23rd International Congress on Modelling and Simulation, Canberra, ACT, Australia, 1 to 6 December 2019mssanz.org.au/modsim2019

Modelling nitrogen transport in sugar cane from soil torunoff from banded surface and buried fertiliser using
HYDRUS2D and a post-processing algorithm
Freeman J Cooka,b,c, Matthew Eylesd, Bruce Cowied, Bronwyn Bosomworthd and Mark SilburneaFreeman Cook & Associates, bThe University of Queensland School of Food and Agriculture, cGriffith
University Australian Rivers Institute, dQueensland Dept of Natural Resources, Mines and Energy
Rockhampton, eQueensland Dept of Natural Resources, Mines and Energy, Toowoomba
Email: Freeman.j.cook@gmail.com

Abstract: Simulated rainfall was applied toTable 1. Modelled (MO) and measured (ME) DIN (NH4-N
sugar cane at the Macknade Researchand NOx-N) losses in runoff two fertiliser treatments.
Station, Herbert region North Queensland, toSimulations with saturated hydraulic conductivity (Ks(1))
determine the loss of nitrogen to runoff forhalved are also shown.
fertiliser placed in a 100 mm wide strip on
Soil
Surface
Subsoilraised beds (spaced 1.8 m apart and a bed
layer 1width of 1.2 m) applied either on the surface
NH4-N
NOx-N
NH4-N
NOx-N
or buried at a depth of 50-150 mm. The sites-1-1-1(kg ha )(kg ha )(kg ha )(kg ha-1)
were covered with shelters between rainfall
ME
MO ME
MO ME
MO
ME
MO
simulations to avoid rainfall ingress, but
evaporation could still take place. ModellingKs(1)0.73 0.09 1.32 0.98 0.12 0.03
1.39
0.84
of these experiments was untaken to estimate
Ks(1)/2 0.73 0.98 1.32 1.29 0.11 0.03
1.39
1.80
nitrogen losses from recently fertilised soils
in wet tropical catchments. The model
parameters can be used to model other possible runoff scenarios. The modelling required a two-dimensionalmodel with multiple solute species transport and chain reaction processes. The HYDRUS2D model (Simunek
et al., 2012) was chosen; however, it cannot model the transfer of solutes to the runoff water. An analyticalmodel, which can transfer of solutes to runoff was developed by Wallach and van Genuchten (1990):−θ s k [ c (t ) − cr ]J (0, t ) =(1)

where J(0,t) is the flux density of solute transferred from the soil surface to the runoff water [M L T ] at timet [T], θs is the saturated volumetric water content at the soil surface [L3 L-3], k is the mass transfer coefficient[L T-1], c(t) is the concentration at the soil surface with time [M L-3] and cr is the concentration in the runoff
water [M L-3], which we set to zero as Wallach and van Genuchten (1990) did. A post-processing method tocompute the solute transport of nitrate, nitrite and ammonium to the runoff using eqn (1) was developed. Thisrequired surface concentrations of the solutes with time in a cross-section across the bed (c(x,t) where x is the
cross-section distance) and integrating both with space to give the mass transfer at time ti, M(s,ti), using:M i ( s , ti ) =−θ s c ( x, ti )dx ≈ θ s

∫

xn

j −1

n −1

∑ [c( x , t ) + c( x , t )] ( x
j +1

i

j

i

-3

j +1

− x j ) / 2, s =( x j +1 − x j )

-1

∑

(2)

∑ (t − t )(3)0=j 0=j 0

and this was then integrated with time to give the mass transferred during the runoff:

M T =k∫T

M i ( s , ti ) =k

m −1

∑[M

m −1

+ M i ] ( ti +1 − ti ) / 2, T =i +10=i 0=i 0

i +1

iwhere s is the length of the runoff surface [L]. The parameters in the model were adjusted to obtain the best fit
with no fertiliser treatment experimental values. These values were used to model surface-applied andsubsurface applied fertiliser. The results are shown in Table 1. The infiltration rate following the first rainfall
was halved, so simulations were performed with saturated hydraulic conductivity of layer 1 halved.
Keywords:

Runoff, nitrogen, HYDRUS2D, hybrid model

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Freeman J Cook et al., Modelling nitrogen transport from soil to runoff
1.

INTRODUCTION

Nitrogen loss in the Wet Tropics is ranked as the highest relative risk to Great Barrier Reef water quality withimproved nitrogen management identified as a priority to improve water quality (The State of Queensland2013). In particular, dissolved inorganic nitrogen (DIN), consisting of ammonium, nitrite, and nitrate, is ofconcern as they are readily bioavailable in the marine environment and can cause algae blooms and have direct
and indirect impacts on corals (Wooldridge et al., 2006;
D’Angelo and Wiedenmann 2014). Sugar cane is a major cropin the Wet Tropics and 84% of the anthropogenic DIN lost in
runoff from this region has been attributed to fertiliser losses
from sugar cane production (Harris, 2001; Waterhouse et al.
2012).
Experiments were carried out in 2014 to measure the nutrient
losses in runoff under simulated rainfall at the Macknade
research station (Cowie et al. 2013, Melland et al., 2019). The
experiments involved treatments of: nil fertilizer; fertiliser
applied in a horizontal band on the surface; and, fertiliser applied
into the subsoil in a vertical band. Simulated rainfall was appliedon three occasions, 7, 20 and 55 days after fertiliser applicationand lasted until 30 minutes of runoff had occurred. During therunoff, the volume of runoff and runoff samples taken werecollected. The experimental design objective was to collectcomparative data on the impacts of fertiliser placement on DIN
runoff relating to time from application to the first rainfall event,and then subsequent rainfall events.
To extend the data, and estimate the effect of therainfall shelter, modelling of the nitrogen loss to therunoff water is required. Models that can do the twodimensional solute transport and transfer of solutes torunoff are generally not available. Here we report thedevelopment of a hybrid model consisting of anumerical model (HYDRUS2D) to calculate the waterand solutes in the soil. From this model we get thesolute concentration with time across the soil surface
using eqns (2) and (3). These surface concentrations
were then used in the analytical model (eqn (1)) to
calculate the mass of solutes transferred from the soil
to the runoff water. To our knowledge, this is the first
application of such modelling in two-dimensions andrepresents a methodology that can be used in manyother applications where the soil solute concentration
will vary in a two- or three-dimensional manner. Suchapplications could be in runoff from urine or dung
patches, fertigation from dripper irrigation or where
fertilisers are applied in bands.
2.

METHODS

2.1.

Site and Soil

Figure 1. Location of site is 20 km northof Ingham in the wet tropics.

Table 2. Soil particle size distribution with themeasured values defined according to the Australianstandard
Depth (m)Australian classification

Upper

lower

Coarse
sand
(%)

Fine
sand
(%)

Silt
(%)

Clay
(%)

0

0.1

20

63.3

10.6

10.6

0.2

0.3

21.8

62.1

12.3

8.8

0.6

0.7

24.8

69.9

5.3

5.4

0.8

0.9

5.6

65.6

13.8

20.7

1.1

1.2

13.2

55.3

15.4

20.7

1.4

1.5

2.5

64.4

15.4

22.4

The trial was conducted in June and July 2014 at the Macknade Research Station, 20 km north of Ingham,
Queensland (Figure 1). The site is located in the Wet Tropics with a long-term average annual rainfall of 2154mm
(http://www.bom.gov.au/jsp/ncc/cdio/weatherData/av?p_nccObsCode=139&p_display_type=dataFile&p_sta
rtYear=&p_c=&p_stn_num=032032). Two soils are present at the site; is a moderately well-drained
Chromosol and a Dermosol with a fine sandy clay loam texture on an 0.8 to 1.0% slope (Table 2).

1092

Freeman J Cook et al., Modelling nitrogen transport from soil to runoff
2.2.

Experimental layout and treatments

The plot-scale experiment was conducted using a
rainfall simulator centred over a recently planted
cane row in a minimum tillage paddock. The
rainfall simulator is described in detail in Loch et al.
(2001). The cane was planted in dual rows in semipermanent raised beds with a 1.8 m row spacing,with no fill-in practices applied. The soil was bare,as the planted cane stalks had barely grown during
the experimental period, and untilled.
Each 1.7 m long by 1.0 m wide rainfall simulator
plot is bounded by a 3-sided metal frame
approximately 3 mm wide by 150 mm deep,
installed 50 to 70 mm into the ground to provide a
hydraulic barrier around the edge (Elledge et al.,2016). The down-slope end of the plot has a metal
plot-front installed which includes a spout to collectrunoff.
Simulated rainfall was applied on three fertiliser
treatments (nil fertiliser, sub-surface and surface) ata mean intensity of 87 mm/h until runoff
commenced. This rainfall rate is similar to the 100
year 30 minute rainfall rate. The period of time therainfall simulation occurred for varied as
application of rainfall continued until 30 minutes ofrunoff had occurred. During the runoff event, acomposite sample was collected by sampling 5
seconds of runoff at 0 minutes (time at which runoff
commenced), then at 5 minute intervals after this up
to 30 minutes after runoff commenced.
Granular fertiliser (Nitrophoska Special: 12%
nitrogen, 5.2% phosphorous, 14.1% potassium and
8% sulphur) was applied on the surface and subsurface at 385.5 kg/ha (46 kg/ha N; 54kg/ha K;
20kg/ha P) immediately after planting.

Table 3. Day of simulated rainfall application andamount of prior rainfall on each plot. N indicates nosimulated rainfall.
Fertiliser
Treatment

Plot no.

Day of Simulated
Rainfall (DAF)
7

20

55

Prior
simulated
rainfall added (mm)Surface

Subsurface

Nil

1

0

55

110

4

N

0

55

7

N

N

0

10

0

55

110

13

N

0

55

16

N

N

0

2

0

55

110

5

N

0

55

8

N

N

0

11

0

55

110

14

N

0

55

17

N

N

0

3

0

N

N

6

N

0

N

9

N

N

0

12

0

N

N

15
N
0
N
Simulated rainfall was applied at three times, 7, 20
18
NN0
and 55 days after fertilisation. For surface andsubsurface fertilised two plots had simulated
irrigation applied to them on all three times, two plots two times and two plots only once (Table 2). The nil
fertiliser treatment plots did not have any plots where repeated rainfall simulations were carried out (Table 2).

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Freeman J Cook et al., Modelling nitrogen transport from soil to runoff
2.3.

Estimation of model parameters

NH4 -N (mg kg -1 )NO3 -N (mg kg -1 )All the soil physical properties in Table 3 were estimated using the data in Table 2 plus bulk density data using
the pedotransfer methods of Cook and Cresswell (2008). These values along with estimates of: the reaction
rates for the nitrogen chain reaction of80
8ammonium to nitrite to nitrate which isab70
7available in HYDRUS2D (Radcliffe andMeasured60
6Modelled
Simunek, 2010); the adsorption coefficient50(Kd) for ammonium (NH4-N) (estimated540
using Vogeler et al. 2011); and the diffusion
430
coefficients, were used to simulate the320
Measured
nitrogen lost in runoff. The final values of the2
Modelled
10
soil physical properties reaction rates and Kds
01
for each of the three layers used in the0
10 20 30 40 50 60
0
10 20 30 40 50 60
DAF (day)DAF (day)modelling are given in Table 4.
Figure 2. Measured and modelled concentration of a)ammonium (NH4-N) and b) nitrate (NO3-N) nitrogen in thesoil with days after fertilisation (DAF).

The plots were covered between simulations
which would have reduced the evaporation. It
was found that adjusting this to a value of
0.25PET (PET is the potential evaporation
16aModelled time to runoff (min)θ (m3 m-3)

0.20
0.18
0.16
0.14

Measured
Modelled
1 to 1 line

0.12
0.10

0

10

20

30

40

50

60

DAF (day)

14

26

b

DAF 7
DAF 20
DAF 55
1 to 1 linec24Modelled runoff (mm)O

0.22

12

10

8

22
20
18
16
14

DAF 7
DAF 20
DAF 55
1 to 1 line

12
10

6

6

8

10

12

14

16

Measured time to runoff (min)

8

8

10

12

14

16

18

20

22

24

26

Measured runoff (mm)Figure 3. Measured and modelled: a) soil water content, b) time to runoff and c) runoff depth. The data isshown with days after fertilisation (DAF) indicated by the symbols.

Modelled Tf (min)Modelled RO (mm)rate) resulted in keeping the soil nitrate concentrations close to the measured values (figure 2). The values werethen adjusted to give the best fit to soil nitrogen
40
16
concentrations (figure 2), soil water content, timeb
Prior rain 0 mma
14
to runoff and runoff depth (figure 3) and NH4-N
Prior rain 55 mm
35
Prior rain 110 mm
12Prior rain 55 mm k2
and NOx-N in runoff (not shown). The mean
Prior rain 110 mm k2
30
10
1 to 1transfer coefficient in Table 4 were used for825
modelling the nitrogen transfer to the runoff water
6
for the subsurface and surface-applied fertiliser.
Prior rain 0 mm
204Prior rain 55 mm
Prior rain 110 mm
The value of 0.015 cm day-1 is very similar to the2
Prior rain 55 mm k2
15
Prior rain 110 mm k2
value for bromide of 0.0138 cm day-1 found by0
1 to 1
10
Wallach and van Genuchten (1990).
10
15
20
25
30
35
40
0 2 4 6 8 10 12 14 16 18 20
Analysis of the data (Cook et al. in prep) had
shown that the plots receiving successive rainfall
simulations, the infiltration rate decreased by half
after the first rainfall simulation. Thus, simulations
were carried out with the saturated hydraulicconductivity (Ks) of layer 1 halved.
3.

RESULTS AND DISCUSSION

Measured Tf (min)Measured RO (mm)Figure 4. Plots of measured versus modelled a) time torunoff (Tf) and b) runoff depth (RO) from plots thatreceived subsurface fertiliser. The results are plotted so thatthe effect of prior rainfall can be discerned. Results are also
shown for plots which received a second rainfall event(prior rain 55 mm) and third rainfall event (prior rain 110mm) with the Ks of layer 1 halved.

The hybrid model was used to simulate thedissolved nitrogen components (NH4-N and NOx-N) in runoff for the subsoil and surface applied fertiliser. Thisis most likely due to modification of the soil structure at the surface.

1094

Freeman J Cook et al., Modelling nitrogen transport from soil to runoff
3.1.

Subsurface fertiliser treatment

Layer

Depth
range (m)θr

10-0.25

0

0.600

6.50

1.650

1.08x10-5

-1.02

40.3

2

0.25-0.50

0.056

0.411

3.07

1.487

8.65x10

1.36

34

3

0.50-0.75

0.043

0.369

4.39

1.100

1.16x10-6

0.5

53

N

D

k

species(m s )

NH4

1.957x10-9NO2

1.912x10NO31.902x10-9

NOx

3.2.

Modelled NOx-N (kg ha-1)

Modelled NH4-N (kg ha-1)

When modelling the subsurface fertiliser treatment, only half the bed had to be modelled as the fertiliser wasplaced in the middle of the bed. The initial
0.12
Prior rain 0 mmbaconcentration was estimated by assuming
3
Prior rain 55 mm
0.10
Prior rain 110 mm
Prior rain 0 mm
that the fertiliser was mixed into the soil in a
Prior rain 55 mm k2
Prior rain 55 mm
Prior rain 110 mm k2
Prior rain 110 mm
0.08
2band 0.02 m wide and 0.1 m deep, l in the soil
1 to 1
Prior rain 55 mm k2
Prior rain 110 mm k2
profile between 0.05 and 0.15 m. The results
0.06
1 to 1
1
show that the time to runoff generation (Tf)0.04
and runoff volume was modelled well by the00.02
simulation (figure 4), especially when the Ks
0.00
of layer 1 was halved following the first
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.00 0.05 0.10 0.15 0.20 0.25 0.30
rainfall simulation. The root mean square of
Measured NOx-N (Kg ha-1)
Measured NH4-N (kg ha-1)
the error (RMSE) for modelled Tf and RO
were 4.10 min and 4.7 mm respectively, andFigure 5. Plots of measured versus modelled a) NH4-N andrefined index of agreement (dr, (Wilmott etb) nitrate plus nitrite (NOx-N) from plots that received
al. 2012), dr = 1 is a perfect model and thesubsurface fertiliser. The results are plotted so that the effectrange of dr is from 1 to -1) 0.56 and 0.71
of prior rainfall can be discerned. Results are also show for
respectively, which indicated that the runoff
plots which received a second rainfall event (prior rain 55
timing and depth was modelled well bymm) and third rainfall event (prior rain 110 mm) with the
HYDRUS2D. The NH4-N mass lost to theKs of layer 1 halved.
runoff water was generally underestimated,
although halving the Ks of layer 1 did increase the modelled NH4-N for plots receiving a second and third
rainfall simulation (figure 5a). The NOx-N was much better modelled but even with halving the Ks of layer 1,
the NOx-N in the runoff for second and third rainfall simulations was less than the measured values (figure 5b).
The RMSE was 0.13 and 1.45 kg-N ha-1 yr-1 for NH4-N and NOx-N respectively with the half Ks values forsecond and third rainfall simulations. The dr was 0.27 and 0.52 for NH4-N and NOx-N respectively with thehalf Ks values for second and third rainfall simulations, which means NOx-N is better predicted with the model
than NH4-N.
Table 3. Soil physical properties for soil layers used in the HYDRUS2D simulations: residual
and saturated volumetric water contents (θr and θs), scaling parameter (α), scaling parameter(n), saturated hydraulic conductivity (Ks), hydraulic conductivity scaling parameter (l) andadsorption coefficient (Kd) for NH4-N. The molecular diffusion coefficients for nitrogenspecies in water (D). The mean and standard error for the transfer coefficient (k) is shown for
NH4-N and NOx-N

2

θs

n

α

Ks

l

(m s )(m )Kd(m3 kg-1)

-1

-1

-6

(cm day-1)-1

0.20±0.04-90.015±0.003

Surface fertiliser treatment

The surface fertiliser was applied in a band 100 mm wide to one side of the centre line of the bed. This meantthat the whole of the bed had to be modelled in order to properly represent the experiment. The fertiliser was
assumed to be mixed into a depth of 0.01 m. Similar to the subsurface fertiliser treatment, simulations of thetime to runoff and runoff depth was modelled well by the HYDRUS2D model with the estimated parameters(figure 6), especially when the Ks of layer 1 was halved for plots where second and third rainfalls occurred.
The model was able to both fit time to runoff with an RMSE of 4.6 min and dr of 0.77 and the runoff depth

1095Freeman J Cook et al., Modelling nitrogen transport from soil to runoff
with and RMSE of 13.3 mm and dr of 0.83 well when values from plots with Ks of layer 1 were used for second
and third rainfall simulations on plots.

Modelled Tf (min)Modelled RO (mm)The modelled NH4-N in runoff for the surface-applied fertiliser was generally greater than the measured values(figure 7a). The modelled NOx-N in the runoff was also greater than the measured values for plots where onlya single rainfall simulation occurred while
20
40
Prior rain 0 mmbplots that had second and third rainfall
Prior rain 0 mm
18aPrior rain 55 mm
Prior rain 55 mm
Prior rain 110 mm
35
16Prior rain 110 mm
simulations had modelled NOx-N values
Prior rain 55 mm k2
Prior rain 55 mm k2
14
Prior rain 110 mm k2
Prior rain 110 mm k2
less than the measured values (figure 7b).
30
1 to 112
1 to 1
Halving the Ks of layer 1 exacerbates the
10258
difference between measured and620modelled for NH4-N but decreased the4215
difference for NOx-N. The RMSE and dr0
for NH4-N mass loss rate were 0.51 kg-N
10
10
15
20
25
30
35
40
0 2 4 6 8 10 12 14 16 18
ha-1 yr-1 and 0.34 for the data with Ks
Measured RO (mm)Measured Tf (min)halved for layer 1 when second and third
rainfall simulations occurred. The RMSE
Figure 6. Comparison of measured and modelled: a) time toand dr of NOx-N 1.07 kg-N ha-1 yr-1 andrunoff (Tf) and b) runoff depth (RO) for the surface applied
0.43 indicated that the model fitted thefertiliser plots. The data is plotted to show the effect of prior
NOx-N data better.
rainfall on the plots. The plots which received second and4.

CONCLUSION

third rainfall simulations (55 and 110 mm of prior rainfall)
had simulations with Ks of layer 1 reduced by half and areshown with k2 in the legend.

1.0
0.5

Prior rain 0 mm
Prior rain 55 mm
Prior rain 110 mm
Prior rain 55 mm k2
Prior rain 110 mm k2
1 to 1

0.0

0.0

0.5

1.0

1.5

Measured NH4-N (kg ha-1)

2.0Modelled NOx-N (kg ha-1)

The modelling of the nitrogen transfer to therunoff indicated that the subsurface-applied
fertiliser model generally underestimates
NH4-N but gets the nitrate approximately
correct. For the surface-applied fertiliser
model, the NH4-N and NOx-N is generally
overestimated. However, the modelledvalues are well within one order ofmagnitude of the measured values, which
given the uncertainty in the model
parameters is encouraging.

Modelled NH4-N (kg ha-1)

The modelling of runoff losses of surface
and subsurface-applied fertiliser showedthat the HYDRUS2D model was able to model the time to runoff and runoff depth well, which would indicatethat the physical parameters are applicable4
for this soil. These parameters would be
Prior rain 0 mmb
2.0aPrior rain 55 mm
suitable for doing further modelling ofPrior rain 110 mm
3
Prior rain 55 mm k2
1.5
water transport for this site.
Prior rain 110 mm k2
1 to 12

10

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Measured NOx-N (Kg ha-1)

Figure 7. Comparison of measured and modelled: a) NH4N and b) nitrogen oxides (NOx-N) for the surface applied
fertiliser plots. The data is plotted to show the effect of priorrainfall on the plots. The plots which received second andthirdrainfall simulations (55 and 110 mm of prior rainfall)
Given the difficulties with modelling solute
hadsimulations
with Ks of layer 1 reduced by halve and aretransport these results are encouraging. This
shown
with k2 in the legend.
hybrid modelling approach is promisingand should be further developed. This modelling approach will allow for better estimates of nutrient mass inrunoff and lead to improved water quality.
ACKNOWLEDGEMENTS
The senior author would like to thank the Queensland Department of Natural Resources Mines and Energy forfunding him to develop this model. The experimental work this paper is based on and the funding of this work
received support from the Australian and Queensland governments’ Paddock to Reef program.

REFERENCES
Cook, F.J., Cresswell, H.P. (2007). Chapter 84 Estimation of Soil Hydraulic Properties. In Soil Sampling andMethods of Analysis. M.R. Carter and E.G. Gregorich (Eds.), Canadian Society of Soil Science, Taylor andFrancis, LLC, Boca Raton, Fl, 1139-1161.

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Freeman J Cook et al., Modelling nitrogen transport from soil to runoff
Cook, F.J., Cowie, B., Turner, R., Silburn, D.M., Eyles, M., Bosomworth, B. (2019). Rainfall induced runoffof nitrogen and phosphorus from recently fertilised beds: 1. Measurements and results. Agriculture
Environment and Ecosystems (In prep.).
Cowie, B.A., DiBella L.P., Davison, L.K., Tang, W.W., Benson, A.J., Poggio, M. (2013). Sub-surface fertiliser
application in sugar cane: Reduced runoff loss under simulated rainfall seven days after application. Paper
Ag 16, Australian Society for Sugar Cane Technology Conference.
D’Angelo, C., Wiedenmann, J. (2014). Impacts of nutrient enrichment on coral reefs: new perspectives andimplications for coastal management and reef survival. Current Opinion in Environmental Sustainability 7,
pp. 82-93.
Elledge, A., Cowie, B., Wallace, S. (2016). Simulated rainfall trials to quantify management practices that
reduce dissolved inorganic nitrogen and sediment in runoff from plant sugarcane in the Herbert catchment,
Wet Tropics. Report of the Herbert Cane Productivity Services Limited, Department of Natural Resources
and Mines, Rockhampton p.18.
Harris, G.P. (2001). Biogeochemistry of nitrogen and phosphorus in Australian catchments, river and estuaries:
effects of land use and flow regulation and comparisons with global patterns. Marine and Freshwater
Research 52, 128-137.
Loch, R.J., Robotham, B.G., Zeller, L., Masterman, N, Orange, D.N., Bridge, B.J. Sheridan, G., Bourke, J.J.
(2001). A multi-purpose rainfall simulator for field infiltration and erosion studies. Australian Journal of
Soil Research, 39, 599-610.
Melland, A.R., Cowie, B., Silburn, D.M., Eyles, M. (2019). Impacts of sugarcane management practices on
nitrogen runoff in the wet tropics of Queensland, Australia. Journal of Environmental Management (Inprep.).
Radcliffe, D.E., Simunek, J. (2010) Soil Physics with HYDRUS: Modelling and Applications. CRC Press,
Taylor and Francis, Boca Raton, 372p.
Simunek J., van Genuchten M. Th., Šenja M., (2012). The HYDRUS software package for simulating twoand three dimensional movement of water, heat and multiple solutes in variably-saturated porous media.
Version 2.0, Technical Manual, PC Progress, Prague, Czech Republic, 258p.
Vogeler, L., Cichota, R., Snow, V.O., Dutton, T., Daly, B. (2011). Pedotransfer functions for estimating
ammonia adsorption in soils. Soil Science Society of America Journal, 75, 324-331.
Wallach, R., van Genuchten, M. Th. (1990). A physically based model for predicting solute transfer from soil
solution to rainfall-induced runoff water. Water Resources Research 26, 2119-2126.
Waterhouse, J., Brodie, J., Lewis, S., Mitchell A. (2012). Quantifying the sources of pollutants in the Great
Barrier Reef catchments and the relative risk to reef ecosystems. Marine Pollution Bulletin 65, 394-406.
Wilmott, C.J., Robeson, S.M., Matsuura, K. (2012). A refined index of model performance. International
Journal of Climatology 32, 2088-2094.
Wooldridge, S., Brodie, J., Furnas M. (2006). Exposure of inner-reefs to nutrient enriched runoff entering theGreat Barrier Reef Lagoon: Post-European changes and the design of water quality targets. Marine Pollution
Bulletin 52 1467-1479.

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