbial C production. As shown in Figure 10, in RWC and XWPRWC microbial respiration was initially more limited than root respiration, but, as the soil dried down, the respiration of RWC, especially the microbial one, remained sustained, because the soil was wetter due to the lower transpiration rates. The hydraulic redistribution in XWPHR permitted larger fluctuations of root C production

Figure 7. Comparison of the C efflux rates between the three models over (a) the length of the simulation period, (b) the period of incipient water stress, and (c) the final part of the simulation period.

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Figure 8. Cumulative C efflux for the three models over the simulation period.

during the day, because of the injection of water near the surface; however, the transpiration rates, which were larger than in the RWC case, with time depleting the soil water storage causing an overall larger decline in C production when compared to RWC.

4. Conclusions A one-dimensional model was presented to couple the soil water flow, heat, and CO2 equations with the aim to compare how different formulations of root water uptake accounting for root water compensation and redistribution affect transpiration rates as well as soil CO2 production and ground efflux. The cumulative Tac of the XWPRWC model was 13% higher than that of the RWC model. The total Tac further increased by 6% when hydraulic redistribution was included in the model. The CO2 production and ground efflux were also affected by the different formulations of root water uptake. The cumulative soil CO2 emissions of the RWC model were 13% higher than those of the XWPRWC model. The implementation of hydraulic redistribution resulted into 11% higher CO2 efflux than that of the XWPRWC model. In addition, the diurnal average CO2 efflux of the XWPHR model had a time lag of almost an hour compared to the RWC and XWPRWC models. Since the total CO2 production rate along the soil column almost entirely balanced the soil CO2 efflux from the soil surface, reductions of CO2 production due to water stress were the main driver of CO2 efflux. The different responses to water stress of roots and soil microbes generated unexpected dynamics of the models over time, with RWC resulting in larger total fluxes over the simulated period although initially starting with the lower rates of the three models. This study highlights the importance of selecting a root water uptake formulation in ecohydrological models, since this affects the estimation of magnitudes and patterns of actual transpiration as well as soil CO2 production and soil CO2 emissions. Recommendations of what root water uptake formulation to use are difficult, since, as suggested by De Willigen et al. [2012], this depends on the application, computational capability, and

Figure 9. Comparison between (a) plant root and (b) soil microbial production of C integrated along the soil profile.

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Figure 10. Time dynamics of the two water stress reduction functions for C production (fs (hs ) and fp (hs )) for the three models.

data availability. However, our study shows that, although it is likely possible to use different models to reproduce the same data through calibration of parameters, the selection of the root water uptake model may lead to estimates of magnitudes and patterns of important associated variables, such as soil CO2 emissions, that might be substantially different from each other.

Appendix A: Functions for the Water, Heat, and CO2 Equations The water retention curve in equation (1) is described by [Van Genuchten, 1980] 𝜃(hs ) = 𝜃r + (

𝜃 s − 𝜃r 1 + |𝛼hs |n

)m ,

(A1)

where 𝜃r (m3 m−3 ) is the residual soil water content, 𝜃s (m3 m−3 ) is the soil water content at saturation, 𝛼 , n (n > 1) and m are empirical parameters, with m = 1 − 1∕n. The hydraulic conductivity is expressed as [Van Genuchten, 1980] [ ( )m ]2 1 1 k(hs ) = ks Se2 1 − 1 − Sem , (A2) where ks (m s−1 ) is the saturated hydraulic conductivity, and Se is the relative saturation calculated as Se =

𝜃 − 𝜃r . 𝜃s − 𝜃r

(A3)

The function fp (hs ) reflects the reduction of the rate of root water uptake affected by the soil moisture condition. The water stress response function of Feddes et al. [1976] was used; this is defined as ⎧ ⎪ ⎪ ⎪ fp (hs ) = ⎨ ⎪ ⎪ ⎪ ⎩

h s ≥ h s1

0 hs1 −hs hs1 −hs2

1 hs −hs4 hs3 −hs4

h s1 > h s > h s2 h s2 ≥ h s ≥ h s3

(A4)

h s3 > h s > h s4

0

h s ≤ h s4 ,

where hs1 , hs2 , hs3 , and hs4 are empirical parameters dependent on soil and vegetation type. The volumetric heat capacity in equation (2) is expressed as C(𝜃) = Cs (1 − 𝜃s ) + Cw 𝜃 + Ca (𝜃s − 𝜃),

(A5)

where Cs and Ca are the volumetric heat capacity for solid and air, respectively. The apparent thermal conductivity in the heat transfer equation is defined as √ 𝜆(𝜃) = b1 + b2 𝜃 + b3 𝜃, (A6) where b1 , b2 , and b3 (W m−1 K−1 ) are empirical parameters. TEODOSIO ET AL.


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In equation (3), the effective dispersion in the soil matrix is given by ) ( | qw | | | DE = (Das 𝜏a )[𝜃s − 𝜃] + Dws 𝜏w + 𝜆w | | KH RTs 𝜃, | 𝜃 |

(A7)

where Das (m2 s−1 ) and Dws (m2 s−1 ) are the diffusion coefficients of CO2 in the gas and dissolved phases, respectively. The parameter 𝜆w (m) is the dispersivity in the water phase, and 𝜏a and 𝜏w are the tortuosity factors in the gas and dissolved phases defined as 7

(𝜃 − 𝜃) 3 𝜏a = s 2 , 𝜃s

(A8)

and 7

𝜏w =

(𝜃) 3 . 𝜃s2

(A9)

The term qE , associated with the water flux, is qE = KH RTs qw .

(A10)

Following Suarez and Simunek [1993], CO2 production of soil microorganisms and plant roots is affected by z, hs , Ts , and ca . The dependence of Π on these variables is described by a series of functions. The reduction of soil microorganisms respiration with depth is defined as fs (z) =

ae−az 0 ∫−d

ae−az dz

,

(A11)

where a (m−1 ) is an empirical constant and d (m) is the root depth. Root respiration varies in depth according to the root distribution, defined as [Vrugt et al., 2001] ) ) ( ( −qz |z| exp 1 − |z| d d − d ≤ z ≤ 0, r(z) = ) ( ) ( 0 −qz |z| ∫−d 1 − d exp d |z| dz

(A12)

where qz is an empirical parameter showing the decrease of root mass with depth. The reduction coefficient fs (hs ) was modified from Simunek and Suarez [1993] and reads ⎧ ⎪ fs (hs ) = ⎨ ⎪ ⎩

1 log hs −log h1 log h1 −log h2

0

hs ≥ h 1 h1 > hs ≥ h2

(A13)

hs < h2 ,

where h1 is the soil water pressure head above which optimal soil respiration occurs, and h2 is the soil water pressure head where the soil CO2 production ceases. The effect of soil water potential on root respiration was modeled using the function fp (hs ) in equation (A4), with hs2 = 0, such that stress at moisture levels near saturation does not occur. Oxygen stress is accounted for with the function f (ca ), which is based on the simplified Michaelis-Menten equation and defined as f (ca ) =

0.21 − ca , 0.42 − ca − KM

(A14)

where KM (m3 m−3 ) is the Michaelis-Menten constant. The value of KM can be either for soil microorganisms (KMs ) or plant roots (KMp ). The effect of temperature f (Ts ) on respiration of both microorganisms and roots is [ ] Ea (Ts − Topt ) f (Ts ) = exp , RTs Topt

(A15)

where Ea (J mol−1 ) is the activation energy of the reaction and Topt (K) is the optimal temperature for CO2 production. TEODOSIO ET AL.


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Journal of Geophysical Research: Biogeosciences Acknowledgments B.T. and E.D. acknowledge the support of the Australian Research Council and the Victoria Department of Economic Development, Jobs, Transport and Resources through the project LP140100871. The different models, including inputs, are provided as supporting information.

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References Almagro, M., J. López, J. Querejeta, and M. Martínez-Mena (2009), Temperature dependence of soil CO2 efflux is strongly modulated by seasonal patterns of moisture availability in a Mediterranean ecosystem, Soil Biol. Biochem., 41(3), 594–605, doi:10.1016/j.soilbio.2008.12.021. Amenu, G., and P. Kumar (2007), A model for hydraulic redistribution incorporating coupled soil-root moisture transport, Hydrol. Earth Syst. Sci., 4(5), 3719–3769, doi:10.5194/hess-12-55-2008. Aroca, R., R. Porcel, and J. M. Ruiz-Lozano (2012), Regulation of root water uptake under abiotic stress conditions, J. Exp. Bot., 63(1), 43–57, doi:10.1093/jxb/err266. Balogh, J., S. Fóti, K. Pintér, S. Burri, W. Eugster, M. Papp, and Z. Nagy (2015), Soil CO2 efflux and production rates as influenced by evapotranspiration in a dry grassland, Plant Soil, 388(1-2), 157–173, doi:10.1007/s11104-014-2314-3. Bonan, G. (2015), Ecological Climatology: Concepts and Applications, Cambridge Univ. Press, Cambridge, U. K., doi:10.1111/j.1745-5871.2009.00640.x. Caldwell, M. M., T. E. Dawson, and J. H. Richards (1998), Hydraulic lift: Consequences of water efflux from the roots of plants, Oecologia, 113(2), 151–161, doi:10.1007/s004420050363. Camargo, G. G. T., and A. R. Kemanian (2016), Six crop models differ in their simulation of water uptake, Agric. For. Meteorol., 220, 116–129, doi:10.1016/j.agrformet.2016.01.013. Carbone, M. S., C. J. Still, A. R. Ambrose, T. E. Dawson, A. P. Williams, C. M. Boot, S. M. Schaeffer, and J. P. Schimel (2011), Seasonal and episodic moisture controls on plant and microbial contributions to soil respiration, Oecologia, 167(1), 265–278, doi:10.1007/s00442-011-1975-3. Chen, D., J. A. E. Molina, C. E. Clapp, R. T. Venterea, and A. J. Palazzo (2005), Corn root influence on automated measurement of soil CO2 dioxide concentrations, Soil Sci., 170(10), 779–787, doi:10.1097/01.ss.0000190512.41298.fc. Couvreur, V., J. Vanderborght, and M. Javaux (2012), A simple three-dimensional macroscopic root water uptake model based on the hydraulic architecture approach, Hydrol. Earth Syst. Sci., 16(8), 2957–2971, doi:10.5194/hess-16-2957-2012. Daly, E., et al. (2009), The effects of elevated atmospheric CO2 and nitrogen amendments on subsurface CO2 production and concentration dynamics in a maturing pine forest, Biogeochemistry, 94(3), 271–287, doi:10.1007/s10533-009-9327-7. Da Rocha, H. R., et al. (2004), Seasonality of water and heat fluxes over a tropical forest in Eastern Amazonia, Ecol. Appl., 14(sp4), 22–32, doi:10.1890/02-6001. Davidson, E., et al. (1998), Soil water content and temperature as independent or confounded factors controlling soil respiration in a temperate mixed hardwood forest, Global Change Biol., 4(2), 217–227, doi:10.1046/j.1365-2486.1998.00128.x. De Jong Van Lier, Q., J. Van Dam, A. Durigon, M. Dos Santos, and K. Metselaar (2013), Modeling water potentials and flows in the soil-plant system comparing hydraulic resistances and transpiration reduction functions, Vadose Zone J., 12(3), 1065–1078, doi:10.2136/vzj2013.02.0039. De Willigen, P., J. Van Dam, M. Javaux, and M. Heinen (2012), Root water uptake as simulated by three soil water flow models, Vadose Zone J., 11(3), 1–14, doi:10.2136/vzj2012.0018. Domec, J.-C., F. Scholz, S. Bucci, F. Meinzer, G. Goldstein, and R. Villalobos-Vega (2006), Diurnal and seasonal variation in root xylem embolism in neotropical savanna woody species: Impact on stomatal control of plant water status, Plant Cell Environ., 29(1), 26–35, doi:10.1111/j.1365-3040.2005.01397.x. Domec, J.-C., J. S. King, A. Noormets, E. Treasure, M. J. Gavazzi, G. Sun, and S. G. McNulty (2010), Hydraulic redistribution of soil water by roots affects whole-stand evapotranspiration and net ecosystem CO2 exchange, New Phytol., 187(1), 171–183, doi:10.1111/j.1469-8137.2010.03245.x. Fang, C., and J. B. Moncrieff (1999), A model for soil CO2 production and transport 1: Model development, Agric. For. Meteorol., 95(4), 225–236, doi:10.1016/S0168-1923(99)00036-2. Feddes, R. A., P. Kowalik, K. Kolinska-Malinka, and H. Zaradny (1976), Simulation of field water uptake by plants using a soil water dependent root extraction function, J. Hydrol., 31(1-2), 13–26, doi:10.1016/0022-1694(76)90017-2. Goffin, S., C. Wylock, B. Haut, M. Maier, B. Longdoz, and M. Aubinet (2015), Modeling soil CO2 production and transport to investigate the intra-day variability of surface efflux and soil CO2 concentration measurements in a Scots pine forest (Pinus sylvestris, L.), Plant Soil, 390(1-2), 195–211, doi:10.1007/s11104-015-2381-0. Hanson, P., S. Wullschleger, S. Bohlman, and D. Todd (1993), Seasonal and topographic patterns of forest floor CO2 efflux from an upland oak forest, Tree Physiol., 13(1), 1–15, doi:10.1093/treephys/13.1.1. Herkelrath, W., E. Miller, and W. Gardner (1977), Water uptake by plants: II. The root contact model, Soil Sci. Soc. Am. J., 41(6), 1039–1043, doi:10.2136/sssaj1977.03615995004100060004x. Hirano, T., H. Kim, and Y. Tanaka (2003), Long-term half-hourly measurement of soil CO2 concentration and soil respiration in a temperate deciduous forest, J. Geophys. Res., 108(D20), 4631, doi:10.1029/2003JD003766. Howard, A. R., M. W. Van Iersel, J. H. Richards, and L. A. Donovan (2009), Night-time transpiration can decrease hydraulic redistribution, Plant Cell Environ., 32(8), 1060–1070, doi:10.1111/j.1365-3040.2009.01988.x. Jarvis, N. (1989), A simple empirical model of root water uptake, J. Hydrol., 107(1-4), 57–72, doi:10.1016/0022-1694(89)90050-4. Jarvis, N. (2010), Comment on “Macroscopic root water uptake distribution using a matric flux potential approach”, Vadose Zone J., 9(2), 499–502, doi:10.2136/vzj2009.0148. Jarvis, N. (2011), Simple physics-based models of compensatory plant water uptake: Concepts and eco-hydrological consequences, Hydrol. Earth Syst. Sci., 15(11), 3431–3446. Jassal, R. S., T. A. Black, M. D. Novak, D. Gaumont-Guay, and Z. Nesic (2008), Effect of soil water stress on soil respiration and its temperature sensitivity in an 18-year-old temperate douglas-fir stand, Global Change Biol., 14(6), 1305–1318, doi:10.1111/j.1365-2486.2008.01573.x. Javaux, M., V. Couvreur, J. Vanderborght, and H. Vereecken (2013), Root water uptake: From three-dimensional biophysical processes to macroscopic modeling approaches, Vadose Zone J., 12(4), 1–16, doi:10.2136/vzj2013.02.0042. Latimer, R., and D. Risk (2016), An inversion approach for determining distribution of production and temperature sensitivity of soil respiration, Biogeosciences, 13(7), 2111–2122, doi:10.5194/bg-13-2111-2016. Lellei-Kovács, E., et al. (2016), Temperature dependence of soil respiration modulated by thresholds in soil water availability across European shrubland ecosystems, Ecosystems, 19, 1460–1477, doi:10.1007/s10021-016-0016-9. Liang, N., T. Hirano, Z. M. Zheng, J. Tang, and Y. Fujinuma (2010), Soil CO2 efflux of a larch forest in northern Japan, Biogeosciences, 7(11), 3447–3457, doi:10.5194/bg-7-3447-2010. Liu, W., Z. Zhang, and S. Wan (2009), Predominant role of water in regulating soil and microbial respiration and their responses to climate change in a semiarid grassland, Global Change Biol., 15(1), 184–195, doi:10.1111/j.1365-2486.2008.01728.x. Manzoni, S., J. P. Schimel, and A. Porporato (2012), Responses of soil microbial communities to water stress: Results from a meta-analysis, Ecology, 93, 930–938, doi:10.1890/11-0026.1.


1967


10.1002/2017JG003831

Mendel, M., S. Hergarten, and H. Neugebauer (2002), On a better understanding of hydraulic lift: A numerical study, Water Resour. Res., 38(10), 1183, doi:10.1029/2001WR000911. Molz, F. J. (1981), Models of water transport in the soil-plant system: A review, Water Resour. Res., 17(5), 1245–1260, doi:10.1029/WR017i005p01245. Moncrieff, J. B., and C. Fang (1999), A model for soil CO2 production and transport 2: Application to a Florida Pinus elliotte plantation, Agric. For. Meteorol., 95(4), 237–256, doi:10.1016/S0168-1923(99)00035-0. Neumann, R. B., and Z. G. Cardon (2012), The magnitude of hydraulic redistribution by plant roots: A review and synthesis of empirical and modeling studies, New Phytol., 194(2), 337–352, doi:10.1111/j.1469-8137.2012.04088.x. Nimah, M. N., and R. J. Hanks (1973), Model for estimating soil water, plant and atmospheric relationships. 1. Description and sensitivity, Soil Sci. Soc. Am. J., 37, 522–527, doi:10.2136/sssaj1973.03615995003700040018x. Patwardhan, A. S., J. L. Nieber, and I. D. Moore (1988), Oxygen, CO2 dioxide, and water transfer in soils: Mechanisms and crop response, Trans. Am. Soc. Agric. Eng., 31(5), 1383–1395. Prieto, I., and R. J. Ryel (2014), Internal hydraulic redistribution prevents the loss of root conductivity during drought, Tree Physiol., 34(1), 39–48, doi:10.1093/treephys/tpt115. Prieto, I., Z. Kikvidze, and F. I. Pugnaire (2010), Hydraulic lift: Soil processes and transpiration in the Mediterranean leguminous shrub Retama sphaerocarpa (L.) Boiss, Plant Soil, 329(1–2), 447–456, doi:10.1007/s11104-009-0170-3. Prieto, I., C. Armas, and F. I. Pugnaire (2012), Water release through plant roots: New insights into its consequences at the plant and ecosystem level, New Phytol., 193(4), 830–841, doi:10.1111/j.1469-8137.2011.04039. Reynolds, L. L., B. R. Johnson, L. Pfeifer-Meister, and S. D. Bridgham (2015), Soil respiration response to climate change in Pacific northwest prairies is mediated by a regional Mediterranean climate gradient, Global Change Biol., 21(1), 487–500, doi:10.1111/gcb.12732. Richardson, J., A. Chatterjee, and G. D. Jenerette (2012), Optimum temperatures for soil respiration along a semi-arid elevation gradient in Southern California, Soil Biol. Biochem., 46, 89–95, doi:10.1016/j.soilbio.2011.11.008. Riveros-Iregui, D. A., B. L. McGlynn, L. A. Marshall, D. L. Welsch, R. E. Emanuel, and H. E. Epstein (2011), A watershed-scale assessment of a process soil CO2 production and efflux model, Water Resour. Res., 47, W00J04, doi:10.1029/2010WR009941. Russo, D., J. Zaidel, and A. Laufer (2004), Numerical analysis of transport of interacting solutes in a three-dimensional unsaturated heterogeneous soil, Vadose Zone J., 3, 1286–1299, doi:10.2113/3.4.1286. Ryel, R., M. Caldwell, C. Yoder, D. Or, and A. Leffler (2002), Hydraulic redistribution in a stand of Artemisia tridentata: Evaluation of benefits to transpiration assessed with a simulation model, Oecologia, 130(2), 173–184, doi:10.1007/s004420100794. Santos, M. A., J. van Lier, J. C. Dam, and A. H. Freire Bezerra (2017), Benchmarking test of empirical root water uptake models, Hydrol. Earth Syst. Sci., 21(1), 473–493, doi:10.5194/hess-21-473-2017. Simunek, J., and D. L. Suarez (1993), Modeling of CO2 dioxide transport and production in soil: 1. Model development, Water Resour. Res., 29(2), 487–497, doi:10.1029/92WR02225. Simunek, J., and J. W. Hopmans (2009), Modeling compensated root water and nutrient uptake, Ecol. Modell., 220(4), 505–521, doi:10.1016/j.ecolmodel.2008.11.004. Siqueira, M., G. Katul, and A. Porporato (2008), Onset of water stress, hysteresis in plant conductance, and hydraulic lift: Scaling soil water dynamics from millimeters to meters, Water Resour. Res., 44(1), 1189–1207, doi:10.1029/2007WR006094. Skaggs, T. H., M. van Genuchten, P. Shouse, and J. Poss (2006), Macroscopic approaches to root water uptake as a function of water and salinity stress, Agric. Water Manage., 86(1), 140–149, doi:10.1016/j.agwat.2006.06.005. Suarez, D. L., and J. Simunek (1993), Modeling of CO2 dioxide transport and production in soil: 2. Parameter selection, sensitivity analysis, and comparison of model predictions to field data, Water Resour. Res., 29(2), 499–513, doi:10.1029/92WR02226. Suseela, V., R. T. Conant, M. D. Wallenstein, and J. S. Dukes (2012), Effects of soil moisture on the temperature sensitivity of heterotrophic respiration vary seasonally in an old-field climate change experiment, Global Change Biol., 18(1), 336–348, doi:10.1111/j.1365-2486.2011.02516.x. Van Genuchten, M. T. (1980), A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Sci. Soc. Am. J., 44(5), 892–898. Verma, P., S. P. Loheide II, D. Eamus, and E. Daly (2014), Root water compensation sustains transpiration rates in an Australian woodland, Adv. Water Resour., 74, 91–101, doi:10.1016/j.advwatres.2014.08.013. Vrugt, J. A., M. T. Wijk, J. W. Hopmans, and J. Simunek (2001), One-, two-, and three-dimensional root water uptake functions for transient modeling, Water Resour. Res., 74, 91–101, doi:10.1029/2000WR000027. Welsch, D. L., and G. M. Hornberger (2004), Spatial and temporal simulation of soil CO2 concentrations in a small forested catchment in Virginia, Biogeochemistry, 71(3), 413–434, doi:10.1023/B:BIOG.0000049350.24911.e9. Yiqi, L., and X. Zhou (2006), Soil Respiration and the Environment, Academic Press, Elsevier, San Diego, Calif., doi:10.1016/B978-012088782-8/50000-0.

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