Water uptake by plants under heterogeneous soil moisture conditions: A
comprehensive numerical and experimental analysis
Anooja Thomas1 · Brijesh Kumar Yadav2 · Jiří Šimůnek3*
1

Department of Agricultural & Biological Engineering, University of Florida, Gainesville, Florida, 32603,
USA2

Department of Hydrology, Indian Institute of Technology Roorkee, Roorkee 247667, India

3

Department of Environmental Sciences, University of California Riverside, Riverside, CA 92521, USA*

Corresponding Author - Jiří Šimůnek, Email: jiri.simunek@ucr.edu

Supplementary TableTable S1: Summary of cumulative potential transpiration (Tp), actual transpiration (Ta),transpiration due to CRWU (TComp), and hydraulically distributed water (THR) (cm) for (a) case 1,(b) case 2, (c) case 3, and (d) case 4.
(a)Case 1
Tp
Ta
TComp
THR

DJ
18.00
12.24
3.84
0.00

CR
18.00
14.24
5.72
0.00

NH
18.00
11.55
3.74
0.00

JF
18.00
11.26
1.96
0.00

FD
18.00
10.12
0.00
0.00

DJ
18.00
16.65
5.14
-0.87

CR
18.00
17.93
6.00
-1.18

NH
18.00
17.87
6.53
-7.13

JF
18.00
15.65
2.58
0.00

FD
18.00
13.91
0.00
0.00

DJ
18.00
12.36
3.56
-0.60

CR
18.00
14.36
4.09
-1.70

NH
18.00
11.31
3.96
-0.07

JF
18.00
11.27
1.97
0.00

FD
18.00
10.13
0.00
0.00

DJ
18.00
17.10
7.72
-1.21

CR
18.00
16.34
4.94
-2.75

NH
18.00
17.47
10.57
-0.18

JF
18.00
11.69
2.19
0.00

FD
18.00
10.29
0.00
0.00

(b)
Case 2
Tp
Ta
TComp
THR
(c)
Case 3
Tp
Ta
TComp
THR
(d)
Case 4
Tp
Ta
TComp
THR

Water uptake by plants under heterogeneous soil moisture conditions: A
comprehensive numerical and experimental analysis
Anooja Thomas1 · Brijesh Kumar Yadav2 · Jiří Šimůnek3*
1

Department of Agricultural & Biological Engineering, University of Florida, Gainesville,
Florida, 32603, USA
2

3

Department of Hydrology, Indian Institute of Technology Roorkee, Roorkee 247667,
India

Department of Environmental Sciences, University of California Riverside, Riverside,
CA 92521, USA*

Corresponding Author - Jiří Šimůnek, Email: jiri.simunek@ucr.edu

Supplementary information 1

1

Simulation of Root Water Uptake and Soil Moisture Dynamics in a Column
Lysimeter

Methods
For the numerical simulation of RWU and soil water in the lysimeter using HYDRUS-1D,
we considered a 55-cm-deep soil profile, which was discretized into 0.5-cm thick intervals. The
parameters for the van Genuchten–Mualem equations, including θs, θr, α, and n were obtained
from the curve fitting of observed h vs θ values and Ks was obtained from the constant-head
permeameter experiment (Table S1). An atmospheric boundary condition (BC) with a surface layer
was used at the top boundary, and the free drainage BC was used at the bottom boundary.
Rainfall/irrigation and evaporation from the soil surface were set to zero. Potential transpiration
was measured from the control as described in Thomas et al. (2020). The initial soil water contents
in the simulation domain were set to be the same values as in the experimental lysimeter setup.
RWU and soil water dynamics were simulated for the four models for nine days. The analysis of
the NH model was omitted as unrealistic behavior was observed.
Table S1. Different parameters used for the simulation of RWU in a column lysimeter.
Parameters
Root hydraulic conductivity (Kr) (DJ model)
Root hydraulic conductance (Krs) (CR model)
Compensatory RWU conductance (Kcomp) (CR model)
Root radius (Ro) (DJ model)
Xylem radius (Rx) (DJ model)
Wilting point (hw)Root-to-leaf pathway conductance (L) (DJ model)
Saturated soil water content (s)Residual soil water content (r)Saturated hydraulic conductivity (Ks)van Genuchten’s Alpha ()Pore-connectivity parameter (l)The pressure head threshold values h1, h2, h3, and h4
van Genuchten’s n (related to the pore size
distribution) (n)2Value
4.1e-61.32e-03
1.75e-04
0.1
0.05-200005.0e-01
0.45
0.0397
55.4
0.038
0.5
-25, -300,

Unit[day-1][day-1][day-1]
[cm]
[cm]
[cm]
[cm day-1][cm3 cm-3][cm3 cm-3][cm day-1][cm-1][-][cm]-1000, -1500
1.256

[-]

RWU and soil water content simulated during different days using the DJ model arepresented in Figure Supl-1:1. Simulated RWU was proportional to the experimentally estimated
RLD with an r-value of 0.99 and 0.98 during days 0 and 2 (Pearson correlation), respectively. On
day 3, when the soil water content dropped below 0.12 cm3/cm-3, CRWU was initiated, and thetranspiration was maintained till day 6, which agrees with the experimental findings (Fig. S1C,
Fig. Supl-1:1BC). CRWU supported the plant survival under localized water stress by contributing
4.18 cm of total actual transpiration of 12.11 cm (Fig. Supl-1:1B). Likewise, HR was observed in
the DJ model from day 4 to 7, as indicated by negative RWU, as shown in Figure Supl-1:1AD andalso by negative transpiration as indicated in Figure S2B, which is in contrast with the data fromthe column lysimeter experiment.
Similarly, in the CR model, CRWU was initiated on day 4 when the soil water content
declined to 0.08 cm3/cm-3, accounting for 18.7% of daily transpiration (Fig. Supl-1:2ABD).
Similar to the DJ model, HR was initiated on day 5 and contributed 0.67 cm of the total 12.11 cm
of actual transpiration (Fig. Supl-1:2ABD). Thus, with the help of CRWU and HR, thetranspiration demand was maintained till day 6 (Fig. S3C). In the JF model, potential transpiration
was maintained till day 5 through CRWU (by contributing 2.85 cm of total transpiration of 11.20cm) (Fig. Supl-1:3ABC, Fig. Supl-1:4). In contrast to the DJ and CR models, the JF model could
not simulate HR due to incompatibility (Fig. Supl-1:3ABE). The earliest onset of water stress wasrecorded in the FD model (from day 5) compared to other models and the experimental
observations.

3

Figure Supl-1:1. Soil water dynamics and RWU in the column lysimeter simulated using the DJmodel: (A) Root water uptake distribution profiles; (B) Potential transpiration (Tp), actual
transpiration (Ta), compensated transpiration (Tcomp), and hydraulically redistributed water (THR);(C) Transpiration reduction function (Ta/Tp); (D) Root water uptake as a function of time anddepth; and (E) Soil water content as a function of time and depth.

4Figure Supl-1:2. Soil water dynamics and RWU in the column lysimeter simulated using the
CR model: (A) Root water uptake distribution profiles; (B) Potential transpiration (Tp), actual
transpiration (Ta), compensated transpiration (Tcomp), and hydraulically redistributed water (THR);(C) Transpiration reduction function (Ta/Tp); (D) Root water uptake as a function of time anddepth; and (E) Soil water content as a function of time and depth.

5Figure Supl-1:3: Soil water dynamics and RWU in the column lysimeter simulated using the
JF model: (A) Root water uptake distribution profiles; (B) Potential transpiration (Tp), actual
transpiration (Ta), compensated transpiration (Tcomp), and hydraulically redistributed water (THR);(C) Transpiration reduction function (Ta/Tp); (D) Root water uptake as a function of time anddepth; and (E) Soil water content as a function of time and depth.

6Figure Supl-1:4: Soil water dynamics and RWU in the column lysimeter simulated using the
FD model: (A) Root water uptake distribution profiles; (B) Potential transpiration (Tp), actual
transpiration (Ta), compensated transpiration (Tcomp), and hydraulically redistributed water (THR);(C) Transpiration reduction function (Ta/Tp); (D) Root water uptake as a function of time anddepth; and (E) Soil water content as a function of time and depth.

7

Water uptake by plants under heterogeneous soil moisture conditions: A
comprehensive numerical and experimental analysis

Anooja Thomas1 · Brijesh Kumar Yadav2 · Jiří Šimůnek3*

1

Department of Agricultural & Biological Engineering, University of Florida, Gainesville,
Florida, 32603, USA

2

Department of Hydrology, Indian Institute of Technology Roorkee, Roorkee 247667, India

3

Department of Environmental Sciences, University of California Riverside, Riverside, CA
92521, USA*

Corresponding Author - Jiří Šimůnek, Email: jiri.simunek@ucr.edu

Supplementary Information 2

Role of root parameters on CRWU and HR in the DJ model

Materials and methods
Root water uptake (RWU) based on the de Jong van Lier et al. (2008, 2012) (DJ) model
can be expressed as:

Si =

(

4 M s,i − M 0

(

)

)

a.Rm
R02 − a 2 Rm2 + 2 Rm2 + R02 ln
R0(= i M s ,i − M 0)(1)where M0 is the matric flux potential at the soil root interface [L2T-1], Ms is the soil matrix flux
potential [L2T-1], R0 is the root radius [L], Rm is the distance between roots [L], and a z is acoefficient that can be expressed as ai = R Rm,i where water content at a radial distance R is equal
to the average soil water content in the root zone. The half distance between roots can be expressedas Rm =

1

 * RLD. In equation (1), the matric flux potential at the soil-root interface ( M 0 ) is afunction of the pressure head at the root-soil interface ( h0 ). Here, M 0 and h0 are unknown, andthey can be derived from the continuity equation with a boundary condition for the soil waterequation within the root system as expressed below:Th0 = hl + a +L1

 ( M s − M 0 ) Rm2 ln
2 K root

R0
Rx

T= hl + a +  ( M s − M 0 )L1(2)

where,

= Rm2 lnR0
Rx

2 K root(3)

where Kroot is the root hydraulic conductivity [L T-1], L1 is the root-to-leaf pathway conductance,
hl is the leaf water potential [L], Rx is the xylem radius [L], and Ta is actual transpiration [L T-1].
From equations (1) and (2) it follows that RDL, Kroot, R0 and Rx play a vital role indetermining the degree of CRWU in the DJ model. Therefore, we performed a comparative
analysis to get the significance of these parameters in estimating CRWU.

Results
To understand the influence of RDL, Kroot, R0 and Rx on the degree of compensation, we
altered each of these parameters in Case 1 (see the main text). We adopted three different levels of
RLD as high (1.2 cm/cm3), medium (0.8 cm/cm3), and low (0.4 cm/cm3) to examine the influenceof varied RLD distributions on plant physiological activities. In the simulation with different RDLs,
the early emergence of water stress was observed for RLD of 0.4 cm/cm3 (on day 9). In comparison,water stress was delayed by 24 hours for RDL of 1.2 cm/cm3 (Fig. Supl-2:1A). The degree ofcompensation was 58.1, 60.5, and 62.9% for RLD of 1.2, 0.8, and 0.4 cm/cm3, respectively (Fig.
Supl-2:1B).

A

B

C

Figure Supl-2:1. Actual and compensated transpiration simulated using the DJ model fordifferent root length densities (RLD) of 1.2, 0.8, and 0.4 cm/cm3: (A) Relative transpiration, (B)Daily compensated transpiration during the simulation period, and (C) Cumulative actual andcompensated transpiration. The solid line indicates cumulative actual transpiration, and thedashed line represents cumulative compensated transpiration.

Similarly, the simulation with RLD of 1.2 cm/cm3 showed an early increase in Tcomp,maximum cumulative Tcomp (4.05 cm), and highest cumulative Ta (12.55 cm) (Fig. Supl 2:1C). On
the other hand, the simulation with RLD of 0.4 cm/cm3 showed a slow increase in Tcomp, and thena sudden decrease after reaching the peak. In this case, the maximum actual and compensatedcumulative transpiration were reduced to 11.79 cm and 3.44 cm, respectively.

A
B

C

Figure Supl 2:2. Actual and compensated transpiration simulated using the DJ model fordifferent combinations of root diameter (R0) and root xylem radium (Rx): (1) R0 =0.05 cm, Rx =0.02 cm, (2) R0 =0.1 cm, Rx = 0.4 cm, and (3) R0 =0.2 cm, Rx = 0.08 cm. (A) Relative transpiration,(B) Daily compensated transpiration during the simulation period, and (C) Cumulative actual andcompensated transpiration measured at different times. The solid line indicates cumulative actual
transpiration, and the dashed line represents cumulative compensated transpiration.

Similarly, we compared RWU under different values of R0 and Rx with RDL kept constant
at 0.4 cm/cm3. The simulations were performed with R0 = 0.05 cm and Rx = 0.02 cm (Case 1), R0= 0.1 cm and Rx = 0.04 cm (Case 2), and R0 = 0.2 cm and Rx = 0.08 cm (Case 3). Interestingly,
cumulative Ta and Tcomp remained similar in all three cases till day 7, showing that CRWU is
independent of the root diameter under the optimal soil water content (Figs. Supl 2:2 BC). As
water stress emerged, the degree of CRWU was higher in Case 3 with a large root diameter, andthis led to a 27-hour delay in the emergence of water stress as compared to Case 1 (Fig. Supl 2:2A).

Figure Supl-2:3. Actual and compensated transpiration simulated using the DJ model fordifferent root hydraulic conductivities Kroot of 0.000025, 0.00005, 0.0001, 0.0002, 0.0004, and
0.0016 cm/day. (A) Relative transpiration, (B) Daily compensated transpiration during thesimulation period, and (C) Cumulative actual and compensated transpiration measured at
different times. The solid line indicates cumulative actual transpiration, and the dashed line
represents cumulative compensated transpiration.

To study the influence of Kroot in the DJ model, the simulations were performed with six
different values for Kroot (0.000025, 0.00005, 0.0001, 0.0002, 0.0004, and 0.0016 cm/day).
Interestingly, for all values of Kroot, cumulative Ta and Tcomp were similar (12.67 ±0.1 cm and
4.03±0.03 cm, respectively) by the end of the simulation (Fig. Supl-2:3.C). However, the patternof Tcomp varied among models. In the simulations with higher values of Kroot (0.0004 and 0.0016
cm/day), Tcomp increased rapidly from the early simulation days, became constant from day 2 to

10, before it started decreasing slowly (Fig. Supl-2:3B). On the other hand, in the simulation witha lower value of Kroot (0.000025 cm/day), Tcomp slowly increased and achieved the highest peakvalue as compared to the other cases and rapidly decreased after that.

RWU and CRWU under dry-down conditions at different steady transpiration
rates
To estimate the relative contribution of CRWU under varying transpiration demands, we
simulated three scenarios with different transpiration demands: high (1.5 cm/day), medium (1cm/day), and low (0.75 cm/day). The simulations were performed for 12, 18, and 24 days,
respectively, such that the cumulative potential transpiration demand is 18 cm in all three cases.
In the simulations with different transpiration demands, Ta was found to vary among the fivemodels. Under the high transpiration demand, the highest of 14.3 cm was observed in the CR
model, while the uncompensated FD model recorded the lowest value of 10.1 cm. Cumulative Ta
in the DJ, NH, JF, and FD models was 12.2, 11.6, 11.3, and 10.1cm, respectively (Fig. Supl-2:4
C, T1). Variations in estimated Ta among models are due to different estimations of Tcomp (3.84,
5.72, 3.74, and 2.0 cm for the CR, DJ, NH, and JF models, respectively) (Fig. Supl-2:4 C, and T1).
Interestingly, the NH model showed CRWU as early as day 0, before the emergence of water
stress, while CRWU emerged on the 2nd day in the DJ model. On the other hand, the CR and JF
models showed a 3-day lag in the onset of CRWU followed by an abrupt increase in its rate (Fig.
Supl-2:4B). In addition, the highest degree of compensation was found to vary among the models,with the CR model having the highest peak value of 88.4%, while the JF model had the lowest of
34.8% (Fig. Supl-2:4B, and T1). The DJ and NH models showed peak values of 60.9% and 45.2%
of total Ta, respectively. Interestingly, the emergence of water stress in the DJ and NH models wascomparable (day 6.4). On the other hand, the JF model showed an early emergence of water stresson day 4.5, and water stress emerged quite early on day 1.75 in the uncompensated FD model (Fig.
Supl-2:4A).
A comparison of Ta for different transpiration demands shows that, in the mechanistic RWU
models, cumulative Ta was higher under a low transpiration demand. This corresponds with anincrease in Tcomp with a decrease in the transpiration demand in mechanistic models (Figs. Supl2:4CFI, and T1, T2, and T3). Among these models, CR showed the maximum increase incumulative Tcomp of 5.72, 5.58, and 6.13 cm for the high, medium, and low transpiration demands,
respectively. The degree of compensation was also found to be high (88.4%, 91.3%, and 94.3%,
respectively) in this model (Figs. Supl-2:4CFI, and T1, T2, and T3). It is also noted that there is adelay in the onset of the transpiration reduction in this model, with a decrease in the transpiration

demand, as compared to the other models (Figs. Supl-2:4ADG, and T1, T2, and T3). Similarly, inthe DJ model, cumulative Ta and Tcomp varied for different levels of transpiration demand.
Remarkably, in the empirical JF model, CRWU was independent of the transpiration demand and,
therefore, cumulative Ta and Tcomp remained the same (11.3 and 2 cm, respectively) for selectedtranspiration rates.

Figure Supl-2:4. Comparison of actual transpiration, a transpiration reduction, andcompensated root water uptake (CRWU) for different daily transpiration demands and different
root water uptake models: (A,B,C, T1) The transpiration demand of 1.5 cm/day and the simulation
period of 12 days. (D,E,F, T2) The transpiration demand of 1.0 cm/day and the simulation periodof 18 days. (G,H,I, T3) The transpiration demand of 0.75 cm/day and the simulation period of 24days. (A,D,G) Transpiration ratio. (B,E,H) The rate of compensated root water uptake. (C,F,I)
Cumulative actual and compensated transpiration. (T1, T2, T3) Summary of Ta, Tp, and Tcomp fordifferent transpiration demands. The solid line indicates cumulative actual transpiration, and thedashed line represents cumulative compensated transpiration.

Water uptake by plants under nonuniform soil moisture conditions: A comprehensive numerical andexperimental analysis

Supplementary Figures
Anooja Thomas1 · Brijesh Kumar Yadav2 · Jiří Šimůnek3*

Department of Agricultural & Biological Engineering, University of Florida, Gainesville, Florida, 32603, USA

1

2Department of Hydrology, Indian Institute of Technology Roorkee, Roorkee 247667, India
3Department of Environmental Sciences, University of California Riverside, Riverside, CA 92521, USA* Corresponding Author -Jiří Šimůnek, Email: jiri.simunek@ucr.edu

A

D

B

E
Dimension of
20*15 cm 20*15 cm
frame% of pixel
27.01%
22%
count
Root area

81.1cm^2 65.9 cm^2

Root Length 405.35cm 329.5 cm

S1

F

S2

S3

S4

SL

Tranpiration (cm/Hour)Cii

Actual transpiration
Potential transpiration

0.25
0.20
0.15

B

0.10

i

0.05
0.00
0

1

2

3 4 5 6Time (Days)

7

8

9

Figure S1. Column lysimeter experiment: (A) Lysimeter experiment setup, (B) Soil moisture recorded at different depths by soil moisture sensors. (C) Actual andpotential transpiration measured using the mass balance method at the lysimeter and the control. (D) Procedure for digital image processing and root length density(RDL) estimation: (i) original image, (ii) processed images of roots. (E) Steps for estimating root length considering the root diameter as 0.2 cm. (F) Root lengthdensity calculated from different compartments using the digit image processing.

A

D

RWU

RWU

B

C

G

E

Soil water content

F

J

RWU

H

Soil water content

I

RWU

cm/daySoil water content

cm3/cm3

K

Soil water content

L

Figure S2. A transpiration reduction function (Ta/Tp) (A, D, G, and J), root water uptake (B, E, H, and K), and soil water content (C, F, I, and L) simulatedusing the DJ (A-C), CR (D-F), NH (G-I), and JF (J-L) models for dry-down conditions with a constant transpiration demand of 1.5 cm/day (Case 1).

A

C

B

D

Figure S3. Soil water contents simulated using the DJ (A), CR (B), NH (C), and JF (D)models for a rainfall event on day 12 and a constant transpiration demand of 1.0 cm/day for
6 hours (Case 2).

A

B

Figure S4. Comparison of CRWU and HR simulated using the five RWU models for (A) free drainage (Case 3) and (B)groundwater table as a bottom boundary condition (Case 4). Solid lines indicate cumulative actual transpiration (Ta), dashedlines indicate transpiration due to CRWU (TComp), and dash-dot lines indicate cumulative hydraulically distributed water (THR).