Root water uptake as simulated by three soil water ...

1

Root water uptake as simulated by three soil water flow

2

models

3 4

1

2

3,4

1

Peter de Willigen , Jos C. van Dam , Mathieu Javaux , Marius Heinen

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Affiliations:

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1

Alterra, Soil Science Centre, Wageningen UR, PO Box 47, 6700 AA Wageningen, the Netherlands

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2

Wageningen University, Soil Physics, Ecohydrology and Groundwater Management Group,

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Wageningen UR, PO Box 47, 6700 AA Wageningen, the Netherlands 3

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Institut für Bio- und Geowissenschaften, Agrosphere (IBG3), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany,

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Earth and Life Institute/ Environmental Sciences, Université Catholique de Louvain, Croix du Sud 2 bte L7.05.02, 1348, Louvain-la-Neuve, Belgium

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*

Corresponding author: P. de Willigen; [email protected]; phone: +31.317.486477

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Number of pages:

24 (excluding tables (5 p), legend to figures (1 p) and figures (10 p))

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Number of Tables:

5

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Number of Figures:

10

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Date submitted:

15-Jan-2012

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Date submitted revision:

11-May-2012

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Comparison of four root water uptake models

1

25

Root water uptake as simulated by three soil water flow

26

models

27

Abstract

28

We compared four root water uptake (RWU) models, of different complexity, that are all embedded in

29

greater soil water flow models. The soil models used were SWAP (1-D), FUSSIM2 (2-D) and RSWMS

30

(3-D). Within SWAP two RWU functions were employed (SWAP-macro and SWAP-micro). The

31

complexity of the processes considered in RWU increases from SWAP-macro, SWAP-micro,

32

FUSSIM2 to RSWMS. The objective of our study was to what extent the RWU models differed when

33

tested under extreme conditions: low root length density, high transpiration rate and low water content.

34

The comparison comprised: 1) the results of the models for a scenario of transpiration and uptake and

35

2) study of compensation mechanisms of water uptake. The uptake scenario pertained to a long dry

36

period with constant transpiration and a single rainfall event. As could be expected the models yielded

37

different results in comparison 1, but the differences in cumulative transpiration are modest due to

38

various feedback mechanisms. In comparison 2 the cumulative effect of different feedback processes

39

were studied. Redistribution of water due to gradients in soil pressure head generated by water uptake

40

led to an increase of cumulative transpiration of 32% and the inclusion of compensation in uptake by

41

the roots resulted in a further increase of 10%. Going from 1-D to 3-D modeling, the horizontal

42

gradients in the soil and root system increased, which reduced the actual transpiration. The analysis

43

shows that both soil physical and root physiological factors are important for proper deterministic

44

modeling of RWU.

45 46

Keywords: model comparison, root length density, root water uptake, root zone, simulation model, soil,

47

transpiration, uptake compensation

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Introduction

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Root water uptake (RWU) is a process included in a broad range of models applied for various

50

purposes from irrigation management to global change predictions. Numerous modeling approaches Comparison of four root water uptake models

2

51

have been developed since Gardner proposed his first water uptake model in soils (Gardner, 1960).

52

Nowadays in soil physics, most soil-plant models are still based on the Richards equation, where a

53

source/sink-term S is added to account for plant uptake ∂θ ∂K (h ) = ∇ ⋅ {K (h )∇ h} − ± S (x , y , z ) ∂t ∂z

54

(1) 3

-3

55

where θ denotes the volumetric water content in soil (L L ), t is time (T), z the vertical coordinate (L),

56

x and y are the horizontal coordinates (L), h the soil water pressure head (L), K(h) the hydraulic

57

conductivity tensor (L T ), and S is a source (+) or sink (-) term (L L T ). In the right-hand part of Eq.

58

(1), the two first terms describe the water flow redistribution between layers or soil locations, while in

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this study the third term describes the uptake by plant roots (using the minus sign at the end in Eq.

60

(1)).

61

Hydrological models using Eq. 1 for water flow modeling in vegetated soils principally differ on two

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aspects: (1) the soil dimensionality (1-D to 3-D) and (2) the dimensionality and definition of their sink

63

term S (i.e. how soil and plants are considered for RWU).

64

The choice of the dimension of the Richards equation essentially depends on the importance of the

65

horizontal fluxes. As soil is generally structured in horizons and plant roots develop downward from

66

soil surface, vertical heterogeneity is usually predominant. Lateral variability is thus assumed to be

67

small or lateral redistribution to be negligible as compared to vertical transfers and heterogeneity. On

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the opposite, when lateral fluxes impact soil water flow dynamics, 2- or 3-D models may be justified.

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Variables like soil type, soil hydraulic status, plant architecture type, sowing pattern, or plant

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transpiration will impact lateral flow patterns.

71

The sink-term in Eq. 1 may also differ in terms of dimensionality. Usually, the choice of a 1-D model for

72

the sink term is justified by the uniform horizontal distribution assumed for root location and soil

73

moisture. The 3-D root architecture is then simplified by means of root specific property to distribute

74

the transpiration within the soil-root domain: root length, root surface, and root mass densities have

75

been proposed (Feddes and Raats, 2004). Simple models include 1-D vertical profiles of root

76

properties but also 2-D or 3-D models exist in which the full root spatial distribution has to be defined

77

(e.g., Vrugt et al., 2001). A specific type of 3-D sink term also exists in which the full 3-D architecture is

78

explicitly accounted for (Javaux et al., 2011).

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How to consider the impact of soil on water uptake magnitude and distribution also differentiates sink

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term approaches. The simplest way of predicting root water uptake distribution without stress is to

-1


3

-3

-1

3

81

assume a dependency on the root properties only. A more complicated one is to base the RWU on

82

root properties and soil hydraulic status (e.g. when the soil matrix potential controls uptake

83

distribution), which allows compensation (Jarvis, 1989). De Jong van Lier et al. (2008) proposed to

84

implement this approach into a 1-D Richards model by implicitly taking into account lateral flow from

85

bulk soil to root followed by a vertical redistribution between soil layers. The most sophisticated

86

approach considers the RWU distribution based on distribution of the water potential gradient between

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soil and root. In the latter case, water potential in the root needs to be explicitly calculated.

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The last difference between RWU routines is how water stress is considered, i.e. how transpiration is

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decreased due to limiting soil conditions. A very common approach is the Feddes empirical model

90

(Feddes et al.,1978) in which the plant water stress is linked to 1-D, 2-D or 3-D soil pressure head by a

91

piecewise linear function. On the opposite, alternative models calculate the root water uptake

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distribution based on the local difference of the water potential between soil and root. Therefore, root

93

potential has to be defined or calculated (De Willigen and van Noordwijk, 1987) or explicitly estimated

94

by a 3-D root water flow model (Doussan et al., 2006). Water stress in the plant can then be defined in

95

function of the root or leaf water potential.

96

When a user has to simulate water flow in a rooted soil, he may choose among a broad range of

97

modeling approaches, which differ in terms of dimensionality (0 to 3-D), of scale of interest and of

98

degree of detail in the description of water flow in the soil and root system. This choice must be based

99

on the available data, the purpose of the simulations, and the validity of assumptions for modeled

100

situation. Table 1 summarizes the possible choices which have to be made together with the

101

underlying assumptions linked to each of them. Although the principle of parsimony would suggest the

102

use of simple models, more sophisticated models, which rely on explicit description of the soil

103

structure and the root architecture, are expected to better represent the non-linear interactions (Vogel

104

and Roth, 2003, Draye et al., 2010). Pierret et al. (2007) suggest that the full 3-D description of root

105

system is needed when soil-plant interactions are simulated. It is expected that more complex models

106

need less calibration but are more demanding in terms of number of input parameters. The

107

computational costs (in memory and CPU) also increase with complexity. Figure 1 summarizes the

108

impacts of model complexity in terms of costs. Low-resolution models use implicit representation of the

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soil and of the root structures, and must usually be parameterized with effective parameters.


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In this study, we will focus on four plant scale hydrological models, which all solve Richards equation

111

for water flow in soil, but differ in terms of dimensionality and complexity of the water uptake

112

subroutine : SWAP (macro and micro version; Kroes et al., 2008; Van Dam et al., 2008), FUSSIM2

113

(Heinen, 2001; Heinen and de Willigen, 1998), and RSWMS (Javaux et al., 2008). Predictive

114

capabilities will not be compared but only simulations of simple scenarios. We focus on how the

115

different assumptions made in these approaches (Table 1) affect their simulation results. The main

116

objective is to show the differences in the four respective root water uptake modules and their impacts

117

on soil and plant water flow simulations.

118

We hypothesize that under relatively wet conditions the four models will predict actual water uptake to

119

be equal to potential water uptake, but they may differ when uptake becomes limiting. For that reason

120

we will consider an artificial situation with a low amount of roots together with a high transpiration

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demand.

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Theory

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In this section, an overview of the four models is given (Table 2). The SWAP model considers vertical

124

(1-D) soil water flow only and has two different RWU sub-models: a macroscopic sub-model (SWAP-

125

macro), which use a 1D stress function, and a microscopic submodel (SWAP-micro), which simulates

126

compensated root water uptake based on soil matrix potential. FUSSIM2 is a 2-D model, which

127

considers a 2D distribution of the root properties with RWU based on a function dependent on root

128

and soil properties and hydraulic status. RSWMS is a 3-D model which explicitly considers the full 3D

129

architecture and simulates water flow and water uptake based on water potential gradients.

130

The reduction in SWAP-macro is determined by the average pressure head in the soil. In SWAP-micro

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the influence of radial soil hydraulic flow and root length density is added. FUSSIM2 adds to these

132

factors the root radial conductance and a single root water potential. Finally, as the most complex

133

model, RSWMS takes in addition the axial conductance into account and solve the root water flow

134

explicitly in 3-D.

135

SWAP-macro

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The actual uptake rate of water (Sa; cm cm d ) from a single soil layer equals the required uptake

137

rate (Sr) multiplied by a reduction coefficient α that is a function of pressure head h in the layer. The

3


-3

-1

5

138

relation between h and α is shown in Fig. 2. For a monolayer, Sr is the potential transpiration (Tp; cm

139

d ) divided by layer thickness (L; cm), so that Sa is given by

140

-1

Sa = α (h )Sr = α (h)

Tp

(2)

L

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In scaling up from a monolayer to a multilayer system, Kroes and van Dam (2003) corrected Sr of a

142

layer by the relative root length density in that layer

143

S r ,i =

L rv ,i n

∑ ∆z i Lrv ,i

(3)

Tp

i =1

-3

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where Lrv,i is the root length density (cm cm ) and ∆zi is the thickness of soil layer i (cm). The total

145

actual uptake rate Ta (cm d ) of the root system follows from the sum:

146

-1

Ta =

n

∑ ∆z i α i (h )S r ,i

(4)

i =1

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Equation (3) implies that in case of small differences in h, leading to an almost constant α, the

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distribution of Sa with depth is almost completely determined by the distribution of Lrv. Summarizing:

149

for a given h and relative root length distribution, the hydraulic properties and absolute Lrv in the soil do

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not play a role. In a dynamic situation where θ is changing, the soil hydraulic functions play a central

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role as these determine the decrease in h for a given decrease in θ and vertical soil water

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redistribution. In case of drought stress in certain parts of the root zone, no compensation by extra root

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water uptake in wetter zones occurs.

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SWAP-micro

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Unlike SWAP-macro, SWAP-micro (De Jong van Lier et al., 2008) takes the gradients of θ and h from

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soil to root into account. In this concept the partial differential equation is solved for radial transport of

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water in a soil cylinder to a root. This transport follows from Eq. (1) in radial coordinates without a sink

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and gravity term:

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∂θ 1 ∂  ∂h  =  RK (h )  ∂t R ∂R  ∂R 

(5)

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where R is the radial coordinate (cm) with R = 0 at the axial center of the root. A solution is achieved

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by assuming that the rate of water content decrease ∂θ/∂t is independent of radial distance. This

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assumption means that the gradient developments around the root can be described as a sequence of

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steady rate situations. Detailed numerical solutions of Eq. (5) show that this assumption is realistic Comparison of four root water uptake models

6

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(Metselaar and De Jong van Lier, 2007). An analytical solution of Eq. (5) can be derived for the matric

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flux potential Φ (cm d ), which is defined as (Raats, 1970):

2

-1

h

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∫ K (h )dh

Φ=

(6)

hw

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where hw is h at wilting point. Solving Eq. (5) for prevailing boundary conditions at the root-soil

168

interface results in the actual root water extraction rate Si at each soil layer in a root system (De Jong

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van Lier et al., 2008; De Willigen et al., 2011):

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(

4 Φi − Φ0

Si = −a

R02

2

R12,i

+2

(

R02

+

)

R12,i

)

 aR ln 1,i  R0

   

(

= w mi ,i Φ i − Φ 0

)

(7)

171

where Φo is matric flux potential at the root-soil interface and is the same for all soil layers, Φ i is the

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average matric flux potential at a particular soil depth, R0 is the root radius, R1,i is radius of root

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influence which depends on the root density ( R12 = 1/ πLrv ) and the factor a equals the relative radius

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at which average soil water contents occurs. For commonly observed values of the root length density

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-3 (0.1 – 5 cm cm ) and root radius (0.01 – 0.05 cm) of arable crops, R1 >> R 0 . So wmi can be given by:

176

4πLrv

w mi =

 a2 − a 2 + ln  πL R 2  rv 0

(8)

   

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By numerical simulations, De Jong van Lier et al. (2006) found for factor a the median value 0.53 (-).

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The total maximum transpiration rate is calculated as the sum of uptake of each layer when Φ0 = 0:

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T max =

n

∑ ∆z i w mi ,i Φ i

(9)

i =1

180

If the sum in Eq. (9) is smaller than or equal to the potential transpiration, Φ0 = 0 and the uptake in

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each layer is calculated with Eq. (7). If, on the other hand, Tmax > Tp , Φ0 is greater than zero and can

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be calculated from: n

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Tp =

∑ ∆z i w mi ,i (Φ i n

i =1

− Φ0

)

∑ ∆z i w mi ,i Φ i →

Φ0 =

i =1

n

− Tp

(10)

∑ ∆z i w mi ,i i =1

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Next, Eq. (7) is used to calculate the extraction rate at each layer. In this way an automatic

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redistribution of extraction rates is simulated: soil water is extracted at those depths that are most

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favorable with regard to Lrv and Φ. The possibility exists that in one or more layers Φ0 > Φi so that in Comparison of four root water uptake models

7

187

those layers water flows from the root into the soil. Contrary to the water uptake routines of FUSSIM2

188

and RSWMS this so-called hydraulic lift is not allowed in SWAP-micro. The water uptake is set to zero

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in these layers, and the calculation is repeated with the remaining layers.

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Summarizing, the water uptake routine in SWAP-micro is an extension of that in SWAP-macro. Next to

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the average pressure head at a certain depth, SWAP-micro takes also into account the gradient

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around the root necessary to transport water to the root. Data input is limited to Lrv and plant wilting

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point. Compensation of root water extraction when certain parts of the root zone experience stress, is

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automatically accommodated. Due to linearization of the radial soil water flow equation with the matric

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flux potential, no iterations are required and the computational effort for the entire root zone is

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relatively small. SWAP-micro neglects the hydraulic gradients inside the root system itself, but

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assumes a constant h at the soil-root interface, with a minimum at wilting point. In this way only the

198

hydraulic resistance in the soil is considered.

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FUSSIM2

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FUSSIM2 is a 2-D model pertaining to a rectangular soil domain, which is divided in a 1-D or 2-D grid

201

of rectangular cells. Transport of water takes place between the cells. Within each cell root water

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uptake (RWU) makes up the sink term in the Richards equation. The RWU in the FUSSIM2 model is

203

based on the results of a microscopic model where a single root is considered (De Willigen and Van

204

Noordwijk, 1987; De Willigen 1990; De Willigen and Van Noordwijk 1991). The radial flow of water to

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and into the root is assumed to consist of two components: 1) flow from bulk soil to root surface, and

206

2) flow from root surface into the root. The first flow is calculated by an equation similar to Eq. (7):

207

S =

Φ i − Φ 0,i

R 02 − 8

3R 12,i 8

(R1,i / R 0 )4 ln(R1,i / R 0 ) + (R1,i / R 0 )2 − 1

(

= w Fus ,i Φ i − Φ 0,i

)

(11)

208

The second flow component, viz. the flow of water from the root surface into the root, is proportional to

209

the difference between the h at the root surface (h0; cm) and that in the root xylem. The latter will be

210

denoted as the root water potential (hR; cm):

211

U i = Lrv ,i K R (h0,i − hR )

(12) -1

3

212

where KR is the conductance of the root (cm d = cm water/(cm root length.cm pressure.d)). The hR is

213

assumed to be the same all over the root system. Transpiration reduction at the leaves is regulated by


8

214

the closure of the stomata as to moderate the leaf water potential (hL; cm). Here, hR is related to hL

215

according to:

hL = hR −

216

Ta LP

(13) -1

217

where LP is the conductance in the path root to leaf (d ), it is calculated as a function of potential

218

transpiration (Zhuang et al., 2001; De Willigen et al., 2011). The actual transpiration (Ta) is a function

219

of the Tp and hL according to the approach of Campbell (1985, 1991): q   hL      Ta = Tp 1 + h     L,1 / 2   

220

−1

(14)

221

Where hL,1/2 is the value of hL where Ta = 0.5Tp, and q is a dimensionless crop specific parameter.

222

Figure 3 gives a graph of Eq. (14). So in total for a system of n layers we have n+2 equations:

(

)

223

wFus,i Φi − Φ0,i = Lrv,i KR (h0,i − hR ), for i = 1,n

224

h L = hR −

TP   h  LP  1 +  L    hL,1 / 2 

q

(16)

   

n

Tp

i =1

 h  1+  L  h   L,1/ 2 

∑ Lrv,i ∆zi KR (h0,i − hR ) =

225

   

(15)

q

(17)

226

Equation (15) states that in the path soil - root surface - xylem there is no accumulation of water, Eq.

227

(16) gives the relation between hL and hR, and Eq. (17) states that transport into the root equals actual

228

transpiration. These equations have to be solved iteratively for the unknowns h0,i (from which Φ0,i

229

follows), hR and hL for a given bulk h in the soil layer (from which Φ follows). Summarizing: the

230

FUSSIM2 water uptake routine does not merely take the soil properties into account, but also the plant

231

properties as radial conductance, and plant conductance. The actual transpiration is a function of the

232

leaf water potential.

233

RSWMS

234

The uptake model in RSWMS is obtained by coupling the 3-D Richards equation for soil water flow to

235

the Doussan equation (Doussan et al., 1998a,b), which explicitly solves the water flow in a root system

236

given its 3-D architecture. This coupling is necessary since the Richards equation (Eq. (1)) needs the


9

237

3-D sink term distribution S(x,y,z) to be known, while the root system solution depends on soil water

238

potential distribution h around the roots. In the coupled model, the sink term for soil voxel j is defined

239

as nj

∑ J r ,i 240

Sj =

i =1

(18)

Vj

241

where the nominator represents the sum of all the radial fluxes of the nj root nodes located inside a

242

soil voxel Jr,i (cm d ) and Vj is the volume of the j-th soil voxel (cm ). The radial flow rate from soil to a

243

root node i is obtained by

244

3

-1

3

(

J r ,i = K r*,i s r ,i hs

i

− h x,i

)

(19) -1

245

where K*r,i is the radial conductivity of node i in d (function of the root segment age and root type), sr,i

246

the root lateral surface hx,i is the xylem water potential for root node i (cm), and hs

247

water potential around root node i. Xylem flow is given in one segment by:

248

 dhx,i dz   J x,i = K x,i  + dl   dl

i

the average soil

(20) 3

-1

249

where dl is the segment length [L] and Kx,i the xylem conductance [L T ] can be a function of the

250

distance to the root tip (root age), the type of root, or the xylem potential but is considered as constant

251

and uniform in this study. To solve the Doussan root flow equation for the whole rooting system, the

252

soil water potential around each root node hs

253

averaged of the soil pressure head hs,k of the 8 nodes which surround the root node i. For coupling the

254

water flow in both the soil and root systems, we used an implicit iterative scheme until the maximum

255

change in root and soil pressure head at all the nodes does not exceed a maximum threshold value

256

and there is no change in the total water uptake between consecutive iterations. By default, the

257

boundary condition (BC) for the root is a potential flux at the root collar (potential transpiration). As the

258

flow equation within the root system is solved, a pressure value is calculated for each root node at

259

each time step, in particular at the root collar. When the pressure head at the root collar node reaches

260

a limiting minimum value hx,lim, the potential flux cannot be sustained anymore (i.e. stomata close in

261

order to keep a constant potential) and the root collar boundary switches from flux-type condition (i.e.

262

the potential transpiration) to head-type boundary condition (i.e., pressure head at the collar is equal to


i

is needed. This is defined as a distance weighed

10

263

hx,lim). When the flux calculated with a water potential at the collar equal to hx,lim is higher than the

264

potential flux, BC is switched back to flux-type.

265

Summarizing, RSWMS fully solves the water flow equation in the soil and in the root systems and

266

estimate the 3-D uptake distribution based on water potential gradient between each root node and

267

the surrounding soil voxel. Water stress is modeled as a switch from flux-type to head-type collar BC,

268

when the collar water potential is beyond a limiting potential value. Therefore, no functional (unique)

269

relationship between soil water potential and optimal transpiration (as the Feddes function) or between

270

the plant water potential and the transpiration are defined.

271

Material and methods

272

To compare the RWU of our four models, we used two different approaches. First, we analyzed their

273

behavior for a scenario of rainfall and potential transpiration pattern. Next, we focused on the

274

compensation occurring in the models SWAP-micro, FUSSIM2 and RSWMS.

275

It must be noted that the solution of the Richards equation without a sink term was checked to be

276

identical between the three main models (De Willigen et al., 2011). So, differences between models

277

obtained in this study can be solely attributed to RWU descriptions and model dimensionality. Due to

278

the differences in dimensionality of the four models, comparison will only be done on 1-D profiles. For

279

that reason FUSSIM2 was used in its 1-D mode, and for RSWMS depth-averaged 1-D profiles were

280

obtained after post-processing the 3-D outcome. Hysteresis was not taken into account, as the models

281

calculate hysteresis effects differently.

282

Soil and Root domains

283

We considered a soil column of 40 cm length and fully rooted. The x and y domains for the 3-D model

284

were 24 cm. The grid spatial resolution was uniformly 1 cm in all directions. At all soil boundaries a no-

285

flow condition is assumed, except for possible precipitation at the soil surface. The soil physical

286

properties are described by the classical Mualem (1976; K(h) or K(θ)) – van Genuchten (1980; θ(h))

287

functions. Three soil types were involved in the comparison: a sand (Zandb3), a clay (Kleib11), and a

288

loam (Leemb13) from a national Dutch soil data base (Wösten et al., 2001; Table 3).

289

A root system was generated with the Root Typ model (Pagès et al., 2004) which was used by the

290

RSWMS model (Fig. 4a). From this 3-D distribution an 1-D Lrv was derived for the SWAP and


11

291

FUSSIM2 models by averaging over the x- and y-direction (Fig. 4b). Results by RSWMS are

292

presented in 1-D after averaging from the 3-D results. As the RWU routines of the four models behave

293

quite similarly when required uptake per cm root is low, i.e. for high root length densities and moderate

294

potential transpiration, we deliberately choose rather low root densities (Fig. 4) and high potential

295

transpiration to emphasize the differences between the root water uptake concepts.

296

Comparison 1: Root water uptake scenario

297

The root water uptake scenario pertains to a constant potential transpiration Tp of 0.4 cm d (= cm

298

water per cm soil surface d ) for 31 days and one precipitation event at day 15 with a rate of 2 cm d

299

for one day. Initially the soil is at hydrostatic equilibrium with h = -700 cm at the bottom. The amount of

300

water corresponding to the initial h distribution was quite different between the three soils: 5.8 cm for

301

Zandb3, 17.7 cm for Kleib11, and 7.7 cm for Leemb13.

302

Table 4 lists the specific input parameters of the four RWU models. The parameters of SWAP-macro

303

were chosen as to comply with the scenarios given above. Those of SWAP-micro are as mentioned by

304

De Jong van Lier et al. (2008). In case of FUSSIM2 KR was derived from the root conductivity given by

305

Javaux et al. (2008) taken into account the value of R0 used here. Values for hL,1/2 and q of the

306

reduction function were taken from Kremer et al. (2008).

307

Results will pertain to time courses of cumulative uptake and root water uptake rates, and to soil depth

308

profiles of volumetric water content θ and pressure head h in the bulk soil.

309

Comparison 2: Compensation mechanisms

310

In all water uptake routines the distribution of actual uptake is governed by distribution of soil pressure

311

head and root length as a function of depth and time. Usually, for a moist soil, distribution of water

312

uptake follows that of root length density. However, when water potential distribution becomes more

313

heterogeneous, water can be extracted there where it is more easily available, independently of the

314

amount of roots. This mechanism driven by water potential differences is called compensation. For this

315

situation we will focus on some results of the uptake scenario.

316

To illustrate the relative importance of the different feedback mechanisms the models FUSSIM2 and

317

RSWMS were used. Initially the soil is at equilibrium with h = -500 at the bottom, and no precipitation

318

occurs in the simulation period of 20 days. Six cases were considered:

-1

2

-1


3

-1

12

319

•

320 321

water between the layers through soil or roots occurs; •

322 323

Case 1: uptake from a particular layer depends only on local pressure head, no exchange of

Case 2: as Case 1, but with exchange of water between the layers by Darcy flow (no root flow);

•

Case 3: uptake from any layer is coupled to that of any other layer via the root radial

324

conductance and the generated plant water potential as done in FUSSIM2, but no exchange

325

of water between layers (root flow but no soil flow);

326

•

327 328

and soil water flow); •

329 330

Case 4: as Case 3, but with exchange of water between the layers by Darcy flow (both root

Case 5: as Case 4 but with a 3-D resolution of the soil and the root water flow (3-D root and soil water flow done by RSWMS) with a negligible axial resistance;

•

Case 6: as Case 5, but with a normal value of axial resistance (given in Table 4).

331

Cases 1 to 4 were evaluated with the FUSSIM2-model, Cases 5 and 6 with the RSWMS model.

332

Comparisons between Cases 1 versus 2 and Cases 3 versus 4 will elucidate the impact of vertical soil

333

redistribution on uptake. By comparing Cases 4 and 5, we could qualitatively evaluate the impact of

334

the 3-D root architecture and water flow, i.e. the horizontal redistribution within layers. Comparison of

335

Cases 5 versus 6 indicates the importance of the axial resistance on uptake.

336

Results for cumulative transpiration are given, as well as the final water content – depth distribution for

337

the 6 Cases.

338

Results

339

Comparison 1: Uptake scenario

340

Cumulative and actual transpirations

341

Both the time courses of cumulative transpiration and transpiration rate are shown in Fig. 5.

342

Interestingly, the cumulative transpiration after 10 days did not differ very much between the models:

343

10% at most (for the clay), while larger differences appeared in terms of transpiration rate or

344

cumulative transpiration (just before the rainfall event). This difference is mainly due to differences

345

between models in stress occurrence time (see the section on stress onset hereafter). FUSSIM2 and

346

SWAP-micro were very similar in their cumulative transpiration behavior. In terms of shape of the Comparison of four root water uptake models

13

347

instantaneous transpiration rate, FUSSIM2 and RSWMS showed similar results, in particular after the

348

rainfall event. For the sandy soil the results of FUSSIM2 and SWAP-micro were very similar. The

349

SWAP-macro generally showed a more gradual decline of root water uptake than the more detailed

350

models, which ultimately resulted in comparable cumulative transpiration amounts.

351

Soil profiles

352

Figure 6 shows the profiles of water content in the bulk soil (θ), the pressure head in the bulk soil (h),

353

and the water uptake after 15.5 days for scenario S1. The profile of water content in bulk soil was quite

354

similar for the four models, mainly governed by the amount of transpired water. The difference in soil

355

pressure head, however, was large. In case of Zandb3, for instance, the difference in water content at

356

depth 8.5 cm between RSWMS and SWAP-macro was 0.01, but that in pressure head more than

357

7000 cm. This is due to the very steep gradient dh/dθ at the prevailing water content. The water

358

uptake rate profiles showed for RSWMS and especially for FUSSIM2 the phenomenon known as

359

hydraulic lift: flow of water from the roots into the soil. Due to the increased availability of infiltrated rain

360

water at the soil surface, water was taken up in the top layer and released in the drier lower layers.

361

This is seen in the right graphs of Fig. 6 as a negative uptake at the bottom layers for both models and

362

for the three soils (except for FUSSIM2 for Zandb3).

363

Figure 7 shows the same variables but now at t = 30.5 days. The water content profiles were similar

364

for all the soils and the models, with hardly a gradient with depth. The water uptake rate distribution

365

differed relatively more between the models, in particular for SWAP-macro under sandy soil and for

366

SWAP-micro in the loam. Note that the water uptake rates were much lower than at t = 15.5 d. It is

367

striking to observe that, despite important differences between the RWU models, the water content

368

profiles remained similar, due to soil and root hydraulic redistributions. While the extraction pattern is

369

controlled by the sink term modeling, the general profile is rather determined by the total amount of

370

water that has been extracted by the plant.

371

Stress onset

372

We observe in Fig. 5 that SWAP-macro suffered from stress right from the start. As the reduction of

373

transpiration begins at a pressure head of -675 cm with this model (see Fig. 2), reduction started

374

immediately with the initial conditions chosen here (pressure heads between -700 and -740 cm). For

375

the other three models, the ranking of the soils is the same: reduction started first for the Zandb3 soil,

376

followed by Kleib11, while Leemb13 was the last to show reduction. Table 5 shows the time of onset of Comparison of four root water uptake models

14

377

transpiration reduction for comparison 1, the cumulative transpiration (cm), and the cumulative uptake

378

as a percentage of the total initial water amount of water + precipitation.

379

Quantitatively, large differences in onset of transpiration appeared, but differences in cumulative

380

transpiration over the period of 30 days were small. Transpiration was the biggest for Leemb13,

381

followed by Kleib11 and then Zandb3. In case of SWAP-micro the onset of the reduction started much

382

later, but the difference in cumulative transpiration between SWAP-micro and SWAP-macro was of the

383

order of 2-6% only. SWAP-micro seemed to have a high capacity of compensation, which allows this

384

model to sustain high transpiration rate longer. However, this high transpiration depleted the soil water

385

profile quicker, which generated a sudden and important decrease when stress occurred. This model

386

has therefore the widest range of transpiration rates. On the opposite, as SWAP-macro generated

387

stress since the beginning, the depletion water was slower and less intense, which generated a slower

388

decrease of transpiration rate.

389

The onset of stress depends on the transpiration rate. In the uptake scenario we adopted a constant

390

potential transpiration rate during the day, which may delay the onset of stress. Therefore we also

391

performed simulations in which the potential transpiration during the day was distributed according to a

392

sinusoidal pattern (data not shown). In case of SWAP-macro the actual transpiration was not affected

393

by the adopted daily pattern of transpiration. In this model the critical pressure head h3 is affected by

394

the daily atmospheric demand, not the instantaneous transpiration flux. SWAP-micro, FUSSIM and

395

RSWMS showed earlier stress onset and larger stress amounts in case of a diurnal cycle. The

396

differences between cumulative transpiration with and without diurnal cycle were the highest for

397

RSWMS, amounting to 20% in case of Leemb13. The RSWMS model appeared to be more sensitive

398

to the instantaneous flux than the other models, due to the 3-D set up of RSWMS. Indeed, plants in

399

RSWMS have a direct access only to the soil voxels located around their roots, which is a much

400

smaller volume that the total soil domain. As soon as the potential demand is high, the local fluxes

401

increase as well, which create a sudden drop of water content and conductivity in the voxels close to

402

the root nodes. As the lateral redistribution is not instantaneous (as it is in 1-D models, when an

403

uniform horizontally-averaged water potential is considered), high flux may create more rapidly local

404

low potentials, which will generate stress earlier. This occurs in particular when transpiration rates are

405

higher, and soil conductivity lower, and soil lateral redistribution does not instantaneously compensate

406

root uptake


15

407

Comparison 2: Compensation

408

Figure 8 presents the water uptake rate – depth profiles for FUSSIM2, RSWMS and SWAP-micro for

409

Zandb3 for times 0.5 and 2.0 d of S1. All models resulted for both times in a total uptake rate of Ta =

410

Tp = 0.4 cm d . However, the depth distributions changed in time. In the beginning the uptake profiles

411

for FUSSIM2 and RSWMS followed the root length density distribution (Fig. 4; also depicted in Fig. 8),

412

but as time progressed there was a change in uptake: more extraction from deeper layers and less

413

near the soil surface. This, however, resulted in a lower (more negative) root water potential. For

414

example, in the case of FUSSIM2, the plant water potential which is assumed to be uniform in the

415

whole xylem network at t = 0.5 d was –3405 cm and –4331 cm at t = 2 d. For RSWMS, the xylem

416

collar water potential (representing the most negative value of the network) varied between –8541 cm

417

at t = 0.5 d and –10404 cm at t = 2 d. As FUSSIM2 assumes a constant plant water potential in the

418

xylem (and therefore at the collar as well), while RSWMS does not, values cannot be strictly

419

compared, but the magnitude and change with time can serve as indicator of the impact of the

420

constant xylem potential assumed by FUSSIM2. The RSWMS model yielded smoother profiles. At

421

later times the compensation could no longer satisfy the demand, resulting in a decrease in root water

422

uptake. The SWAP-micro model resulted in quite different uptake patterns. Even in the beginning the

423

SWAP-micro uptake didn’t follow the root length density distribution.

424

The results for the 6 Cases to ultimately demonstrate the effect of compensation mechanisms are

425

depicted in Figs. 9 and 10. Going from Case 1 to Case 4 the actual cumulative uptake increased, and

426

the time of start of transpiration reduction increased as well. The difference between Cases 5 and 6

427

reflected the effect of increasing the axial xylem resistance to flow inside the root system resulting in a

428

decreased uptake and earlier onset of transpiration reduction.

429

Discussion

430

The results of the uptake scenario revealed that over longer time periods the cumulative root water

431

uptake did not differ much between the four RWU models. However, differences showed up in times of

432

onset of transpiration reduction and in uptake rates as a function of soil depth. In order to explain

433

these outcomes, we have carried out analyses regarding the compensation mechanisms in the soil –

434

root domain.

-1


16

435

Compensation mechanisms

436

Figure 9 showed the evolution of the cumulative transpiration for the 6 Cases. By comparing Case 1

437

with Case 2 we assessed the impact of soil water redistribution alone on plant transpiration, it

438

amounted to an increase of 32%. A much smaller increase was found in comparing Cases 3 and 4:

439

3%. When vertical water flow is considered transpiration was always higher and the profile of water

440

content was smoother (Fig. 10). Comparison of Cases 1 and 3 showed the effect of coupling the

441

uptake rates via the root water potential, leading to an increase in transpiration of 41%. The

442

transpiration in Case 3 was higher than that of Case 2 (about 7%) and the average gradient in water

443

content lower but the profile was less smooth. Case 4 resulted in more than 45% increase with respect

444

to Case 1. Cases 2 and 4 differed by the fact that root compensation is accounted for: in that case, the

445

transpiration was the highest: water is redistributed between wet and dry zones, but in addition, the

446

plant root itself was capable of taking up more water in wetter zone. This definitely improved the

447

uptake capacities of the plant as observed in terms of cumulative transpiration (Case 4, Fig. 9 and

448

stress occurrence). When 3-D soil and root simulations were performed (Case 5), it was observed that

449

water uptake decreased dramatically at the end. This impact is due to the 3-D water flow in soil and

450

roots. In general, due to previous uptake, roots are located in zones where the water potential is

451

substantially lower than the horizontally averaged water potential (as considered in 1-D models), which

452

resulted in a lower water availability. In addition lateral water flow in 3-D was explicitly solved with the

453

Richards equation and local uptake cannot instantaneously be compensated with incoming water from

454

non-rooted soil voxels (15.5% of the soil nodes were located around a root node). This generated

455

earlier stress and lower uptake for Case 5 than for Case 4. In case the xylem conductivity was

456

accounted for (Case 6), we observed that cumulative transpiration decreased even more (Fig. 9; 3%

457

less than Case 5) and less water was extracted from deeper zones (Fig. 10, Case 6). Note that in this

458

study we were only interested in uptake at the grid (layer) scale (i.c. 1 cm), and not at the drying

459

patterns around individual roots. For a discussion on the latter the reader is referred to, e.g.,

460

Schroeder et al. (1009) or Metselaar and De Jong van Lier (2011).

461

Water flow in soil (redistribution) and roots (compensation) tended to homogenize the uptake profile

462

(Cases 1 to 4 in Fig. 10). Even when 3-D water flow is accounted for water profiles were more

463

homogeneous due to compensation and high axial conductance (Case 5). However, stress appeared


17

464

quicker and cumulative transpiration is deeply affected by the 3-D distribution of the water flow, due to

465

high sensitivity to water hydraulic conditions close to the root surface.

466

The compensation in all three models occurs as a “natural” consequence of the description of uptake,

467

contrary to attempts to force compensation by postulation of empirical parameters, the value of which

468

can only be obtained by calibration (Šimůnek and Hopmans, 2009; Jarvis, 2010).

469

Differences between SWAP-macro- and SWAP-micro

470

In SWAP-macro the root water uptake reduction function did not depend on soil type or absolute root

471

density. The reduction function of SWAP-micro makes the effect of both soil type and absolute root

472

density explicit. Strikingly, in case of SWAP-macro the reduction generally starts at the highest soil

473

water pressure heads, and shows a gradual decline of the reduction factor when pressure heads

474

decrease. Also, SWAP-macro does not account for root water uptake compensation when some parts

475

of the root zone are stressed. This caused the early onset of the reduction period in the experiment

476

(Table 5) and the more smooth fluctuations in transpiration rate (Fig. 5).

477

In contrast, SWAP-micro showed a strong decline of the reduction factor when soil water pressure

478

heads decreased. Also stress in parts of the root zone, automatically resulted in increased root water

479

uptake in regions with more favorable soil moisture and root density conditions. This is for instance

480

visible in the water uptake rate profile (Fig. 6). The rain shower caused increased soil moisture

481

contents in the top soil, where root densities were the highest. This caused the very large root water

482

uptake rates in the top soil as simulated by SWAP-micro. Therefore, compared to SWAP-macro,

483

SWAP-micro showed a much later onset of the reduction period and more rapid fluctuations of the

484

transpiration rate (Fig. 5).

485

Although SWAP-micro makes more physical mechanisms explicit (absolute root density, soil hydraulic

486

functions, root water uptake compensation), the number of root water uptake related input parameters

487

is significantly reduced (Table 4). SWAP-macro requires determination of 5 semi-empirical input

488

parameters and the relative root density profile, while SWAP-micro requires as input the minimum

489

pressure head at the interface soil-root and the absolute root density profile. The SWAP-micro concept

490

is not sensitive to common root radius values.


18

491

Difference between FUSSIM2 and SWAP-micro

492

Compared to SWAP-micro, FUSSIM2 adds the radial hydraulic resistance in the roots and moves the

493

boundary condition back from the soil-root interface to the root xylem. In this way a larger part of the

494

soil-root system is integrally simulated. Also the boundary condition is differently formulated. SWAP-

495

micro defines a minimum pressure head at the soil-root interface, which can be reached irrespective of

496

the soil water flux rate towards the roots. FUSSIM2 employs the Campbell relative transpiration as

497

function of xylem water pressure head (Eq. (14)).

498

In case of FUSSIM2, the onset of root water uptake reduction started at higher soil water pressure

499

heads and the decline of the reduction factor with decreasing pressure heads was more gradual. This

500

can be attributed to the inclusion of the radial hydraulic resistance and the use of the Campbell

501

function. The effect of absolute root density on the reduction function was similar for SWAP-micro and

502

FUSSIM2.

503

The root water uptake rate after the rain shower on dry soil showed different patterns for both models

504

(Fig. 6). In case of SWAP-micro the transpiration demand was delivered by the moist upper soil

505

compartments with the highest water contents and root densities. It is assumed that, irrespective of the

506

radial soil water flux the minimum pressure head can be reached. This caused the root water uptake

507

reduction in the lower parts of the root zone to be fully compensated by the increased uptake in the

508

upper soil compartments. FUSSIM2 showed this increased uptake in the upper soil layer also, but the

509

increase was limited by the increased radial hydraulic head loss in the root system and the Campbell

510

function. In addition, FUSSIM2 accommodated hydraulic lift, which is clearly visible in Fig. 6. Although

511

the root water uptake was distributed over plant transpiration and water exfiltration in dry soil layers,

512

the potential plant transpiration could be reached.

513

Due to the damping effect of the root radial hydraulic resistance, the Campbell function and the

514

hydraulic lift, the transpiration rates simulated by FUSSIM2 showed less rapid fluctuations than

515

SWAP-micro (Fig. 5). Nevertheless, the cumulative transpiration over longer periods was quite similar

516

for both models (Fig. 5).

517

Difference between FUSSIM2 and RSWMS

518

Three points differentiate RSWMS from FUSSIM2: (1) soil water flow is solved in 3-D, (2) root water

519

flow is solved in 3-D, and (3) there is an axial resistance to water flow in the xylem.


19

520

The consequence of these for FUSSIM2 is that an instantaneous equilibrium is assumed to occur

521

horizontally in the soil at a given distance to the root and also in the root (i.e., the xylem pressure head

522

is uniform and equal to the collar pressure head). This will generally lead to an increase of the

523

pressure head gradient between soil and root for FUSSIM2 as the xylem pressure head is more

524

negative (due to high xylem conductance) and soil pressure head is less negative (due to

525

instantaneous redistribution). It was observed that uptake predicted with RSWMS is always lower than

526

with FUSSIM2 and that stress was always more pronounced in RSWMS (Figs. 5 and 8).

527

The impact of 3-D soil and root water flow and of the negligible pressure head gradient were

528

discriminated in Figs. 9 and 10. It is observed that the 3-D redistribution effect (Case 5 versus Case 4)

529

is the most important. The high xylem conductance affected the depth of uptake and, with a lower

530

magnitude, the stress occurrence.

531

Conclusions

532

This study compared four different sink-terms by running virtual experiments. These RWU models, of

533

different complexity, were all embedded in a greater model computing transport of soil water: SWAP

534

(1-D), FUSSIM2 (2-D) and RSWMS (3-D). Within SWAP two RWU functions were employed: a

535

macroscopic function (Feddes et al., 1978; SWAP-macro), and a microscopic RWU model (De Jong

536

van Lier et al., 2008; SWAP-micro). In FUSSIM2 the RWU model of De Willigen and van Noordwijk

537

(1987) is used, and the RWU model in RSWMS is obtained by coupling the Richards equation to the

538

Doussan equation (Doussan et al., 1998a,b), which explicitly solves the water flow in a root system

539

given its 3-D architecture. Besides the differences in dimensionality of the models, the complexity of

540

the processes considered in root water uptake increases from SWAP-macro, SWAP-micro, FUSSIM2

541

to RSWMS. Our main observations are that:

542

•

543 544

Differences between modeled transpirations appeared to be relatively small for sandy soils, and increased at fine textured soils and with day-night conditions.

•

In general, differences were smaller in total mass balance (final cumulative transpiration) and

545

water content than in terms of pressure head and water uptake rate profiles. This is explained

546

by the fact that water content and transpiration directly relate to mass balance and are,

547

therefore, only affected by stress onset, while pressure head dynamics is also affected by

548

water flow predictions, which differed a lot between models. Comparison of four root water uptake models

20

549

•

Model complexity does not imply an absolute over- or under-estimation of the transpiration.

550

Cumulative transpiration and stress onset were generally impacted more by soil type than by

551

model choice.

552

•

Differences between day-night versus constant transpirations were higher for FUSSIM2 and in

553

particular for RSWMS. Indeed, 1-D models rely on the assumption that (a) the plant has

554

access to all the water in a given layer, or (b) that the horizontal redistribution is

555

instantaneous. While this assumption does not impact differences between models for wet,

556

high conductive cases under low transpiration, this is very discriminant under high

557

transpiration and low K.

558

•

Non-instantaneous lateral redistribution dramatically differentiates RSWMS from the other

559

models. It seems that lateral redistribution generates important differences for the prediction of

560

cumulative transpiration.

561

•

For situations where water availability is not limiting, as was the case in the beginning of our

562

scenarios, the four RWU models yielded actual uptake rates equal to the potential

563

transpiration demand. However, when the soil dried out, differences between the models

564

occurred.

565

A model, by definition, is a simplification of part of the real world. In making a model one tries to leave

566

out as much as possible, with the aim to include only the processes, which really do matter for the

567

phenomena one wants to study. It is, therefore, difficult to give a general recommendation as to which

568

of the models discussed here can best be used, as this depends on the purpose of the user, the

569

computation power and the data availability (e.g., Feddes and Raats, 2004; Hopmans and Bristow,

570

2002). For instance, if one is interested in simulation of the transpiration in the growing season and

571

data on distribution of root length density are not available SWAP-macro seems a suitable choice. At

572

the other end of the spectrum one finds the model RSWMS that is more flexible and by which

573

subtleties of differences in radial an axial conductance can be investigated.

574

Another example is the actual flow pattern in the root zone. If this flow pattern is predominantly

575

vertical, as in close, uniform covered cultivated soils, a one-dimensional approach as used by SWAP-

576

macro and SWAP-micro may suffice. However, at two-dimensional or radial symmetric flow patterns

577

for instance in case of drip irrigation, FUSSIM2 might be more suitable. In case of three-dimensional

578

structure, a 3-D model like RSWMS seems more justified.


21

579

A main aspect of this model comparison is that root water uptake requires the combination of soil

580

physical and root physiological knowledge. Many researchers and models focus either on the soil

581

system, or on the root system. This analysis shows that both systems significantly affect the root water

582

uptake fluxes. We expect most reliable vadose zone modeling results from models that properly

583

address both the root and soil system.

584

The depicted root water extraction patterns for two strictly defined scenarios and four clearly different

585

models may serve as a reference for other, alternative root water uptake modeling concepts.

586

The next step of this comparison study should involve a comparison to real transpiration data. This

587

would allow us to investigate differences between model parameter identification through inverse

588

modeling and model stability or representativeness under different soil water status.

589

References

590

Campbell, G.S. 1985. Soil physics with BASIC. Elsevier, Amsterdam, the Netherlands.

591

Campbell, G.S. 1991. Simulation of water uptake by plant roots. In J. Hanks and J.T. Ritchie (eds.),

592

Modeling Plant and Soil Systems. Agronomy Monograph 31, pp. 273-285. ASA CSSA SSSA,

593

Madison, WI.

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Clausnitzer, V., and J.W. Hopmans. 1994. Simultaneous Modeling of Transient 3-Dimensional RootGrowth and Soil-Water Flow. Plant and Soil. 164:299-314. De Jong van Lier, Q., K. Metselaar, and J.C. van Dam. 2006. Root water extractions and limiting soil

597

hydraulic conditions estimated by numerical simulation. Vadose Zone J. 5:1264-1277.

598

doi:10.2136/vzj2006.0056.

599

De Jong van Lier, Q., J.C. van Dam, K. Metselaar, R. de Jong, and W.H.M. Duijnisveld. 2008.

600

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601

7:1065-1078. doi: 10.2136/vzj2007.0083.

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De Willigen, P. 1990. Calculation of uptake of nutrients and water by a root system. Nota 210, DLO Institute for Soil Fertility Research, Haren, the Netherlands. De Willigen, P., and M. van Noordwijk. 1987. Roots, plant production and nutrient use efficiency. PhD Thesis, Wageningen Agricultural University, the Netherlands. De Willigen, P., and M. van Noordwijk. 1991. Modelling nutrient uptake: from single roots to complete

607

root systems. Simulation and systems analysis for rice production (SARP). In: F.W.T. Penning de

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Vries, H.H. van Laar, and M. J. Kropff (Eds.), Simulation and systems analysis for rice production

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De Willigen P., J.C. van Dam, M. Javaux, and M. Heinen. 2011. Comparison of the root water uptake

613

term of four simulation models. Alterra report 2260. Wageningen, the Netherlands. Available at

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http://content.alterra.wur.nl/Webdocs/PDFFiles/Alterrarapporten/AlterraRapport2260.pdf.

615

Doussan, C., L. Pages, and G. Vercambre, 1998a. Modelling of the Hydraulic Architecture of Root

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Systems: an Integrated Approach to Water Absorption - Model Description. Annals of Botany

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Doussan, C., G. Vercambre, and L. Pagès. 1998b. Modelling of the hydraulic architecture of root

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Doussan, C., A. Pierret, E. Garrigues, and L. Pagès. 2006. Water uptake by plant roots: II - Modelling

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Comparison with experiments. Plant and Soil 283:99-117.

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Draye, X., Y. Kim, G. Lobet, and M. Javaux. 2010. Model-assisted integration of physiological and

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environmental constraints affecting the dynamic and spatial patterns of root water uptake from

626

soils. J. Exp. Botany, 61(8):2145-2155. doi:10.1093/jxb/erq077.

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Feddes, R.A., P.J. Kowalik, and H. Zaradny. 1978. Simulation of field water use and crop yield. Simulation Monographs. PUDOC, Wageningen, the Netherlands. Feddes, R.A., and P. Raats, 2004. Parameterizing the soil-water-plant root system. In: R.A. Feddes,

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G.H. De Rooij, and J.C. van Dam (Eds.), Unsaturated-zone modeling, pp. 95–141. Kluwer

631

Academic Publishers, Wageningen, the Netherlands.

632

Gardner, W.R., 1960. Dynamic Aspects of Water Availability To Plants. Soil Sci. 89:63-73.

633

Heinen, M. 2001. FUSSIM2: brief description of the simulation model and application to fertigation

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scenarios. Agronomie 21:285-296. doi:10.1051/agro:2001124 Heinen, M., and P. de Willigen. 1998. FUSSIM2. A two-dimensional simulation model for water flow,

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solute transport and root uptake of water and nutrients in partly unsaturated porous media.

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Quantitative Approaches in Systems Analysis No. 20, DLO Research Institute for Agrobiology and

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Soil Fertility and the C.T. de Wit Graduate School for Production Ecology, Wageningen, the

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Netherlands.

640 641 642

Hopmans, J.W., and K.L. Bristow. 2002. Current capabilities and future needs of root water and nutrient uptake modeling. Advances in Agronomy, 77, 103-183. Javaux, M., T. Schroeder, J. Vanderborght, and H. Vereecken. 2008. Use of a three-dimensional

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detailed modelling approach for predicting root water uptake. Vadose Zone J. 7:1079–1088.

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doi:10.2136/vzj2007.0115.


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Javaux M., X. Draye, Cl. Doussan, J. Vanderborght, and H. Vereecken. 2011. Root water uptake:

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towards 3-D functional approaches. In: J. Glinski, J. Horabik, and J. Lipiec (Eds.), Encyclopaedia of

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Agrophysics. Springer, The Netherlands. p.717-721.

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Jarvis, N.J. 1989. A simple empirical model of root water uptake. J. Hydrol. 107:57-72.

649

Jarvis, N.J. 2010. Comment on ‘Macroscopic root water uptake distribution using a matric flux potential

650 651

approach’. Vadose Zone J. 9:499–502. doi:10.2136/vzj2009.0148. Kremer, C., C.O. Stöckle, A.R. Kemanian, and T. Howell. 2008. A canopy transpiration and

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photosynthesis model for evaluating simple crop productivity models. In: L.R. Ahuja, V.R. Reddy,

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S.A. Saseendran, and Qiang Yu (Eds.), Response of crops to limited water: Understanding and

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modeling water stress effects on plant growth processes. ASA, CSSA, SSSA, Madison, WI.

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Kroes, J.G., and J.C. van Dam. 2003. Reference manual SWAP version 3.03. Alterra report 773.

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Wageningen, the Netherlands. Available at

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Kroes, J.G., J.C. van Dam, P. Groenendijk, R.F.A. Hendriks, and C.M.J. Jacobs. 2008. SWAP version

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3.2.: theory description and user manual. Alterra report 1649, Wageningen, 284 p.

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Metselaar, K., and Q. De Jong van Lier. 2007. The shape of the transpiration reduction function under plant water stress. Vadose Zone J. 6:124-139. Metselaar, K., and Q. De Jong van Lier. 2007. Scales in single root water uptake models: a review, analysis and synthesis. Eur. J. Soil Sci., 62, 657-665. Mualem, Y. 1976. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 12:513-522. doi:10.1029/WR012i003p00513 Pagès, L., G. Vercambre, J.-L. Drouet, F. Lecompte, C. Collet, and J. Le Bot. 2004. Root Typ: a

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generic model to depict and analyse the root system architecture. Plant and Soil 258:103-119. doi:

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Pierret, A., Doussan, C., Capowiez, Y., Bastardie, F., and L. Pagès. 2007. Root functional

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architecture: A framework for modeling the interplay between roots and soil. Vadose Zone J. 6:269-

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281.

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Raats, P.A.C. 1970. Steady infiltration from line sources and furrows. Soil Sci. Am. Proc.34:709-714.

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Schroeder, T., M. Javaux, J. Vanderborght, B. Koerfgen, and H. Vereecken. 2009. Implementation of a

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microscopic soil-root hydraulic conductivity drop function in a soil-root architecture water transfer

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model. Vadose Zone J. 8:783-792. doi: 10.2136/vzj2008.0116.

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Šimůnek, J., and J.W. Hopmans. 2009. Modeling compensated root water and nutrient uptake. Ecol. Model. 220:505–521. doi:10.1016/j.ecolmodel.2008.11.004. Taylor, S.A., and G.M. Ashcroft, 1972. Physical Edaphology. Freeman and Co., San Francisco, California, p. 434-435. Comparison of four root water uptake models

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681 682 683

Van Dam, J.C., P. Groenendijk, R.F.A. Hendriks, and J.G. Kroes. 2008. Advances of modeling water flow in variably saturated soils with SWAP. Vadose Zone J. 7:640-653. Van Genuchten, M.Th. 1980. A closed form equation for predicting the hydraulic conductivity of

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unsaturated soils. Soil Sci. Soc. Am. J. 44:892-898.

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doi:10.2136/sssaj1980.03615995004400050002x.

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Vogel, H.J., and K. Roth. 2003. Moving through scales of flow and transport in soil. J. Hydrol. 272:95106. Vrugt, J.A., M.T. van Wijk, J.W. Hopmans, and J. Šimůnek. 2001. One-, two-, and three-dimensional root water uptake functions for transient modeling. Water Resour. Res. 37:2457–2470. Wösten, J.H.M., G.J. Veerman, W.J.M de Groot, en J. Stolte. 2001. Waterretentie- en

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doorlatendheidskarakteristieken van boven- en ondergronden in Nederland: de Staringreeks.

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Vernieuwde uitgave 2001. Alterra-rapport 153, Alterra, Wageningen, the Netherlands.

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Zhuang, J., K. Nakayama, G-R Yu, and T. Urusjisaki. 2001. Estimation of root water uptake of maize:

694

an ecological perspective. Field Crops Res. 69:201-213. doi:10.1016/S0378-4290(00)00142-8.

695


25

696

List of Figures

697 698

Figure 1. Model complexity and costs.

699 700

Figure 2. Reduction coefficient (α) as a function of pressure head (h) as used in SWAP-macro.

701 702

Figure 3. Relative transpiration as a function of plant water potential (Eq. (14)). Parameters: q = 7,

703

hL,1/2 = 16600 cm.

704 705

Figure 4. Root architecture considered in the 3-D RSWMS model (left) and the corresponding 1-D root

706

length density distribution with depth (right).

707 708

Figure 5. Time course of cumulative transpiration and transpiration rate for the three soils in

709

comparison 1.

710 711

Figure 6. Distribution of water content of the bulk soil (θ), pressure head of the bulk soil (h) and water

712

uptake rate with depth at t = 15.5 d in comparison 1.

713 714

Figure 7. As Fig. 6 for t = 30.5 d in comparison 1.

715 716

Figure 8. Distribution of water uptake with depth at two times as calculated by FUSSIM2, RSWMS and

717

SWAP-micro for soil Zandb3. At all given times the total uptake was equal to the potential

718

transpiration. Data obtained from comparison 1.

719 720

Figure 9. Time course of cumulative transpiration and different compensation mechanisms as

721

calculated with FUSSIM2 and RSWMS Explanation of Case 1 – Case 6: see main text.

722 723

Figure 10. Water content profiles after 20 days of transpiration for different compensation mechanisms

724

as calculated with FUSSIM2 and RSWMS. Explanation of Case 1 – Case 6: see main text.

725 Comparison of four root water uptake models

26

726

Table 1. Type of modeling approaches for root water uptake and their underlying related hypotheses.

727

Hypotheses are given for using the most complex choice (in bold in the second column). Feature

Parameter

Hypothesis

Soil dimension

1-, 2-, 3-D

Soil lateral fluxes are of importance

Sink term dimension

1-, 2-, 3-D

Root uptake is affected by non-uniform horizontal distribution of soil and root

Root architecture

Implicit/explicit

Architecture and root properties impact RWU

Root water uptake

Root properties/ soil water

Distribution of the water potential in roots and in

distribution

distribution/ soil and root

soil affect RWU

water distribution Stress

Explicit/implicit

No unique function, depends on water potential in the plant or in the soil.

728 729


27

730

Table 2. Characteristics features of the four models. SWAP

FUSSIM2

RSWMS

macro

micro

Soil dimension

1-D

1-D

2-D

3-D

Sink term dimension

1-D

1-D

2-D

3-D

Root architecture

Implicit

Implicit

Implicit

Explicit

Root water uptake

Function of root

Function of flux

Function of flux

based on soil-root

distribution

distribution

matrix potential

matrix potential

potential gradients

Stress

Explicit function

Implicit function

Explicit function

Implicit function of

of soil water

of soil available

of the leaf water

the collar water

potential

water

potential

potential

731 732


28

733

Table 3. Mualem - van Genuchten parameters for three soils of the Dutch Staring series (Wösten et

734

al., 2001). Soil

θr

θs

name

cm cm

Zandb3

0.02

0.46

15.42

Kleib11

0.01

0.59

Leemb13

0.01

0.42

3

-3

α

λ

n

-

-

0.0144

-0.215

1.534

8.0

0.0195

-5.901

1.109

12.98

0.0084

-1.497

1.441

Ks 3

cm cm

-3

cm d

-1

cm

-1

735 736


29

737

Table 4. Model specific input data with respect to root water extraction. Model

Input parameter

Symbol

Value

SWAP-

Critical soil water pressure head at Thigh

h3h

-600 cm

macro

(Taylor & Ashcroft, 1972) Critical soil water pressure head at Tlow

h3l

-900 cm (Taylor & Ashcroft, 1972)

Pressure head at wilting point

h4

-15000 cm

Level of high atmospheric demand

Thigh

0.5 cm d

Level of low atmospheric demand

Tlow

0.1 cm d

SWAP-

Minimum pressure head at interface soil-root

hw

-15000 cm

micro

Root radius

R0

0.075 cm

Relative radial distance of mean water

a

0.53 (-)

content

-1

-1

(De Jong van Lier et al., 2008)

FUSSIM2

Root radial conductance

KR

-5

-1

8.143 10 cm d

(Javaux et al., 2008) Half value of leaf water potential

hL,1/2

16600 cm (Kremer et al., 2008)

Exponent in reduction function

q

7 (-) (Kremer et al., 2008)

Conductance in the path root to leaf

Lp

-4

-1

1.029 10 d

Zhuang et al. (2001) RSWMS

Limiting collar xylem water potential

hx,lim

-15000 cm (Doussan et al., 1998a,b) -1

Xylem conductance

Khx

0.0432 cm³ d

Radial root conductivity

Lr

1.77728 10 d

-4

-1

738 739


30

740

Table 5. Time of onset of the reduction period and the cumulative transpiration realized in 30 d for the

741

different models in comparison 1. Onset reduction period (d)

Cumulative transpiration (cm) (Percentage of total initial water + precipitation)

Model

Zandb3

Kleib11

Leemb13

Zandb3

Kleib11

Leemb13

SWAP-macro

0.0

0.0

0.0

5.81 (74)

6.35 (32)

7.09 (73)

SWAP-micro

5.5

10.0

13.0

5.46 (70)

6.80 (35)

7.30 (75)

FUSSIM2

4.5

5.0

8.0

5.66 (72)

7.06 (36)

7.59 (78)

RSWMS

2.5

4.0

8.5

5.14 (66)

6.29 (32)

7.30 (75)

742 743


31