GLOBAL SENSITIVITY ANALYSIS FOR A MODEL DESCRIBING
TWO-STEP NITRIFICATION IN A BIOFILM
D. Brockmann1 and E. Morgenroth1, 2*
Department of Civil and Environmental Engineering and 2Department of Animal Sciences, University of
Illinois at Urbana-Champaign, USA
emorgenr@uiuc.edu
1
The objective of biological wastewater treatment is to remove both organic carbon and nitrogen. Nitrogen
elimination is usually achieved by nitrification and denitrification. As nitrifying bacteria are slow growing
organisms a long biomass retention time is required to keep them in the system. Bacteria in a biofilm are
growing in a matrix attached to a substratum and are protected from washout. Thus, biofilms can provide an
ecological niche for slow growing bacteria. Biofilm models are complex models describing conversion processes
as well as mass transport of dissolved and particulate components within the biofilm. Biofilm models are highly
non-linear models and the uncertainties in the model parameters are of different dimensions. Hence, global
sensitivity methods are necessary to analyse the uncertainty in the model output and to allocate output
uncertainties to the uncertainty in the parameters. As a single simulation with a biofilm model can take minutes
to hours sensitivity analysis methods based on Monte Carlo simulations are often not feasible. Thus,
computational more efficient methods are required for sensitivity analysis of biofilm models.
In this abstract, we present the results of a sensitivity analysis for a biofilm model for two-step nitrification. The
sensitivity analysis was carried out by first using the method of Morris [1] for screening for important
parameters. Then, the Fourier Amplitude Sensitivity Test (FAST) [2, 3] was applied only to the reduced set of
important parameters to decrease the computational effort for calculating quantitative sensitivity measures.
The biofilm model describes bacterial growth and respiration of ammonium and nitrite oxidising bacteria (AOB
and NOB; [4]). Parameters considered for sensitivity analysis include (1) stoichiometric and kinetic parameters,
(2) mass transfer parameters (internal and external), (3) biofilm parameters (e.g. biofilm thickness, biofilm
density), and (4) reactor operation conditions (influent concentration of ammonium, flow rate, temperature,
dissolved oxygen concentration in the bulk phase). It was assumed that all parameters except the influent
concentration of ammonium and the inflow rate have a uniform distribution. Both, the ammonium concentration
in the influent as well as the flow rate were normally distributed. In total, 22 parameters were considered for
sensitivity analysis.
A Morris screening on eight levels was carried out to determine the 10 most influencing parameters.
Evaluating 10 trajectories resulted in 230 simulations. Subsequently, the extended FAST method [5] was applied
to the reduced set of 10 important parameters to obtain quantitative sensitivity measures. The ranges and
distributions of the 10 parameters were the same as used for the Morris screening. The remaining parameters
were assumed to be of minor importance and were fixed to their default values. 650 simulations were carried out
for calculating FAST first-order and total sensitivity indices. For the whole set of 22 parameters, at least 1430
simulations would be necessary to calculate first-order and total sensitivity measures of the extended FAST. All
simulations were performed using AQUASIM [6]. SIMLAB (2004) Version 2.2, simulation environment for
uncertainty and sensitivity analysis developed by the Joint Research Centre of the European Commission, was
used for the pre- and post-processing.
Sensitivity measures were calculated for the flux of ammonium and nitrate through the biofilm surface for
continuous reactor operation in steady state. The screening method of Morris resulted in the following 10 most
influencing parameters (Table 1): the dissolved oxygen concentration in the bulk phase (CO2,bulk), the thickness of
the external boundary layer (Ll), the diffusion coefficient for oxygen (DO2), the endogenous respiration rates of
AOB (bAOB), the affinity constants for oxygen for AOB and NOB (KO2,AOB and KO2,NOB), the affinity constant for
ammonium for AOB (KNH4,AOB), the affinity constant for nitrite for NOB (KNO2,NOB), the growth rate for NOB
(NOB), and the biomass density (Xf,tot). The ranking of the 10 most important parameters according to the
estimated means () and standard deviations () of the distributions of elementary effects were similar in this
case.
The results of the extended FAST show that the variance in both output variables is mainly driven by two
parameters (Table 1): the dissolved oxygen concentration in the bulk liquid and the thickness of the external
boundary layer, which models the external mass transfer resistance. The thickness of the external boundary layer
accounts for approximately 58-70% of the output variance of the flux of NH4-N and approximately 36-51% of
the output variance of the flux of NO3-N. The contribution of the dissolved oxygen concentration in the bulk
liquid to the output variance of the flux of NH4-N and NO3-N is 35-46% and 33-48%, respectively. Hence,
determining the thickness of the external boundary layer thickness and decreasing the variation in the dissolved
oxygen concentration in the bulk phase would reduce the uncertainty in the model output noticeably. Besides the
two parameters mentioned above, the affinity constants for oxygen of the AOB and NOB contribute distinctly to
the output variance of the flux of NO3-N. All other parameters account for only 2% and 7% of the output
variance of the flux of ammonium and nitrate, respectively based on the first-order sensitivity indices. Note, that
the results of the extended FAST are conditional on the choice of the fixed parameters.
Table 1: Parameter ranking of the 10 most important parameters according to the sensitivity measures  and 
of the screening method of Morris and first-order and total sensitivity measures of the extended FAST
Parameter
bAOB
KO2,AOB
KO2,NOB
KNH4,AOB
KNO2,NOB
NOB
DO2
Ll
CO2,bulk
Xf,tot
Morris 8-level


5
7
4
5
10
11
8
8
7
3
11
10
3
4
1
1
2
2
9
9
Flux NH4-N
extended FAST
first-order
total order
0.0008
0.02265
0.0352
0.09164
0.0184
0.27005
0.0003
0.02114
0.0013
0.02224
0.0050
0.05975
0.0043
0.03904
0.5775
0.69893
0.3539
0.45809
0.0128
0.10632
Morris 8-level


6
4
3
3
4
8
9
6
2
2
5
7
11
11
7
9
1
1
8
5
Flux NO3-N
extended FAST
first-order
total order
0.0046
0.0341
0.2174
0.4023
0.1357
0.2374
0.0002
0.0190
0.0061
0.0351
0.0475
0.2540
0.0038
0.0315
0.3557
0.5147
0.3255
0.4777
0.0060
0.0942
Biofilm models can provide results for state variables for the bulk phase as well as for the biofilm matrix.
However, most of the state variables can be observed only in the bulk phase of the reactor. Particularly with
regard to subsequent parameter estimation, sensitivity analysis of a biofilm model should therefore focus on the
state variables in the bulk phase.
Screening the parameter space for important parameters and applying a more detailed global sensitivity
method only to a reduced set of important parameters is a computational efficient method for calculating
quantitative sensitivity measures for models with long execution times.
Acknowledgement:
This study was supported by a research fellowship to Doris Brockmann from the Deutsche
Forschungsgemeinschaft (DFG) under grant No. BR 3556/1-1 and a CAREER award to Eberhard Morgenroth
from the US National Science Foundation under grant No. BES-0134104.
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