HYDRUS
ROOT GROWTH MODULE
VERSION 1.02

Technical ManualbyAnne Hartmann1,2
andJirka Šimůnek2
July 2016
1

Technical University of Dresden, Germany
2
Department of Environmental Sciences
University of California Riverside
Riverside, CA, 92521, USA1

2

Abstract
Hartmann, A. and J. Šimůnek, HYDRUS Root Growth Module, Version 1.02, Hydrus Software
Series 5, Department of Environmental Sciences, University of California Riverside, Riverside,
California, USA, p. 37, 2016.
This report documents version 1 of the HYDRUS root growth module. The Root Growth module
was developed as a supplemental module of the HYDRUS software package (both Hydrus-1Dand HYDRUS (2D/3D), to model the root growth as a function of different environmental
stresses. The root growth model is based on the approach developed by Jones et al. (1991). The
model assumes that various environmental factors can influence the root development undersuboptimal conditions. These environmental factors are characterized by various growth stressfactors. Root growth and the development of root length density then depend on environmental
factors when the stress factor approach is used. This text provides a detailed description of theimplemented model, as well as several test examples demonstrating various features of thismodel.

3

DISCLAIMER
This report documents version 1 of the HYDRUS root growth module. The Root Growth module
was developed as a supplemental module of the HYDRUS software package (both Hydrus-1Dand HYDRUS (2D/3D), to model the root growth as a function of different environmental
stresses. The software has been verified against selected test cases. However, no warranty isgiven that the program is completely error-free. If you do encounter problems with the code, finderrors, or have suggestions for improvement, please contact one of the authors at
Anne Hartman
Email: Hartmann_Anne@gmx.de
Jirka Šimůnek
Tel/Fax: 1-951-827-7854
Email: jiri.simunek@ucr.edu

4Table of Contents
ABSTRACT .......................................................................................................................... 3
DISCLAIMER...................................................................................................................... 4
TABLE OF CONTENTS .................................................................................................... I
LIST OF FIGURES .......................................................................................................... III
LIST OF TABLES .............................................................................................................IV
IMPLEMENTATION OF INTERACTIONS BETWEEN PLANT ROOTS, SOIL
PROPERTIES, AND WATER FLOW CONDITIONS IN SOIL INTO HYDRUS-1D 1
1.
2.
3.
4.

5.
6.
7.
8.
9.

General Information ................................................................................................... 1
Description of the Rooting Pattern using the Root Length Density Functions.......... 2
Root Growth Simulation ............................................................................................ 3
Environmental Factors Affecting Root Growth ......................................................... 5
4.1. Static Factors ..................................................................................................... 5
4.2. Dynamic Factors ............................................................................................... 6
Actual Root Distribution ............................................................................................ 9
Calculation Steps ..................................................................................................... 11
Detailed Description of the Root.in File for HYDRUS-1D..................................... 12
Detailed Description of the Root.out File for HYDRUS-1D ................................... 14
A Demonstrative HYDRUS-1D Example ............................................................... 15

IMPLEMENTATION INTO HYDRUS-2D .................................................................... 21
10. Detailed Description of the Root.in File for HYDRUS-2D..................................... 22
10. A Demonstrative HYDRUS-2D Example ................................................................. 25
REFERENCES ................................................................................................................... 29i

ii

List of Figures
Figure 1.

Schematic illustration of the potential root length density distribution (left)
being modified due to various stress factors to the actual root length density
distribution (right). ....................................................................................................1

Figure 2.

Graphical representation of implemented root length density models. .....................2

Figure 3.

Scheme of the calculation procedure.......................................................................11

Figure 4.

Simulated potential and actual root length density distributions under drought
conditions. ...............................................................................................................15

Figure 5.

Simulated potential and actual root length density distributions under increased
drought conditions. ..................................................................................................16

Figure 6.

Simulated potential and actual root length density distributions under increased
drought conditions and when considering the influence of texture and bulk
density on the rooting depth. ...................................................................................16

Figure 7.

Simulated potential and actual root length density distributions when
considering the influence of texture and bulk density on the rooting depth andwith higher water contents. .....................................................................................17

Figure 8.

Simulated potential and actual root length density distributions when
additionally considering the influence of hydrotropism..........................................17

Figure 9.

Simulated potential and actual root length density distributions for a soil systemwith two different soil materials. The second material is embedded between
two layers of the same material. ..............................................................................18

Figure 10. Simulated potential and actual root length density distributions for a soil systemwith two different soil materials as in Figure 9. After reaching the maximum
growth stage, the root system starts to die...............................................................19
Figure 11. Results of the potential and actual root system development for different times(simulated by HYDRUS-2D) when irrigation is applied at the entire soil
surface. ....................................................................................................................26
Figure 12. Results of the potential and actual root system development for different times(simulated by HYDRUS-2D) when irrigation is applied in the top left corner. .....27iii

List of Tables
Table 1.

Root length density distribution models implemented in HYDRUS-1D (zr is thenormalized root depth). ...............................................................................................2

Table 2.

Stress factors influencing root growth. .......................................................................4

Table 3.

Description of the Root.in file for HYDRUS-1D. ....................................................12

Table 4.

Input parameter settings for the demonstrative HYDRUS-1D example. .................20

Table 5.

Description of the Root.in file for HYDRUS-2D .....................................................22

Table 6.

Input parameter settings for the demonstrative HYDRUS-2D example ..................25

iv

Implementation of Interactions Between Plant Roots, Soil
Properties, and Water Flow Conditions in Soil
into HYDRUS-1D
1. General Information
The standard version of HYDRUS-1D (Šimůnek et al., 2008) does not consider the feedback
between the root growth and conditions in the soil and the root growth is fully defined using
input parameters (Šimůnek and Hopmans, 2009). In the modified version of HYDRUS-1D
described in this text, the root growth and the roots spatial distribution is dynamically affected byvarious environmental factors such as soil water content or soil temperature.
Input parameters describing interactions between plant roots, soil properties, and water flow
conditions in soils required by a modified HYDRUS-1D code are provided using a new input file
Root.in. To use these new options in connection with the GUI of HYDRUS-1D, in the “RootGrowth Parameter” window select that the root depth should be specified “With Time-Variable
Boundary Conditions”.
The implemented approach is based on the root growth model of Jones et al. (1991). The model
assumes that various environmental factors influence the root development under suboptimal
conditions, which are characterized by various growth stress factors. Root growth and thedevelopment of root length density then depend on environmental factors when the stress factor
approach is used.
The calculation of the actual root length density distribution is based on the use of the potential(root distribution) shape functions. Such functions represent the potential root length density
distribution under optimal development conditions when no restrictions on the root growthoccur. Due to sub-optimal environmental conditions, a potential root distribution can be altered
to an actual root distribution. Figure 1 shows a possible transformation of the potential root
length density distribution to an actual distribution.

Figure 1. Schematic illustration of the potential root length density distribution (left) being
modified due to various stress factors to the actual root length density distribution (right).
12. Description of the Rooting Pattern using the Root Length Density
Functions
For describing the potential root length density distribution the user can choose between fivedifferent root length density distribution functions (Hao, 2005; Jones et al., 1991; and Vrugt etal., 2001). Table 1 lists the implemented models (equations) of relative root length density
distribution functions and Figure 2 shows their graphical representations. The root length density
distribution model proposed by Vrugt et al. (2001) is the most flexible model. Users need to
specify the parameters pz and z* in the Root.in file, which are there referred to as PZ and Zv,
respectively. Functions shown in Figure 2 (4a and 4b) were obtained by different parametersettings in the root length density distribution model of Vrugt et al. (2001).
Table 1. Root length density distribution models implemented in HYDRUS-1D(zr is the normalized root depth).
Model

b(zr)

Reference

1

2.938-2.462zr

modified after
Zuo et al. (2004)

2

4.522(1 − z r ) 5.228 ⋅ e (9.644 z r )3

2.21 − 3.72 z r + 3.46 ⋅ ( z r ) 2 − 1.87( z r ) 24
5[1 − z r ]e
(1 −

−

2.426

Wu et al. (1999)
Vrugt et al. (2001)Pzz *− z r
zm

Jones et al. (1991)

zr 3
)
3

Root length density distributions calculated by these models represent the potential root lengthdensity distribution pattern which would be obtained under optimal conditions when norestrictions of root growth, such as hydrotropism and root senescence were considered. All
models are expressed using a normalized root depth, which is scaled to get the actual rooting
depth.

Figure 2. Graphical representation of implemented root length density models.
2

3. Root Growth Simulation
Users can choose between three different approaches to describe the potential root growth. In
addition to the approach currently available in HYDRUS-1D (using the time-dependent logistic
growth function; the first approach), the root growth can be simulated either as a time-dependent
process (the second approach) or as a thermal time dependent process (the third approach) using
the sinusoidal growth function. When the root growth is considered to be dependent either ontime or thermal time, the RGR parameter in the Root.in file should be set to 1 or 2, respectively.
In both the first and second approach, root growth depends on time. When the second approachis used, the following equation is used to calculate the potential increase (ddi) of the rooting
depth (Hao, 2005):
 

 
t
=
ddi  RD  0.5 + 0.5 ⋅ sin  3.03 ⋅ P − 1.47    − Z jtM   (1)When this equation is used, the maximum rooting depth (RD), and the time to maturity (tM) haveto be provided. Zj represents the potential rooting depth at the previous time step.
When the second approach is used, users can specify whether planting takes place during thesimulated period, has already occurred at a specific time before the start of the simulation, or
occurs at the beginning of the simulation. Users have to specify the time after planting (tP) andhow much time to maturity of the crop (tM) is left at the start of the simulation. If planting takes
place after the start of the simulation, the parameter tP should be set equal to 0 and the additionalparameter ∆tP (time to planting) has to be set to the time when planting takes place after the startof the simulation. The tM parameter then has to be set to the remaining time to the crop maturity
at the time of planting. If planting takes place at the beginning of the simulation or has alreadytook place before that, the ∆tP parameter has to be set equal to 0 and the initial rooting depth has
to be specified using the Dp parameter (the planting depth). The units of the parameters referring
to a time have to be equal to units used in HYDRUS.
When the root growth is considered to be dependent on thermal time, the RGR parameter has tobe set to 2. The following equation is used to calculate the potential increase in root growth(Ireson, 2009):
dd=
TG ⋅ Dtti(2)where TG is an empirical factor, which can be changed by the user, and Dtt [°C.day] represents asingle day thermal time, which is calculated using the following equation:
Dtt =min[Tmax − Tmin ; max(0; Tc − Tmin )]3(3)

where Tcan represents the mean daily canopy temperature, which has to be provided by users as
an additional boundary condition. These values are specified in an additional input file Temp.In.
Users have to provide the mean temperature for each day of the calculation.
Tmax and Tmin represent the maximum and minimum temperatures for the development of aparticular crop. These parameter values have to be provided by users, together with the upper
limit of the cumulated thermal time (TTmax) when root growth stops.
The actual increase (dr) of the rooting depth is calculated by reducing the potential increase in
the rooting depth due to stress factors (SF):d=ddi ⋅ min( SF )r

(4)Stress factors influencing the vertical penetration of roots according to Jones et al. (1991) arelisted in Table 2. The stress factors range from 0 (no growth) to 1 (no stress).
Table 2. Stress factors influencing root growth.
Parameter

Stress Factor

ST

Temperature stress

SCa

Calcium deficiency

SAl

Aluminum toxicity

SSt

Soil strength

SAe

Aeration stress

SCF

Excessive coarse fragments

44. Environmental Factors Affecting Root Growth
The user can define whether a particular stress factor is considered during the simulation or not.
According to Jones et al. (1991), stress factors can be divided into static and dynamic stressfactors. Stress factors due to aluminum toxicity, calcium deficiency, and coarse fragments are
considered to be static. Stress factors due to temperature stress and/or soil strength (which
depends on water content) are considered to be dynamic.
4.1. Static Factors
When the aluminum stress is to be considered, the AYN parameter in the Root.in file has to be
set to 1. To consider the stress factor due to aluminum toxicity, the threshold value of aluminum
saturation at which root growth is first affected (AlA) and the value at which it is completely
inhibited (AlX) have to be provided by the user. The user also has to specify the amount of KClextractable Al (AlE) and the value of the sum of NH4OAC-extracted bases (sum of bases, SMB).
According to Jones et al (1991), the aluminum saturation (AlS) is calculated first using the cationexchange capacity (CEC):= SMB + AlE
CEC
=
Als

AlE
⋅100
CEC

(5)

The stress factor due to aluminum saturation is then calculated as:=
S Al

Al X − AlS
Al X − Al A

Al A ≥ AlS ≥ Al X

(6)

When the calcium stress is to be considered, the CYN parameter in the Root.in file has to be set
to 1. With regards to the stress due to calcium deficiency, the user has to define threshold values,
at which root growth begins to be affected (CaA) and completely inhibited (CaX). The amount of
exchangeable calcium (Ca) has to be provided as well. According to Jones et al. (1991), thestress factor is calculated using the calcium saturation (CaS):
=
CaS

Ca
⋅100
CEC + 10−20

CaS − Ca X=SCa
Ca A − Ca X

(7)

Caa ≥ CaS ≥ Ca X

Jones et al. (1991) states that coarse fragments reduce the volumetric water holding capacity andnutrient availability approximately in proportion to their volumetric fraction. To consider the5effect of coarse fragments on root growth, the user has to specify the volume fraction of particles
bigger than 2 mm (ROK) for each material. The stress factor is then calculated as:
SCF= 1.0 − ROK(8)

The influence of coarse fragments can be neglected by setting the value of FYN to 0.
4.2. Dynamic Factors
According to Jones et al. (1991), the soil strength stress factor is determined using the bulk
density, soil texture, and the water content. The bulk density above which root growth isnegligible at the optimum soil water content (BDX) and the bulk density below which root growthis negligible at the optimum soil water content (BDO) is calculated first using the weight percent
of sand (Sand) for each material:
BDX =1.6 + 0.004 ⋅ Sand
1.1 + 0.005 ⋅ Sand
BDO =

(9)

A factor for the interacting effects of texture and bulk density of the moist soil is then calculated
as follows:=
S BD 1=S BD

BDX − BD
BDX − BDO=S BD 0BD < BDO
BDO ≥ BD ≥ BDX(10)BD > BDXThe bulk density (BD) has to be thus provided by the user for each material. The effect of thebulk density can be neglected by setting the BDYN parameter to 0.
Soil water contents lower than the soil water content, for which SBD was determined, will
increase the soil strength and thereby reduce rooting. To consider the influence of the watercontent on soil strength and root growth, the parameter describing the fractional water content(θf) of each soil layer is calculated and used to evaluate the soil strength stress factor (SS):
=
θf 0

θ −θL
θU − θ L
=
θf 1

=
θf

θ < θLθU ≥ θ ≥ θ L
θ > θUSS =S BD ⋅ sin(1.57 ⋅ θ f )

6

(11)

where θ is the water content at each time step, θL is a lower limit of the plant-extractable soil
water for the fine soil fraction, and θU is a drained upper limit of the soil water for the fine soil
fraction. In our implementation, instead of the water content, users have to define the soil
tension, which is then used to calculate the corresponding water content using the soil hydraulicproperties.
To consider the effect of poor aeration in highly saturated soils, the model calculates a criticalwater-filled porosity (θeC) (critical effective saturation) from the soil texture:θ eC =
0.4 + 0.004 ⋅ Clay
Clay =
100 − Sand − Silt

(12)

where Sand, Silt, and Clay are weight percentages of the sand, silt, and clay soil fractions. The
user has to provide information about the percentages by weight of sand (Sand) and silt (Silt).
To define a user-specified critical water filled porosity θeC, the parameter CW has to be set to 1
(otherwise the value has to be 0) and the defined value has to be assigned to the parameter
CWFP in the input file. The aeration stress factor (SAe) is then calculated as:
S Ae = S FT + (1 − θ e ) ⋅1 − S FT
1 − θ eC(13)

θ e < θ eC=
S Ae 1

where θe is the water-filled porosity (effective saturation), which is defined as the ratio of thewater content in each node at each time step and the saturated water content, θs, which isprovided as a parameter of the soil hydraulic properties for each material. SFT is a parameter
defining the fraction of normal root growth when the pore space is saturated (0-1) and has to be
set by the user. Setting SFT equal to 1 means that flooding has no effect on root growth. Setting
SFT equal to 0 means that there is no root growth in saturated soils. The value of SFT therefore
depends on the crop type.
To consider the stress due to soil temperature the user can choose between two approaches. The
first approach considers only the stress due to low temperature. The second approach also
considers for stress due to high soil temperatures.
When the first approach of Jones et al. (1991) is used, the user has to specify a minimum
temperature when the root growth starts (Tmin) and the optimum temperature for root growth(TOpt). The temperature stress factor is then calculated as:
ST 0=

T < Tmin
T − Tmin 
sin 1.57 ⋅ST =TOpt − Tmin 

ST 1
=

7

T ∈ (Tmin , TOpt )T > TOpt(14)

where T is the soil temperature calculated by HYDRUS-1D.
When using the second approach the user has to also specify a value of the maximum
temperature for root growth (Tc) and the value of the shape coefficient ct. The temperature stressfactor is then calculated using the following equation (Yin et al., 1995; Yin and van Laar, 2005):
TOpt −Tmin






T (t ) − Tmin TC −TOpt  Tc − T (t )ST (t , T ) =⋅
 T − T   T − T 
c
Opt


 Opt min 




S=
0
TC < T (t ) < Tmin
T (t , T )

ct

(15)

This equation leads to a typical bell shaped temperature response curve. If there is no data
available to determine the fitting parameter ct, its value can be set to 1 (Yan and Hunt, 1999; Yinand van Laar, 2005).

8

5. Actual Root Distribution
The actual root depth is used to calculate the potential pattern of the root length density
distribution using the root length density distribution models. The potential increase in therooting depth, calculated as a function of either time or thermal time, is reduced using theminimum of the six stress factors, producing the actual increase in the rooting depth. In the onedimensional model (i.e., HYDRUS-1D), the stress factor values in the last node containing roots
are considered for the reduction.
A potential increase in the root length distribution (RLDgp) is calculated as the difference
between the root length distribution at the current and previous time steps. An increase in theroot length density in each node can be reduced or increased due to root senescence orhydrotropism, respectively.
The root senescence (Sen) is calculated according to Jones et al. (1991):
Sen= rated ⋅ RLDgp ⋅ [1 + max(1 − θ f ,1 − S Ae )](16)

where rated is the scaling factor defining the influence of root senescence (0-1). This approachassumes that root senescence can be increased due to low water availability or poor aeration.
The user can also consider the phenomena of hydrotropism. When hydrotropism is to beconsidered during the simulation, the HYD value has to be set to 1 (otherwise to 0). In the onedimensional approach, the hydrotropism can only be used to increase the root length density
distribution in wet parts of the root zone. Within the current implementation, this phenomenon isevaluated as a function of the fractional water content (θf, eq. (11)). An increase of the potential
root length density due to hydrotropism (HydTr) is calculated as follows:
HydTr =rateg ⋅ RLDgp ⋅ θ 3f

(17)

where rateg is a scaling factor (0-1) defined by the user. The potential increase in the root lengthdensity distribution (RLDgp) is multiplied by the third power of θf, which gives nodes with a θfvalue close to 1 a higher weight than to those with a value close to 0. A value of θf close to 1
indicates a high water availability. When the scaling factor rateg is set to 1, in nodes with θf closeof 1, the same amount of the potential increase in the root length density is added due tohydrotropism. By defining the value of rateg, the influence of hydrotropism can be adjusted
manually.
The actual root length density distribution (RLDbeta) is calculated as:
RLD=( RLDgp ) − Sen + HydTr
ga
RLD=
RLDbeta (t − 1) + RLDga
beta (t )9(18)where RLDga represents an actual increase in the root length density, and Sen and HydTr describe
a decrease and an increase in the root length density due to root senescence and hydrotropism,
respectively.
The death of roots after reaching maturity can be calculated in two different ways when thetime-dependent root growth is considered. By setting the parameter RSC to 1, the user can
specify cumulative time (tRD), at which the roots are considered to be dead. Between this point
and time when plants reach maturity, the roots are dying at a constant death rate:
 t − tM =
Sen RLDD ⋅  t RD − tM 

3

(19)

where RLDD is the actual distribution of the root length density at maturity (tM).
By setting RSC to 2, the death of roots after reaching maturity is calculated using the rootsenescence approach:
Sen = (ti − ti −1 ) ⋅ rateDeath ⋅ RLDD ⋅ [1 + max(1 − θ f ,1 − S Ae )](20)

The Sen value is added at each time step after reaching maturity to values at previous time steps.
To calculate the actual root length density distribution at each time step, the sum is subtracted
from RLDD. When the root growth is considered to be dependent on thermal time, only thesecond approach is applicable.

106. Calculation Steps
Figure 3 summarizes the calculation procedure of the new modeling approach of root growth.
The static stress factors are calculated just one time at the beginning of the simulation. The
dynamic stress factors are updated at each time step. In the last but one step (Fig. 3), theaccumulation of roots in soil layers with higher water availability is considered. This can lead toa further increase in the actual increase due to hydrotropism (see hydrotropism).

Figure 3. Scheme of the calculation procedure.

11

7. Detailed Description of the Root.in File for HYDRUS-1D
Table 3 below gives a detailed description of the Root.in file and Table 5 provides an example ofthis file for the demonstrative example described in the text below.
Table 3. Description of the Root.in file for HYDRUS-1D.
RecordType Variable

1-8

-

9
9
9
9
9
9
9
9

Integer BDYN
Integer FYN
Integer TYN
Integer AYN
Integer CYN
Integer SYN
Integer AEYN
Integer RSYN

=1: the bulk density stress factor is considered; =0: is not=1: the coarse fragment stress factor is considered; =0: is not=1: the temperature stress factor is considered; =0: is not=1: the aluminum toxicity stress factor is considered; =0: is not=1: the calcium deficiency stress factor is considered; =0: is not=1: the soil strength stress factor is considered; =0: is not=1: the aeration stress factor is considered; =0: is not=1: root senescence is considered; =0: is not

10-13

-

Comment lines.

14

Integer RDM

14

Integer HYD

Root distribution function=1: Zuo et al. (2004)=2: other=3: Wu et al. (1999)=4: Vrugt et al. (2001)=5: Jones et al. (1991)=1: hydrotropism is considered; =0: is not

15-18

-

-

Comment lines.

19
19

Real
Real

PZ
Zv

Parameter of the Vrugt function, has to be specified if RDM=4
Parameter of the Vrugt function, has to be specified if RDM=4-

Comment lines.

20-24 --

Description

-

25
25
25
25
25

Real RDX
Real PD
Real TBS
Integer TOP
Integer TA

25
25
25
25
25

Real
Real
Real
Real
Real

25

Integer CW

CAA
CAX
ALA
ALX
SFT

Comment lines.

Maximum rooting depth
Planting depth (dp)Base temperature for root growth (Tmin) (°C)
Optimum temperature for root growth (Topt) (°C)
=0: temperature stress calculated according to Jones et al. (1991) (eq. 11)=1: temperature stress calculated using the bell shaped function (eq. 15)
Calcium saturation (%) below which root growth is reduced (CaA)
Calcium saturation (%) below which root growth is negligible (CaX)
Aluminum saturation (%) below which root growth is unaffected (AlA)
Aluminum saturation (%) above which root growth is negligible (AlX)
Fraction of normal root growth when the pore space is saturated (0-1) (SFT)=0: no growth in saturated soil
=1: no effect of flooding on root growth=0: critical water filled porosity is calculated via particle distribution (eq. 12)=1: critical water filled porosity is set to CWFP

12

25

Real

CWFP

User defined critical water filled porosity

26

-

-

Comment line.

27
27

Real
Real

TC
Ct

Ceiling temperature for the bell shaped temperature stress approach (Tc)
Parameter for flexibility of the bell shaped temperature response curve (ct)
=1: if no data for fitting this parameter is available

28-31

-

-

Comment lines.

32
32
32
32
32
32
32
32

Real
Real
Real
Real
Real
Real
Real
Real

SAN
SIL
BD
ROK
SMB
EAL
CA
ULh

32

Real

LLh

Sand content of the soil (%), measured as a percent by weight
Silt content of the soil (%), measured as a percent by weight
Bulk density of the fine earth fraction (mg/m³)
Coarse fragments as a fraction of soil volume (0-1)
Sum of bases (cmol/kg); set as default when AYN and CYN=0
Extractable aluminum (cmol/kg); set as default when AYN=0 (AlE)
Exchangeable calcium (cmol/kg); set as default when CYN=0
Upper limit of the pressure head for the plant extractable soil water (θU) for thefine earth fraction (enter pressure head as a positive value)
Lower limit of the pressure head for the plant extractable soil water (θL) for
fine earth fraction (enter pressure head as a positive value)

32-40

-

-

41
41
41

Integer RGR
Real drate
Real grate=1: time dependent root growth; =0: root growth depends on thermal time
Scaling factor to define the influence of root senescence (rated) (0-1)
Scaling factor to define the influence of hydrotropism (rateg) (0-1)

42-49

-

Comment lines.

50

Integer TDT-

Comment lines.

=1: sine function for time dependent root growth is used; =2: Verhulst-Pearllogistic growth function is used
Real DAP
Time after planting (for TDT=1) (tp)Real DTM
Time to maturity (for TDT=1) (tM)Real DTP
Time to planting (for TDT=1) (∆tp)
Real DRD
Time to death of the root system (for TDT=1)
Real tRMin
Initial root growth time (for TDT=2)
Real tRHarv Harvest time (for TDT=2)
Real tRPeriod Time period (for TDT=2)
Integer ir
1: root growth parameter in Verhulst-Pearl logistic growth function is specified
by users, 0: it is calculated using HYDRUS-1D standard code
Real rvalue of root growth parameter in Verhulst-Pearl logistic growth function when
ir=1

50
50
50
50
50
50
50
50
50
51-52

-

-

Comment lines.

53

Integer RSC=1: roots are dying until DRD is reached; =0: root growth ends at ∆tM androoting depth remains constant

54-58

-

-

Comment lines.

59

Real

TDM

59
59

Real
Real
59 Real

TDB
TTH
TG

Maximum temperature for the development of a particular crop, when RGR=0(TMax)
Basal temperature for the development of a particular crop, when RGR=0 (TMin)
Thermal time threshold for the root development, when RGR=0 (ttM)
Empirical growth factor, when RGR=013

8. Detailed Description of the Root.out File for HYDRUS-1D
Table 4 below gives a detailed description of the Root.out file. The Root.out file provides profile
information about the root length density and stress factors at different points in time.

Table 4. Description of the Root.out file for HYDRUS-1D.
Variable

Description

RLD

Root length density

SCa
SAl
SBD
SCF
SST
SAE
ST

Calcium deficiency stress factor
Aluminum toxicity stress factor
Bulk density stress factor
Coarse fragments stress factor
Soil strength stress factor
aeration stress factor
temperature stress factor

14

9. A Demonstrative HYDRUS-1D Example
Figure 4 shows the simulation results for the development of the root system under drought
conditions with the parameter setting specified in Table 5. The soil profile is homogeneousconsisting of the first material described in Table 5. The soil hydraulic parameters were estimatedusing the Rosetta module of HYDRUS-1D from the textural information. The soil consists ofapproximately 50 % silt, 40 % clay, 10 % sand. The atmospheric boundary conditions is used at
the soil surface. The potential evaporation and transpiration rates increase stepwise at the
beginning of the simulation and remain at a constant rate during the rest of the simulation.
Irrigation takes place every few days. A free drainage boundary condition was used at the bottomof the soil profile.

Figure 4. Simulated potential and actual root length density distributions
under drought conditions.

Figure 5 shows the results for the same settings as above, but with an increase in water extraction
due to a higher transpiration rate. Additionally, irrigation values were reduced to produce
stronger drought conditions. The results show that due to reduced water availability, the actual
development of the root system is reduced. The root length density is reduced in soil depths,
where the soil gets very dry. An increase in the potential transpiration rate leads to a greater
decrease in the actual root length density distribution due to an increased stress.

15

Figure 5. Simulated potential and actual root length density distributions
under increased drought conditions.
The results also show that the simulated rooting depth is reduced compared with to the specified
potential maximum rooting depth (RDX=120 cm) defined in the input file. Note that the potential
root length density distributions shown in the graphs already consider the reduced rooting depth
due to stress factors. The reduction in the rooting depth is the result of the soil strength factor(SYN=1) and the aeration stress factor (AEYN=1). In this case, no further stress factors wereconsidered, which could lead to a reduction in the rooting depth.

Figure 6. Simulated potential and actual root length density distributions under increased drought
conditions and when considering the influence of texture and bulk density on the rooting depth.
16Figure 6 shows the results for the same settings, except that the effects of texture and bulk
density of moist soil (BDYN=1) were considered. The results show a strong reduction in therooting depth due to the considered effects of the bulk density. Together with the low water
availability, these settings produced an undeveloped root system.
Figure 7 shows the results for the same settings, except with higher water contents (and thus
more water being available to plant roots), which produced a root system with a greatly reduced
rooting depth, but with a higher root length density compared to that shown in Figure 6.

Figure 7. Simulated potential and actual root length density distributions when considering theinfluence of texture and bulk density on the rooting depth and with higher water contents.

Figure 8. Simulated potential and actual root length density distributions when additionallyconsidering the influence of hydrotropism.
17

Figure 8 shows simulated results when hydrotropism was considered (HYD=1) together with anincrease in water availability due to a higher irrigation amount and frequency and a reduced
potential transpiration. The results show an increase in the root length density in soil depth withmore available water.
Figure 9 shows simulated results for a root system with the same settings as before, but withdifferent soil horizons. The second material described in Table 5 is located between 20 and 50
cm. Although the hydraulic conductivities of the two soil materials were almost the same, thesecond material consists of a higher amount of silt and sand and less clay compared to thesurrounding material. The results show that due to different properties of the additional soil
horizon, which affects water availability and oxygen supply, the development of the root system
is different in this soil horizon. Note that the absolute values of the root length density are notimportant for the distribution of the root water uptake throughout the soil profile, since the root
length density function is always normalized.

Figure 9. Simulated potential and actual root length density distributions for a soil system withtwo different soil materials. The second material is embedded between two layers of the samematerial.
Figure 10 shows simulations results for the same conditions as in Figure 9, except that thesimulation was extended to 200 days. After reaching maturity after 90 days, the root systemstarted dying because of root senescence.

18

Figure 10. Simulated potential and actual root length density distributions for a soil system withtwo different soil materials as in Figure 9. After reaching the maximum growth stage, the rootsystem starts to die.

19

Table 5. Input parameter settings for the demonstrative HYDRUS-1D example.
! Input file for advanced root zone calculation! To use this option set the root depth specification in the GUI to Time-Variable Boundary! Conditions. Set the iRootDepthEntry in the Selctor.In-File to 3.
****! Choose which stress factors should be considered for limiting root development! by setting the following values to 0 (no consideration) or 1 (consideration)
****
BDYN
FYN
TYN
AYN
CYN
SYN
AEYN
RSYN
0
0
0
0
0
1
1
1
****
! Specify which root density distribution model should be used and whether you want to regardhydrotropism****
RDM HYD
20****! When RDM = 4; Specify parameter for Vrugt-function:
****
PZ
Zv
6
0
****
! Specify parameters needed for describing root development. Keep parameter values at default
when no! Consideration of these stress factor is chosen
****
RDX
PD
TBS
TOP
TA
CAA
CAX
ALA
ALX
SFT
CW
CWFP
120
0.001
19.0
21.0
0
15.0
0
43.0
90.0
0
1
0.9
TC
Ct
30
1
****
! Additional material information, set as many as materials
****
SAN
SIL
BD
ROK SMB EAL
CA
ULh
LLh
11.6 50.4 1.53 0
10.1 0
18.7
325
8000
23.5 63.8 1.29 0
10.1 0
5.60
325
8000
****
___________________________________________________________________________________________________________________________ Root Growth__________________________________________________________________________________________________________________________________________****! Specify which type of root growth should be used: time dependent: 1, thermal-time dependent: 2
****
RGR
drate
grate
1
0.1
1
****
! When RGR = 1, specify the number of days after planting and how many days to maturity of! the crop are left at the start of the simulation. If the planting takes place after the! start of the simulation set DAP to 0 and specify the days to planting at the start of the! simulation (DTP), specify then the days to maturity of the crop upon the time of planting.
! If simulation starts with planting or the planting already took place, then set DTP to 0.
****
TDT
DAP
DTM
DTP
DRD
tRMin
tRHarvtRPeriod
ir
r
1
0
90
0
120
0
90
365
1
0.366
****
RSC
2
****
! When RGR = 2, specify the maximum and minimum temperature for development for the particular! crop in °C, set cumulative thermal time, at which root growth stops
****
TDM
TDB
TTH
TG
34.0
1.0
1000 0.02__________________________________________________________________________________________

20

Implementation into HYDRUS-2D
The above-described stress factor approach was also implemented into the HYDRUS-2D code.
At present, only the time-dependent growth functions are used to calculate a potential increase of
the rooting depth. The thermal-time-dependent root growth approach is not yet implemented.
Only the two-dimensional root distribution function of Vrugt et al. (2001) is used to describe thepotential two-dimensional root length density distribution.
The calculation of the actual increase in the rooting depth differs in the two-dimensional modelfrom the one in the one-dimensional model. In the two-dimensional code, the minimum stressfactors in all nodes containing roots are averaged to give an average stress factor for the wholeroot system. This average stress factor is used to reduce the potential increase in the rm and zm
parameters between two time steps. These parameters describe the maximum rooting lengths in
the radial and vertical directions.
No attempts have been made to implement hydrotropism into the 2D code. The death of the rootsystem after reaching the maximum growth stage is calculated by using the second approachdescribed for the 1D model.

21

10.Detailed Description of the Root.in File for HYDRUS-2D
Table 6 below gives a detailed description of the Root.in file and Table 7 provides an example ofthis file for the demonstrative example described in the text below.

Table 6. Description of the Root.in file for HYDRUS-2D.

Record Type

Variable Description

1-2

-

-

3
3
3
3
3

Logical lHoriz
The Vrugt function is used also for horizontal distribution
Logical lRootGrowth The rooting depth (and the horizontal extent of the root zone) is time
variable, described using Verhulst-Pearl logistic growth function
Integer nPlant Number of plants
Integer lRootEF The new root growth approach is used
Logical lrDeath The death of roots after reaching maturity is calculated.

4

-

-

Comment line

5
5
5

Real
Real
Real

rZm
rZ0
rA

The maximum rooting lengths in the z- direction [L]The depth of the maximum uptake intensity [L]The empirical factor pz

Comment lines.

The following two lines are given only when lHoriz = .true.
6--

Comment line

7
7
7
7

Real
Real
Real
Real

rRm
The maximum rooting lengths in the x- direction [L]rR0
The radius of the maximum uptake intensity [L]rB
The empirical factor px
rCenter(nPlant) x-coordinate of the center in the horizontal direction (for nPlants).
The following six lines are given only when lRootGrowth = .true.

8

-

-

Comment line

9

Integer iRFak

9
9
9
9

Real
Real
Real
Real

Method to calculate the root growth factor, r.
= 0; the root growth factor is calculated from given data [xRMed, tRMed].
= 1; the root growth factor is calculated based on the assumption that 50% of
the rooting depth, (xRMax+xRMin)/2., is reached at the midpoint of thegrowing season, (tRMin+tRHarv)/2.
tRMin
Initial time of the root growth period [T].
tRMed Time of known rooting depth (set equal to zero if iRFak=1) [T]tRHarv Time at the end of the root water uptake period [T]tRPeriod Time period at which the growth function repeat itself.

10

-

-

Comment line

11

Real

rZMin

11

Real

rZMed

Initial value of the rooting depth at the beginning of the growth period(recommended value = 1 cm) [L]
Value of known rooting depth (set equal to zero if iRFak=1) [L]

22

11

Real

rZMax

Maximum rooting depth, which may be reached at infinite time [L]The following two lines are given only when lHoriz = .true.

12

-

-

Comment line

13

Real

rRMin

13

Real

rRMax

Initial value of the rooting radius at the beginning of the growth period(recommended value = 1 cm) [L].
Maximum rooting radius, which may be reached at infinite time [L].

14

-

-

Comment line

15
15
15
15
15
15
15
15

Integer BDYN
Integer FYN
Integer TYN
Integer AYN
Integer CYN
Integer SYN
Integer AEYN
Integer RSYN

=1: the bulk density stress factor is considered; =0: is not=1: the coarse fragment stress factor is considered; =0: is not=1: the temperature stress factor is considered; =0: is not=1: the aluminum toxicity stress factor is considered; =0: is not=1: the calcium deficiency stress factor is considered; =0: is not=1: the soil strength stress factor is considered; =0: is not=1: the aeration stress factor is considered; =0: is not=1: root senescence is considered; =0: is not

16

-

-

Comment line

17
17
17
17
17
17
17

Real
Real
Real
Real
Real
Real
Real

TBS
TOP
CAA
CAX
ALA
ALX
SFT

17

Real

CW

17
17

Real
Real

CWFP
ULh

17

Real

LLh

Base temperature for root growth (Tmin) (°C)
Optimum temperature for root growth (Topt) (°C)
Calcium saturation (%) below which root growth is reduced (CaA)
Calcium saturation (%) below which root growth is negligible (CaX)
Aluminum saturation (%) below which root growth is unaffected (AlA)
Aluminum saturation (%) above which root growth is negligible (AlX)
Fraction of normal root growth when the pore space is saturated (0-1) (SFT)=0: no growth in saturated soil
=1: no effect of flooding on root growth=0: critical water filled porosity is calculated via particle distribution (eq. 12)=1: critical water filled porosity is set to CWFP
User defined critical water filled porosity
Upper limit of the pressure head for the plant extractable soil water (θU) for thefine earth fraction (enter pressure head as a positive value)
Lower limit of the pressure head for plant extractable soil water (θL) for fineearth fraction (enter pressure head as a positive value)

18

-

-

Comment line

19
19
19
19
19
19
19

Real
Real
Real
Real
Real
Real
Real

SAN
SIL
BD
ROK
SMB
EAL
CA

Sand content of the soil (%), measured as a percent by weight
Silt content of the soil (%), measured as a percent by weight
Bulk density of the fine earth fraction (mg/m³)
Coarse fragments as fraction of soil volume (0-1)
Sum of bases (cmol/kg); set as default when AYN and CYN=0
Extractable aluminum (cmol/kg); set as default when AYN=0
Exchangeable calcium (cmol/kg) ; set as default when CYN=0

20

-

-

Comment line

21

Real

drate

Scaling factor to define the influence of root senescence (rated) (0-1)

22

-

-

Comment line

23

Integer TA=0: temperature stress calculated according to Jones et al. (1991)=1: temperature stress calculated with the bell shaped function

23

23
23

Real
Real

TC
iCt

Ceiling temperature for the bell shaped temperature stress approach (Tc)
Parameter for flexibility of the bell shaped temperature response curve (ct)
=1: if no data for fitting this parameter is available

24

-

-

Comment line

24

Integer TDT

24
24

Real Tm
Integer ir

24

Real

r

=1: Verhulst-Pearl logistic growth for time dependent root growth is used;=2: sine function is used (iTDT)Time to maturity (for TDT=2) (tM)
=1: root growth parameter in the Verhulst-Pearl logistic growth function is
specified by users,=0: it is calculated using HYDRUS-1D standard code (iRGR)
value of root growth parameter in the Verhulst-Pearl logistic growth function
when ir=1 (RGR)

24

10. A Demonstrative HYDRUS-2D Example
Figure 11 shows the results of the potential and actual root system development simulated by
HYDRUS-2D for the parameter settings specified in Table 7. The considered soil ishomogeneous consisting of approximately 50 % sand, 30 % clay, and 20 % silt. The soil
hydraulic parameters were estimated using the Rosetta module of HYDRUS-2D and the soil
textural information given in Table 7. The atmospheric boundary condition was defined using theconstant potential evaporation and transpiration rates of 0.1 mm/d and 5 mm/d, respectively,
throughout the whole simulation time. Irrigation was considered to take place on days 1, 6, 8, 17,
and 42, with the amount of 10 mm each day on the entire soil surface. A free drainage boundary
condition was used at the bottom of the soil profile.
Only one plant in the middle of the domain was considered. The roots were considered to growfor 45 days. After reaching the maximum growth stage, the root system was considered to startdying due to root senescence. The reduction of the rooting depth is a result of the influence of thesoil strength factor (SYN=1), the aeration stress factor (AEYN=1), and the effects of texture andbulk density of moist soil (BDYN=1).

Table 7. Input parameter settings for the demonstrative HYDRUS-2D example.
*** Root Distribution Function Input *********************************************
Horizontal distribution
RootGrowth nPlant lRootEF lrDeath
t
t
1
t
t
rZm
rZ0
rA
100
20
1
rXm
rX0
rB
rCenterrCenter
30
0
1
25
iRFak
tRMin
tRMed
tRHarvtRPeriod
1
5
0
45
60
rZMin
rZMed
rZMax
5
0
80
rRMin
rRMax
5
75
BDYN
FYN
TYN
AYN
CYN
SYN AEYN RSYN
1
0
0
0
0
1
1
1
TBS
TOP
CAA
CAX
ALA
ALX
SFT
CW
CWFP
ULh
LLh
19
21
15
0
43
90
0
1
0.9
325
8000
SAN
SIL
BD
ROK SMB EAL
CA
54.4 18.4 1.51 0
10.1 0
8.1
drate
0.1
TA TC iCT
1 30
1
TDT Tm ir r
2
60 1
0.334
*** End of the Root.in File ******************************************************

25

Figure 11. Results of the potential and actual root system development for different times(simulated by HYDRUS-2D) when irrigation is applied at the entire soil surface.
Figure 12 shows the results for the same soil, the same stress factor settings, and the same
simulation time as above, except for a few changes in the root growth settings. In this case theroot system needs the entire simulation time to reach maturity. Additionally, a spatiallyasymmetric irrigation was applied at the soil surface. Irrigation was applied with a rate of 2
mm/d between days 30 and 50 only in the top left corner (the first 10 cm of the soil surface)26

while the rest of the soil surface remained un-irrigated and exposed only to evaporation.
Potential evaporation was set to of 0.1 mm/d from the beginning until day 15, to 1 mm/d
between days 16 and 18, and to 2 mm/day from day 19 until the end of the simulation. Potential
transpiration was set to 0.1 mm/d between the first day and day 11. From day 12 to day 29
potential transpiration was set to 1 mm/d and to 2 mm/d from day 30 until the end of simulation.
The results show that this asymmetric irrigation produced an unequal development of the rootsystem. The root system is more developed on the left hand side of the transport domain wheremore water is available compared to the right hand side of the transport domain where less wateris available. Again, the results are compared to the potential root length density, which represents
the case when the influence of the environmental factors is neglected.

Figure 12: Results of the potential and actual root system development for different times(simulated by HYDRUS-2D) when irrigation is applied in the top left corner.

27

28

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29