Supporting Information for the manuscript:
Long-term environmental inventory factors for land application
of differently treated source-separated organic municipal waste
By Hiroko Yoshida1§, Martin P. Nielsen2, Charlotte Scheutz1, Lars S. Jensen2,
Sander Bruun2, Thomas H. Christensen1
1
Department of Environmental Engineering, Technical University of Denmark, Kgs. Lyngby, Denmark
2
Department of Plant and Environmental Sciences, University of Copenhagen, Thorvaldsensvej 40,
Frederiksberg 1871, Denmark
§
Corresponding author
This document contains 23 figures which supplement the discussion and they were referenced in the result and
discussion part of the manuscript and the detail description of statistical meta-modeling process, including the
extract of R code used.
1. Supplementary figures
Figure SI-1: Change in the contribution of each of the input variables (N application rate, application year,
crop, soil type, precipitation pattern) to the total sum of squares of output variables (crop yield, nitrate
leaching, nitrous oxide emission) for 3 different fertilizer types (MF mineral fertiliser, MSW-D digestate,
MSW-C compost) over a 100 years simulation period
Figure SI-2: Crop yield, nitrate leaching, nitrate runoff surface to water, and N2O emissions for a coarse
sandy soil (CS) under average Danish precipitation scheme (DK)as a function of N application of mineral
fertilizer (MF), digested organic waste (MSW-D) and composted organic waste (MSW-C) for simulation
periods ranging from 3 years to 100 years. The error bars represent 95% confidence interval calculated as 1.96
x standard errors. The same aspect of the graph were adjusted to be the same as the mineral fertilizer, hence the
slope is directly comparable between three fertilizers for each fate of N.
Figure SI-3: Harvest, nitrate leaching, nitrate runoff surface to water, and N2O emissions for a clayey soil
(CL) under average Danish precipitation scheme (DK)as a function of N application of mineral fertilizer
(MF), digested organic waste (MSW-D) and composted organic waste (MSW-C) for simulation periods
ranging from 3 years to 100 years. The error bars represent 95% confidence interval calculated as 1.96 x
standard errors. The same aspect of the graph were adjusted to be the same as the mineral fertilizer, hence the
slope is directly comparable between three fertilizers for each fate of N.
Figure SI-4: Crop yield, nitrate leaching, nitrate runoff surface to water, and N2O emissions for a coarse
sandy soil (CS) under average East German precipitation scheme (DE) as a function of N application of
mineral fertilizer (MF), digested organic waste (MSW-D) and composted organic waste (MSW-C) for
simulation periods ranging from 3 years to 100 years. The error bars represent 95% confidence interval
calculated as 1.96 x standard errors. The same aspect of the graph were adjusted to be the same as the mineral
fertilizer, hence the slope is directly comparable between three fertilizers for each fate of N.
Figure SI-5: Crop yield, nitrate leaching, nitrate runoff surface to water, and N2O emissions for a sandy
loam soil (SL) under average East German precipitation scheme (DE) as a function of N application of
mineral fertilizer (MF), digested organic waste (MSW-D) and composted organic waste (MSW-C) for
simulation periods ranging from 3 years to 100 years. The error bars represent 95% confidence interval
calculated as 1.96 x standard errors. The same aspect of the graph were adjusted to be the same as the mineral
fertilizer, hence the slope is directly comparable between three fertilizers for each fate of N.
Figure SI-6: Crop yield, nitrate leaching, nitrate runoff surface to water, and N2O emissions for a clayey
soil (CL) under average East German precipitation scheme (DE) as a function of N application of mineral
fertilizer (MF), digested organic waste (MSW-D) and composted organic waste (MSW-C) for simulation
periods ranging from 3 years to 100 years. The error bars represent 95% confidence interval calculated as 1.96
x standard errors. The same aspect of the graph were adjusted to be the same as the mineral fertilizer, hence the
slope is directly comparable between three fertilizers for each fate of N.
Figure SI-7: Crop yield, nitrate leaching, nitrate runoff surface to water, and N2O emissions for a coarse
sandy soil (CS) under average Dutch precipitation scheme (NL) as a function of N application of mineral
fertilizer (MF), digested organic waste (MSW-D) and composted organic waste (MSW-C) for simulation
periods ranging from 3 years to 100 years. The error bars represent 95% confidence interval calculated as 1.96
x standard errors. The same aspect of the graph were adjusted to be the same as the mineral fertilizer, hence the
slope is directly comparable between three fertilizers for each fate of N.
Figure SI-8: Crop yield, nitrate leaching, nitrate runoff surface to water, and N2O emissions for a sandy
loam soil (SL) under average Dutch precipitation scheme (NL) as a function of N application of mineral
fertilizer (MF), digested organic waste (MSW-D) and composted organic waste (MSW-C) for simulation
periods ranging from 3 years to 100 years. The error bars represent 95% confidence interval calculated as 1.96
x standard errors. The same aspect of the graph were adjusted to be the same as the mineral fertilizer, hence the
slope is directly comparable between three fertilizers for each fate of N.
Figure SI-9: Crop yield, nitrate leaching, nitrate runoff surface to water, and N2O emissions for a clayey
soil (CL) under average Dutch precipitation scheme (NL) as a function of N application of mineral
fertilizer (MF), digested organic waste (MSW-D) and composted organic waste (MSW-C) for simulation
periods ranging from 3 years to 100 years. The error bars represent 95% confidence interval calculated as 1.96
x standard errors. The same aspect of the graph were adjusted to be the same as the mineral fertilizer, hence the
slope is directly comparable between three fertilizers for each fate of N.
Figure SI-10: Crop yield response curve after 5, 25 and 100 years of simulation for each crop and climate
combination. The dotted line present the cutoff between high response zone (left to the dotted line) and low
response phase (right to the dotted line).
Figure SI-11: Cumulative crop yield response curve after 100 years of simulation for nine crop and
climate combinations. The dotted line present the cutoff between high response zone (left to the dotted line) and
low response phase (right to the dotted line). DK stands for average precipitation in Denmark, DE in East
German, and NL in the Netherlands. The data points were jittered to show the distribution.
Figure SI-12: Cumulative nitrate leaching over 100 years of simulation for each crop and climate
combination. The dotted line present the cutoff between high response zone (left to the dotted line) and low
response phase (right to the dotted line). DK stands for average precipitation in Denmark, DE in East German,
and NL in the Netherlands. The data points were jittered to show the distribution.
Figure SI-13: Cumulative nitrate loss to surface water over 100 years of simulation for each crop and
climate combination. The dotted line present the cutoff between high response zone (left to the dotted line) and
low response phase (right to the dotted line). DK stands for average precipitation in Denmark, DE in East
German, and NL in the Netherlands. The data points were jittered to show the distribution.
Figure SI-14: Cumulative N2O emission over 100 years of simulation for each crop and climate
combination. The dotted line present the cutoff between high response zone (left to the dotted line) and low
response phase (right to the dotted line). DK stands for average precipitation in Denmark, DE in East German,
and NL in the Netherlands. The data points were jittered to show the distribution.
Figure SI-15: Change in cumulative crop yield response in high response phase for 100 years. The
uncertainty range represents the estimated 95% confidence interval. DK stands for average precipitation in
Denmark, DE in East German, and NL in the Netherlands.
Figure SI-16: Change in cumulative emission factors for N2O emissions in high response phase over 100
years. The uncertainty range represents the estimated 95% confidence interval. DK stands for average
precipitation in Denmark, DE in East German, and NL in the Netherlands.
Figure SI-17: Change in cumulative emission factors for nitrate leaching in high response phase over 100
years. The uncertainty range represents the estimated 95% confidence interval. DK stands for average
precipitation in Denmark, DE in East German, and NL in the Netherlands.
Figure SI-18: Change in cumulative emission factors for nitrate introduction to surface water in high
response phase 100 years. The uncertainty range represents the estimated 95% confidence interval. DK stands
for average precipitation in Denmark, DE in East German, and NL in the Netherlands.
Figure SI-19: Change in cumulative crop yield response in low response phase for 100 years. The
uncertainty range represents the estimated 95% confidence interval. DK stands for average precipitation in
Denmark, DE in East German, and NL in the Netherlands.
Figure SI-20: Change in cumulative emission factors for N2O emissions in low response phase over 100
years. The uncertainty range represents the estimated 95% confidence interval. DK stands for average
precipitation in Denmark, DE in East German, and NL in the Netherlands.
Figure SI-21: Change in cumulative emission factors for nitrate leaching in low response phase over 100
years. The uncertainty range represents the estimated 95% confidence interval. DK stands for average
precipitation in Denmark, DE in East German, and NL in the Netherlands.
Figure SI-22: Change in cumulative emission factors for nitrate introduction to surface water in low
response phase 100 years. The uncertainty range represents the estimated 95% confidence interval. DK stands
for average precipitation in Denmark, DE in East German, and NL in the Netherlands.
2. Description of statistical analysis
2.1. Overview of the simulation set up and input variables
Figure 1 presents an overview of the input variables explored in this study. The input variable includes 11
fertiliser application rates, three soil types, three precipitation regimes, eight crop types in the application year
and eight application years. In total, 6336 simulation outcomes are recorded for crop yields and four other N
emission pathways for each simulation day.
The results of the simulation are organised in the data frame as presented in Table 1. The outcomes of the
simulations are aggregated over a simulation period ranging from one to 100 years. The assessment was
conducted for each simulation year independently, which means that the data frame for the statistical analysis
contains five columns for input variables (soil, precipitation, fertiliser application rate, application year, crop
planted in the application year) and one column for the output variable (crop yield for a certain simulation
year). In this study, the crop yield response over a 25-year simulation period is selected as an example, but
exactly the same procedure was repeated 100 times to cover the entire simulation period and the other N
emission pathways.
Table 1 Example of Daisy’s simulation result format. Crop yield is given kg-N ha-1.
Soil
Precipitation
Crop
Application
Year
Fertiliser
DK
DK
DK
DK
DK
DK
DK
DK
DK
:
:
:
NL
CS
CS
CS
CS
CS
CS
CS
CS
CS
:
:
:
CL
Spring Barley
Spring Barley
Spring Barley
Spring Barley
Spring Barley
Spring Barley
Spring Barley
Winter Barley
Winter Barley
:
:
:
Winter
Wheat4
1961
1962
1963
1964
1965
1966
1967
1961
1962
:
:
:
1967
30
30
30
30
30
30
30
30
30
:
:
:
330
Crop
yield
at year 1
23.261
19.482
24.651
20.557
19.605
18.086
17.345
-96.396
0
:
:
:
0
Crop yield
at year 25
:
:
:
:
:
:
:
:
:
:
:
:
:
23.829
19.197
24.523
19.621
17.76
16.918
15.825
-20.654
19.152
:
:
:
169.71
:
:
:
:
:
:
:
:
:
:
:
:
:
Crop
yield at
year 100
23.647
-63.11
93.481
22.557
-48.516
104.42
19.938
27.05
20.842
:
:
:
181.45
2. 2. Assessment of the contribution of input variables to the total sum of squares
Figure 2 presents the temporal change in the contribution of input variables to the total sum of squares
between crop yield and the results approximated by a linear regression model. First, a linear regression model
(eq. 1) between the simulation output and the five input variables (soil, precipitation regime, crop for
application year, application year, fertiliser level) was developed:
Y = αgG + αhH + αiI+ αjJ+ αkK+ε ----- eq-1
where Y is Daisy’s simulation output (e.g. crop yield in kg N ha-1), G is soil type as a fixed input variable, αg is the
fixed effect coefficients for soil type, H is precipitation as a fixed input variable, αh is the fixed effect coefficients
for precipitation, I is crop type as a fixed input variable, αi is the fixed effect coefficients for crop type, J is the
application year as a fixed input variable, αj is the fixed effect coefficients for the application year, K is the
fertiliser application rate as a fixed input variable, αk is the fixed effect coefficients for the fertiliser application
rate and ε is the residual errors of the model.
Next, an analysis of variance (ANOVA) was applied to evaluate if there were any variations between the output
from the Daisy simulation and the approximated result from the linear regression line. A p-value below 0.05
was used as a criterion for rejecting the null hypothesis. The ratio between the sum of squares for each input
variable for the total sum of squares was used as an indicator for the importance of each input variable in
explaining variations in the outcome of the Daisy simulations.
The abovementioned analysis can be realised by following R code,
______________
# Prepare input data file
Data<- Table1
Harvest<-Data$Harvest
Soil<-Data$Soil
Precipitation<-Data$Precipitation
Fertilizer<-Data$Fertilizer
Crop<-Data$Crop
Year<-Data$Year
Data<-data.frame(Soil, Precipitation, Crop, Year, Fertilizer, Harvest)
# Set Year and Fertilizer application rate as factorial variable
Year<-as.factor(Year)
Fertilizer<-as.factor(Fertilizer)
# Prepare the output file
Sumsq<-matrix(nrow=6, ncol=1)
Pval<-matrix(nrow=6, ncol=1)
# Fit linear regression model
Model<-lm(Harvest~ Fertilizer+Year+Crop+Soil+Precipitation)
# Conduct ANOVA test
Summary<-anova(Model)
# Extract P value
Pval<-Summary[1:6,5]
# Calculate the contribution to the total sum of squares
Sumsq<-Summary[1:6,2]
SumsqSum<-colSums (Sumsq, na.rm = FALSE, dims = 1)
SumsqSum<-c(rep(SumsqSum, each = 6))
SumsqV<-as.vector(Sumsq)
SumsqPct<-SumsqV/SumsqSum
2. 3. Deriving emission factors
The evaluation of each input variable to the total sum of squares confirmed that the soil and precipitation
variable has a major influence on N emissions into the environment (Fig. 2, Fig SI-1). Therefore, the emission
factor was derived by dividing the dataset into nine soil-climate combinations. From now on, the dataset from
the sandy loam soil with average Danish precipitation for the 25-year simulation period is used as an example
and is given in Table 2.
Table 2 Daisy simulation results for the soil-climate combination of sandy loam soil with average Danish
precipitation for a 25-year simulation period. Crop yield is given in kg-N ha-1.
Fertiliser
Crop
30
30
30
30
30
30
30
30
30
:
:
:
330
Spring Barley
Spring Barley
Spring Barley
Spring Barley
Spring Barley
Spring Barley
Spring Barley
Winter Barley
Winter Barley
:
:
:
Winter Wheat4
Application
Year
1961
1962
1963
1964
1965
1966
1967
1961
1962
:
:
:
1967
Crop yield
at year 25
23.829
19.197
24.523
19.621
17.76
16.918
15.825
-20.654
19.152
:
:
:
169.71
A linear mixed effect model was constructed for three input variables (fertiliser application level, crop in
application year and application year) and output variables (crop yield and emissions) while considering the
interaction between crop and application year as being random. This is described in eq-2:
Yijk = αX + β + Zij + εijk ----- eq-2
where Yijk is output variables (crop yield or emission in kgN ha-1) for a particular combination of i (application
year), j (crop) and k (fertilisation levels), x is the fixed effect variable (fertiliser application rate in kgN ha-1), α is
the fixed effect coefficients, β is the fixed effect intercept, Zij is the random effects from the interaction
between the crop and application year and εijk is the residual errors of the model. The dataset is divided into
high and low response phases. The high response phase corresponds to the N fertiliser application rate from 30
to 180 kg min N ha-1 for MF and from 30 to 120 kg min N ha-1 for treated organic fertiliser. One linear mixed
model was fitted to each phase for each simulation year.
The abovementioned analysis can be realised by following R code,
______________
#Harvest in high response for MF
Data<- Table2
Y<-Data$Harvest[1:384]
X<-Data$Fertilizer[1:384]
Crop<-Data$Crop[1:384]
Year<-Data$Year[1:384]
Model1<-lmer(Y~X+(1|Year:Crop))
#Harvest in low response for MF
Data<- Table2
Y<-Data$Harvest[385:704]
X<-Data$Fertilizer[385:704]
Crop<-Data$Crop[385:704]
Year<-Data$Year[385:704]
Model2<-lmer(Y~X+(1|Year:Crop))
______________