This document evaluates the macropore component of the RZWQM2 model in simulating subsurface drainage and peaks at hourly time steps. It tests the model at experimental sites in Ontario and Iowa using hourly rainfall and drainage data during peak drainage periods. The results show that while the macropore component did not significantly improve long-term drainage simulations, it did improve the model's ability to simulate hourly drainage peaks compared to simulations without the macropore component. A sensitivity analysis also found that simulated flow was not sensitive to changes in macroporosity and radius parameters.

1. Assessment of Macropore
Component of RZWQM2 in
Simulating Hourly Subsurface
Drainage and Peaks
Changchi Xian1, Zhiming Qi1, Liwang Ma2, Matthew W. Sima3,
Matthew J. Helmers4, Tie-Quan Zhang5, Robert W. Malone6, and
Quanxiao Fang7
1 Department of Bioresource Engineering, McGill University, Sainte-Anne-de-Bellevue, QC, H9X 3V9, Canada.
2 USDA-ARS Rangeland Resources and Systems Research Unit, Fort Collins, CO 80526, USA.
3 Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ, 08544 U.S.A.
4 Department of Agricultural and Biosystems Engineering, Iowa State University, Ames, IA, 50011. USA.
5 Harrow Research and Development Center, Agriculture and Agri-Food Canada, Harrow, ON, N0R 1G0, Canada
6 USDA-ARS National Laboratory for Agriculture and the Environment, Ames, IA, USA.
7 Qingdao Agricultural University, Qingdao, China.
The 11th International Drainage Symposium
RZWQM2: Root Zone Water Quality Model version 2 or higher

2. Outline
•Introduction
•Objectives
•Materials and Methods
•Results and Discussion
•Conclusion
2

3. Introduction
• Preferential flow: a common phenomenon in tile drained field
with macropores (cracks) due to heavy soil texture
• Macropore flow directly contributes to subsurface drainage
and chemical losses in tile flow
3
Adapted from Radcliffe et al. (2015).
Cracks in a tile drained field in Onatrio in

4. Introduction
• Macropore flow is considered in many hydrological models and
applied to tile drainage simulation, such as APEX, HYDRUS,
MACRO, MIKE SHE, PEARL, DRAINMOD and RZWQM2
• Hourly rainfall should be used to improve macropore flow
simulation, especially for initiation of macropore flow (Malone
et al., 2004; Fox et al., 2007).
• However, few studies have evaluated drainage model’s
macropore component using hourly rainfall and drainage data.
4
http://soilandwater.bee.cornell.edu/
Askar et al., 2020

5. Objectives
•To test the macropore component of RZWQM2
at an hourly time step, focusing on drainage
peak periods when the macropore component
would be activated
5

6. Materials and Methods
•Experimental Site: Ontario and Iowa
6

7. Materials and Methods
•Experimental Site: Drainage layout
7
10 rows of each crop
15.2 m
S
C O
O Y
38 m R B
N E
A
N
Border Tile Border Tile
Sampling Sump
Site Layout (m) soil crop
Spacing depth
Iowa 7.6 1.06 clay loam corn-soybean
Ontario 3.81 0.85 clay loam corn-soybean
Table 1. Drainage layout, soil and crop

8. Materials and Methods
•Data used
8
Site Peak Period Peak
No. Date of Period No. Time
Observed
Peak Drain Flow
Rate (mm hr-1)
Iowa
𝑃1-1
𝐼𝑜𝑤𝑎
1 19 – 23 August 2007 1 21 August 2007 20:00 6.0
Ontario
𝑃1-1
𝑂𝑛𝑡
1 27 – 29 June 2008 1 28 June 2008 1:00 4.6
𝑃1-2
𝑂𝑛𝑡
1 27 – 29 June 2008 2 28 June 2008 15:00 5.2
𝑃2-1
𝑂𝑛𝑡
2 25 – 27 May 2011 1 26 May 2011 10:00 4.0
Table 2. Peak drainage flow periods and individual events employed in hourly
analysis of RZWQM2 model accuracy
Ontario data: Spring 2008 – 2012
Iowa Data: 2004-2009

9. Materials and Methods
•Macropore Component in RZWQM2 Model
9
Soil macropores are classified into cylindrical and planar
Cracks at the Ontario site, 2018
𝑲𝒎𝒂𝒄
𝒄𝒚𝒍𝒊𝒏𝒅.
=
𝑷𝒎𝒂𝒄 𝝆𝒈𝒓𝟐
𝟖ŋ
𝑲𝒎𝒂𝒄
𝒑𝒍𝒂𝒏𝒂𝒓
=
𝑷𝒎𝒂𝒄 𝝆𝒈𝒅𝟐
𝟏𝟐ŋ
Hydraulic conductivity of pores 𝑲𝒎𝒂𝒄 (Poiseuille’s law, cm/hr):
𝑷𝒎𝒂𝒄: macroporosity (cm3/cm3)
r: radius of cylindrical pores (cm)
d: width of planar pores (cm);
ŋ:dynamic viscosity of water (36 g/hr/cm)

10. Materials and Methods
•Macropore Component in RZWQM2 Model
10
Cracks at the Ontario site, 2018
Infiltration rate Vr (Poiseuille’s law, cm2/hr):
𝐻𝑐: the capillary drive term for the soil matrix
(cm)
∆𝑡1: the first time step in model calculation (h)
𝑽𝒓
𝒄𝒚𝒍𝒊𝒏𝒅𝒓.
= 𝟐𝝅𝒓
𝟐𝒌𝒎𝒂𝒄𝑯𝒄 𝜽𝒔𝒂𝒕 − 𝜽𝒊
𝟎. 𝟓𝜟𝒕𝟏
𝑽𝒓
𝒑𝒍𝒂𝒏𝒂𝒓
=
𝟐𝒌𝒔𝒂𝒕𝑯𝒄 𝜽𝒔𝒂𝒕 − 𝜽𝒊
𝒕

11. •Model Parameterization for Ontario Site
11
Measured Calibrated
Depth
(m)
ρ
(Mg m-3)
Sand
(g g-1)
Silt
(g g-1)
𝐾𝑠𝑎𝑡
ver
(mm h-1)
𝐾𝑠𝑎𝑡
lat
(mm h-1)
Soil moisture content, θ (mm3 mm-3)
Soil matric potential, 𝜓𝑚 (kPa)
θsat
0 kPa
θ10
-10kPa
θfc
-33 kPa
θpwp
-1500kPa
θr
-ꚙkPa
0-0.25 1.326 0.299 0.363 9.2 17 0.5 0.383 0.325 0.198 0.040
0.24-0.45 1.391 0.238 0.349 38 68 0.475 0.378 0.3363 0.240 0.090
0.45-0.80 1.391 0.257 0.33 30 60 0.475 0.371 0.3299 0.236 0.090
0.80-1.20 1.391 0.243 0.359 20 40 0.475 0.390 0.347 0.246 0.090
1.20-3.00 1.391 0.243 0.359 5 20 0.475 0.390 0.347 0.246 0.090
3.00-3.09 1.391 0.243 0.359 0.1 20 0.475 0.390 0.347 0.246 0.090
Table 2. Measured and calibrated soil hydraulic properties at the Ontario site
Soil depth
(m)
Macroporosity
(mm3 mm-3)
Radius of
cylindrical
pores (mm)
Width of
cracks (mm)
Length of
cracks (mm)
Average
length of
aggregate (mm)
Fraction of
dead end
pores
0-0.25 0.0003 1 0 0 100 0.01
0.25-0.45 0.0003 0 1 100 100 0.3
0.45-0.80 0.0003 0 1 50 50 0.5
0.80-1.20 0.0003 0 1 50 50 0.8
Table 3. Calibrated parameters for the RZWQM2 macropore component at the Ontario site

12. •Model Parameterization for Iowa Site
12
Table 6. Calibrated parameters for the RZWQM2 macropore component at the Iowa site
Soil
depth (m)
Macroporosity
(mm3 mm-3)
Radius of
cylindrical
pores (mm)
Width of
cracks
(mm)
Length of
cracks
(mm)
Average length
of aggregate
(mm)
Fraction of
dead end pores
0-0.10 0.001 2 0 0 100 0.001
0.10-0.20 0.001 0 2 100 100 0.01
0.20-0.30 0.001 0 2 100 100 0.05
0.30-0.40 0.001 0 2 100 50 0.1
0.40-0.60 0.001 0 2 50 50 0.3
0.60-0.90 0.001 0 2 50 50 0.5
0.90-1.20 0.001 0 2 50 50 0.8

13. Results and Discussion
•Simulations with and without macropores in
Ontario: low time resolution (weeks/months)
13
Figure 1. Observed cumulative drainage flow and drainage flow simulated
by RZWQM2 without macropore (NoMP) and with macropore (MP)
component for all sampling periods at the Harrow, Ontario, Canada
experimental site.
Periods can be weeks or
months in 2008-2012
NoMP: no macropore;
MP: macropore

14. Results and Discussion
•Simulations with and without macropores in
Ontario: low time resolution (weeks/months)
14
Model accuracy
statistics†
Ontario Iowa
NoMP MP NoMP MP
PBIAS -18.20% -13.19% 6.47% 10.43%
NSE 0.48 0.46 0.71 0.73
IoA 0.74 0.72 0.76 0.76
Table 6. Model accuracy statistics for no macropore (NoMP) and with macropore (MP)
simulation of drainage in periods with RZWQM2, Ontario and Iowa sites.
NoMP: no macropore;
MP: macropore

15. Results and Discussion
•Simulations with and without macropores in
Ontario: Hourly
15
Figure 2. Hourly rainfall, observed drainage, and drainage simulated by
RZWQM2 without macropore (NoMP) and with macropore (MP) component
for the Ontario site, Period 1, peaks 𝑷𝟏-𝟏
𝑶𝒏𝒕
𝒂𝒏𝒅 𝑷𝟏-𝟐
𝑶𝒏𝒕
.
NoMP:
no macropore;
MP:
macropore

16. •Simulations with and without macropores in
Ontario: Hourly
16
NoMP:
no macropore;
MP:
macropore
Peak(s) Model
accuracy
statistic†
Simulated
NoMP MP
𝑃1-1
𝑂𝑛𝑡
PBIAS -39.97% -11.28%
𝑃1-2
𝑂𝑛𝑡
PBIAS -51.59% -20.85%
𝑃2-1
𝑂𝑛𝑡
PBIAS -50.69% -31.35%
𝑃1-1
𝐼𝑜𝑤𝑎 PBIAS -51.92% 67.63%
Cumulative value (mm over Period)
𝑃1-1
𝑂𝑛𝑡
+ 𝑃1-2
𝑂𝑛𝑡 PBIAS 56.52% 89.49%
NSE 0.48 0.25
IoA 0.58 0.52
𝑃2-1
𝑂𝑛𝑡
* PBIAS -0.76% 5.46%
NSE 0.47 0.46
IoA 0.77 0.75
𝑃1-1
𝐼𝑜𝑤𝑎
PBIAS -25.07% -7.40%
NSE 0.54 0.36
IoA 0.68 0.71
Table 7. Model accuracy
statistics for predicted
drainage peak, amount, and
timing by RZWQM2 with no
macropore component
(NoMP) and with macropore
component (MP) Ontario
(POnt) and Iowa (PIowa) sites.

17. •Simulations with and without macropores in
Iowa: Daily
17
Figure 4. Observed daily drainage flow and daily drainage flow simulated
by RZWQM2 without (NoMP) and with (MP) macropore component for
the Iowa site.
NoMP: no macropore;
MP: macropore

18. •Simulations with and without macropores in
Iowa: Hourly
18
NoMP:
no macropore
MP:
macropore
Figure 5. Hourly rainfall,
observed drainage, and
drainage simulated by
RZWQM2 without (NoMP)
and with (MP) macropore
component for the Iowa site,
Period 1 (19-23 August 2007),
peak 𝑷𝟏-𝟏
𝑰𝒐𝒘𝒂
.
Peak(s) Model
accuracy
statistic†
Simulated
NoMP MP
𝑃1-1
𝐼𝑜𝑤𝑎
PBIAS -25.07% -7.40%
NSE 0.54 0.36
IoA 0.68 0.71
Table 7. Model accuracy statistics for predicted drainage peak by RZWQM2
with no macropore component (NoMP) and with macropore component
(MP) at the Iowa site.

19. •Sensitivity Analysis
19
Figure 6. Macropore flow sensitivity to changes in RZWQM2 macropore
component parameters at the Ontario site.

20. Conclusion
•For long-term drainage simulation using RZWQM2
model, the effects of implementing the macropore
component on drainage were not significant (6 and
3.7% increase for ON and IA, respectively)
•When focusing on drainage peak periods on an hourly
scale, the macropore component did improve the
model performance in simulating hourly drainage peaks.
•The sensitivity test showed that the simulated flow with
macropore component is not sensitive to microporosity
and radius.
20

21. Thank you & Questions?
Zhiming Qi
Associate Professor
Department of Bioresource Engineering
McGill University
Montreal Area, Quebec, Canada
zhiming.qi@mcgill.ca

28. Introduction
• Preferential flow: a common phenomenon in tile drained field with
macropores (cracks) due to heavy soil texture
•
A system by which the water level on or in the soil is controlled to
enhance agricultural crop production.
28
http://www.extension.umn.edu/agriculture/water/agricultural-
drainage-publication-series/

29. Introduction
• Root Zone Water Quality Model (RZWQM)
- original RZWQM
- modified RZWQM
• Drainage equations
- steady state equations
- transient equations
29

30. Methods:
Different equations to simulate drainage
•Steady state equations:
Steady-state equations assume that drainage outflow
is equal to the net recharge over a given period of time.
Hooghoudt’s equation:
30

31. •Transient equations:
Recharge and discharge are different, water table is
fluctuating.
31
van Schilfgaarde equation:
Methods:
Different equations to simulate drainage
Where,

32. •Transient equations:
Integrated Hooghout’s Equation is developed as a
solution to Boussinesq equation
32
Methods:
Different equations to simulate drainage
Where,

33. Results
Observed 2007-2008 cumulative drainage flow and equivalent values simulated with
the original or modified RZWQM using ssH, inH and vanS equations
33
Parameter Observed RZWQM Model
Drainage equation
Original (𝑅𝑍𝑊𝑄𝑀0) Modified (𝑅𝑍𝑊𝑄𝑀𝑅)
ssH inH vanS ssH inH vanS
Cumulative
drainage
[mm (2 y)-1]
810.4 920.9 931.6 931.6 862.8 862.3 862.4
———————— Model accuracy statistics for daily drainage 2007-2008 ———————
PBIAS — 13.65
%
14.96
%
14.96
%
6.48% 6.41% 6.42%
NSE — 0.40 0.41 0.41 0.71 0.70 0.70
IoA — 0.69 0.70 0.70 0.76 0.76 0.76

34. Results
• Hourly drainage simulation for rainfall events
To explore the performance of these equations at a more precise scale,
hourly simulation results were plotted in four typical and reasonable
drainage periods. (Results from modified RZWMQ only)
34

35. Results
35