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9th European Waste Water Management Conference
12-13 October 2015, Manchester, UK
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Organised by Aqua Enviro Limited
THE IMPACT OF DATA AVAILABILITY ON PREDICTIVE ACCURACY OF
WASTEWATER TREATMENT WORKS MODELS
Ashagre, B. B.1* Fu, G.1 Davidson, K.2 Butler, D.1
1University of Exeter, UK, 2Scottish Water, UK *Corresponding author [email protected]
Abstract
In order for wastewater treatment works (WwTW) models to be used with confidence for active control
it is important to perform model calibration to accurately represent its performance. Data is usually a
limitation in achieving high levels of calibration since it can be costly and time consuming. Thus it is
important to carefully assess the minimum data requirement and determine the need for further data
collection. This study assesses how far model performance can be improved by considering more
frequent and perhaps costly monitoring .This is achieved by comparing simulated quality indicators
with a measured dataset after performing sensitivity analysis to identify parameters to which the
model is most sensitive. WwTW models are tested using three different datasets of increasing number
of quality variables. Calibration accuracy, as measured using R2 and RMSE goodness-of-fit tests,
increases for TSS and NH3-N concentrations as compared to the baseline for scenarios two and
three, albeit still with low absolute values. In this case study, the results indicate the importance of
characterising influent wastewater organic matter and nitrogen concentrations to reduce prediction
uncertainty and help build confidence in the use of models for active control.
Keywords
Active control, calibration, data reconciliation, wastewater treatment
Introduction
Future demand for model based control of wastewater treatment works is expected to increase. In
Europe, including the UK, models are mostly a research subject whereas in other parts of the world
like North America Wastewater Treatment Works (WwTWs) are predominantly used as an
engineering tool in practice (Hauduc et al. 2009). This is now changing in the UK, and water utilities
have started to incorporate WwTW models in decision making, process control and optimisation.
According to UKWIR (2013) WwTW models are now being used for advanced process control and
this practice is expected to increase significantly in the future due to tighter regulations and the
potential of this approach to save energy, chemical usage and greenhouse gas emissions. One of the
challenges is the availability of data and their quality.
High quality data is crucial for the effective use of WwTW models. The reliability of model results is
strongly linked to the amount of the data used to set up and calibrate the model (Rieger et al. 2010).
A carefully designed and collected dataset can reduce time for the subsequent modelling study and
also can increase the confidence in using the model for practical application. In addition, data scarcity
and low quality data can distort the simulation results and increase the chance of faulty conclusions,
which might lead to very expensive decisions and/or could cause breaching of licenses.
Historical data can be used to understand the long-term behaviour of the treatment works. Dynamic
modelling for control purposes requires high resolution spatial and temporal data, which includes sub-
daily monitoring of various parameters. Stoichiometric/kinetic data can also be monitored to
accurately estimate the model parameters. However, this can be costly and demand experience to
achieve all these datasets. Thus, it is important to determine what level is sufficient for the model-
based study.
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The importance of monitoring wastewater within the WwTW has been suggested to be crucial both for
design and modelling purposes (Gernaey et al. 2006, Melcer 2003, Metcalf & Eddy 2004, Rosén et al.
2003), but the question is what level of data is sufficient to have reasonable confidence in the model
to be used for active control purpose. The aim of this paper is therefore to investigate the model
performance using different levels of dataset. Hence, two scenarios were used in this study, in
addition to a baseline scenario, each with a different level of data availability in order to set up and
calibrate the model. The differences in model performance among the scenarios are used to assess
the benefit of using the specific dataset considered in the corresponding scenario.
Methodology
The case study
The case study wastewater treatment works has a design capacity of 15,000 P.E. (Population
Equivalent) with current load of 16,000 PE or a throughput of 89L/s. The incoming flow enters the works
through an inlet chamber and passes to a band screen. Screened sewage passes under a weir and
flows below 3 x DWF (90L/s) flow to a grit trap and any flow above 3 x DWF bypasses to the storm
tanks. Following screening and de-gritting, the sewage gravitates into a wet well from where it is pumped
by 3 duty/standby/assist pumps to the oxidation ditch for secondary treatment. Based on the water level
in the inlet wet well at the pumping station, water will return from the storm tanks and the liquor buffer
tank back to the wet well through gravity. The return flows combined with online sewage flow are then
pumped to the oxidation ditch which has a capacity of 2980m3 and a maximum depth of 4m. The
schema of the whole treatment work is presented in Figure 1.
In this study, the IWA Benchmark Simulation Model 2 (BSM2) was used to model the WwTWs under
consideration. BSM2 uses the MATLAB® platform and was built using Simulink®. By modifying the
existing typical wastewater scheme into BSM2, the scheme and processes of the existing wastewater
treatment plant were represented.
Biochemical processes in oxidation ditches have previously been modelled using ASM1 (e.g. (Abusam
and Keesman 1999, Abusam et al. 2003, 2001) and it has been suggested that 10 continuously stirred
reactors are sufficient for adequate representation of the aeration configuration (Abusam and Keesman
1999). In this instance, twelve reactors were found to be the required amount to represent the
configuration of blowers and the influent and effluent flows from the ditch.
From the oxidation ditch, the biologically treated sewage (the 'mixed liquor’) passes into two final
settlement tanks. The final effluent from the settlement tank overflows over a weir into an outlet channel
from where it gravitates to a sampling chamber and is discharged into the nearby river.
The two final settlement tanks are modelled as a single tank with a surface area of 928 m2 and volume
of 1628 m3, using the a ten-layer model, based on Takács et al. (1991). This assumes no biological
activity occurs in the final settlement tanks.
Dataset
Data monitoring locations are shown in Figure 1 and the data availability corresponding to these
points is discussed in this section. The model was run to simulate 200 days; the first 100 days were
used to warm up the model, the next 100 days were used for calibration purposes.
The flow data were used to cross check control philosophies collected from operational manuals and
interview with operators, to complete the hydraulic balance and assess the hydraulic performance of
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the work (the hydraulic performance of the WwTW is not the focus of this paper and won’t be
discussed further) flow to the WwTW, to inlet well, to oxidation ditch from inlet well, RAS and SAS
flow, and final effluent.
Water level data were used to estimate the return flow rate from storm tanks to inlet wet well. The inlet
wet well level and the flow from the inlet well to the oxidation ditch were used to create a correlation
between flow from pumping station and water level in the inlet wet well. This correlation was used to
model the flow from inlet wet well to oxidation ditch based on water level in the wet well. The 15
minute time step influent flow was used in the dynamic influent model input dataset.
Quality data were available on a daily basis, which were measured using a daily composite sample.
These measured quality data include; biochemical oxygen demand (BOD), total suspended
solids(TSS), ammonia (NH3-N or SNH), pH, temperature, soluble reactive phosphorus (SRP), and total
phosphorus (P). Most of these measured quality data from the influent wastewater, except SRP and
P, were used in creating dynamic influent flow concentrations which are discussed in the baseline
model calibration section.
Figure 1 shows location of points where data was available. The available information at each location
varies both in content and temporal resolution. Points 1, 4, and 7 have flow data at 15 minutes time
step and daily average data on wastewater quality. Data points 8, 11, and 18 have only daily average
quality data. Some only have flow data at 15 minutes time step, this includes; data points 3,5,12, and
13. Imported wastewater and sludge from different works are deployed at point 2 and 16 respectively.
Volume and time at which the wastewater/sludge imported was available. Data on volume and time of
surplus activated sludge (SAS) removal is available, point 14. Data on wells’ and tanks’ level at point
9, 10, 15, 17, and 19 were available at 15 minutes time step. Mixed liquor (MLSS) level and dissolved
oxygen (DO) within the oxidation were measured at 15 minutes time step, point 6.
Figure 1: Scheme of the wastewater treatment work
Screens
Grit trap
Inlet wet well
Oxidation
ditch
Storm tank 1 Tanks
Final settlement tank 1
Final settlement tank
2
Final effluent
chamber
Screen to skip
Combined sewer
network
Tankered imports
Sludge dewaterin
g tank
Super-natant pump well
Decanted liquor
chamber
Sludge holding
tank Centrifuge
Liquor buffer tank
Sludge cake
Final
effluent
SAS impor
1 3 4
5 6
10
9
18
8
17
14 13
12
15
7
16
19
11
2 Backwash
water
Wastewater
RAS/SAS/Sludge
Liquor return
Storm water
Screenings/grit
Potable water
Grit to skip
RAS
SA
S
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Model calibration
In order to assess what data set plays a crucial role in improving model calibration accuracy in
simulating TSS and NH3-N, three different scenarios were assessed. The first scenario, which is the
baseline, was set up using available data but it was assumed that MLSS and DO data were not
available and were not used in model calibration. In the second scenario, which is the MLSS and DO
scenario, the 15 minutes time step data was known and were used for model calibration. In the last
scenario, a different approach in characterising influent wastewater was used. The details on each of
the scenario are discussed below.
Baseline
The WwTW model contains information on operational procedures, existing set points for control
purposes, and infrastructure details such as dimensions, maximum capacity and working capacity. In
addition, commonly monitored parameters such as flowrates which were monitored at a 15 minute
time step at the influent and effluent points, and daily average influent and final effluent measured
quality indicators (TSS and NH3-N) were used. TSS and NH3-N were measured using a daily
composite sample for each day of the whole calibration period. Converting the daily data into sub
daily data and fractionation of COD was carried out by imitating the sub daily pattern of pollutants
from the BSM2 model and using fractions used in Gernaey et al. (2005),.
The model inputs that are required to characterise influent wastewater are given in Table 1.
Table 1: BSM2 model inputs: Influent wastewater characteristics
Soluble COD Particulate COD Nitrogen Others
Soluble inert organic matter (SI) Particulate inert organic matter (XI)
Nitrate and nitrite nitrogen (SNO)
Oxygen (SO)
Readily biodegradable substrate (SS)
Slowly biodegradable substrate (XS)
NH3 nitrogen (SNH) Alkalinity (SALK)
Active heterotrophic biomass (XB,H)
Soluble biodegradable organic nitrogen (SND)
Total Suspended solid (TSS)
Active autotrophic biomass (XB,A)
Particulate biodegradable organic nitrogen (XND)
Flow rate
Particulate products arising from biomass decay XP
Temperature
The influent wastewater concentration of XB,A, particulate products arising from biomass decay (XP),
oxygen (SO), and nitrate and nitrite nitrogen (SNO) were assumed to be zero (Jeppsson et al. 2007).
The particulates concentration; particulate inert organic matter XI, slowly biodegradable substrate XS,
and active heterotrophic biomass XB,H were estimated from the measured daily average TSS and
fractions used in Gernaey et al. (2005).
Readily biodegradable substrate SS is the difference between the soluble inert organic matter (SI) and
the total soluble COD (bCOD). bCOD was estimated from measured biochemical oxygen demand
(BOD) and the ratio between ultimate biological oxygen demand (UBOD) and BOD; for typical
domestic wastewater UBOD⁄BOD is equal to 1.5 (Metcalf & Eddy 2004). Using synthesis yield
coefficient of 0.67(Jeppsson et al. 2007), bCOD was estimated to be equivalent to 75% of BOD. Since
the measured BOD has considerable gaps, correlation between BOD and TSS was used to generate
a complete BOD dataset. The correlation in Figure 2 showed a significant correlation between BOD
and TSS with a regression coefficient R2 equal to 0.615.
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Figure 2: Correlation of measured BOD and TSS
The soluble inert organic matter, SI, was estimated to be 21mg/L which was based on the ratio
between total average of measured TSS and total average of TSS in Jeppsson et al. (2007).
For this case study, the raw influent diurnal ammonia concentration (SNH) was estimated based on the
ratio between daily measured SNH and the daily average of SNH from BSM2 dynamic influent data.
Due to data paucity on total Kejldhal nitrogen, the particulate organic nitrogen XND were estimated by
using BSM2 XND and the ratio of daily measured average SNH of the WwTW and the daily average of
SNH of BSM2. SND was calculated using the fraction; fraction of organic nitrogen that is soluble and
degradable (𝑆𝑁𝐷_𝑓𝑟 = 0.247) of the total organic nitrogen, and fraction of organic nitrogen that is
particulate and degradable (𝑋𝑁𝐷_𝑓𝑟 = 0.753) (Gernaey et al. 2005).
Using MLSS and DO data
In this case the modeller has data on Mixed Liquor Suspended Solid (MLSS) and Dissolved Oxygen
(DO) in the oxidation ditch at 15 minutes time steps. The MLSS data were used to further calibrate the
SAS flow control operation and the DO data were used to calibrate the DO control feedback loop
used in the model. MLSS and DO at 15 minutes time steps were used to understand the DO control
and SAS removal better. The SAS control was revised and its removal operation was triggered based
on the MLSS level in the oxidation ditch. The SAS removal in the baseline was set up to be instigated
once every other day to discharge 200m3 of SAS into the sludge holding tank. In this scenario, the
removal operation was continuous but the SAS removal would not be instigated if MLSS is lower than
3000 mg/L. The DO control in the baseline was set up using a PID (Proportional Integral Derivative)
controller to a set point of 0.75mg/L. In this scenario DO control is set up the same as the baseline but
the blower will switch off if the DO level in the oxidation ditch is higher than 2.25mg/L. In addition, the
sensor in the baseline line was ‘type A’ which is close to an ideal sensor but in this scenario, by
observing the measured DO level in the oxidation ditch, sensor type B was selected which is a
intermittently measuring sensor with a time delay of 10 minutes and a measuring interval of 5 minutes.
Using a phenomenological influent generator to estimate pollutant concentrations
In this case, modelling WwTWs has become standard practice in order to implement automated
controls and optimisation of waste water treatment works’ operations. Water service providers accept
that a detailed characterisation of the wastewater organic matter is crucial in modelling wastewater
treatment works. This can be achieved by fractionating the total COD into fractions with different
microbiological properties (Henze et al. 2000).
y = 0.3945x + 120.33R² = 0.615
0
100
200
300
400
500
600
700
800
900
1000
0 500 1000 1500 2000
BO
D m
g/L
TSS mg/L
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Due to data limitations the benefit of characterising wastewater influent to the WwTW was assessed
in this study by generating pollutant patterns using a phenomenological wastewater generator model
(Gernaey et al. 2011). This produced wastewater influent data for the BSM2 taking into account
process control and optimisation. Since the model is ‘open source’, users can modify the original
structure in order to customise the model for a specific study area in hand. Considering that this
approach is flexible, and easily linked to BSM2, it was used in this scenario to characterise
wastewater influent to the WwTW.
Sensitivity analysis, calibration and model performance
It is essential to calibrate developed models due to the uncertainty in model structure, model
parameters or underlying uncertainties in the (incomplete) measured data. In complex process-based
models, calibration can be a complex and time-consuming process due to high numbers of model
parameters and the poor identifiability associated with large parameter sets. Sensitivity analysis helps
to identify the parameters that most influence the model output and hence, reduce the number of
parameters to consider for calibration purposes.
The sensitivity is carried out using one-factor-at-a-time (OAT) approach in order to identify the most
significant parameters for model calibration purposes. Since the focus was to identify the most
sensitive parameters for the purpose of model calibration, evaluation criteria that indicate the WwTWs
model’s performance in simulating TSS and NH3-N were used. The evaluation criteria assess how
close or far simulated TSS and NH3 are from measured TSS and NH3-N respectively both in terms of
pattern and residual error. This was represented by the use of statistical tests, the Root-Means-
Square-Error (RMSE),𝑹𝑴𝑺𝑬= √∑(𝒚𝒊−𝒙𝒊)𝟐
𝒏 1, and
coefficient of regression R2, 𝑹𝟐=∑[(𝒙𝒊−�̅�)×(𝒚𝒊−�̅�)]𝟐
[∑(𝒙𝒊−�̅�)𝟐]×[∑(𝒚𝒊−�̅�)𝟐] 2.
𝑹𝑴𝑺𝑬 = √∑(𝒚𝒊−𝒙𝒊)𝟐
𝒏 1
Where; 𝑦𝑖 is simulated daily average final effluent quality indicator (TSS or NH3-N), 𝑥𝑖 is measured
daily average (TSS or NH3-N), 𝑛 is number of data point or days used for analysis.
𝑹𝟐 =∑[(𝒙𝒊−�̅�)×(𝒚𝒊−�̅�)]𝟐
[∑(𝒙𝒊−�̅�)𝟐]×[∑(𝒚𝒊−�̅�)𝟐] 2
Where; �̅� is the average of the measured daily average values, �̅� is the average of the simulated daily
average values.
The R2 and RMSE of the uncalibrated model were calculated first. The percentage change in the
value of these evaluation parameters due to change in value of sensitivity parameter was assessed in
order to identify the most sensitive parameter, for example, percentage change in R2 in simulating
TSS at literature average and upper bound of b_H.
The wastewater treatment parameters listed (kinetic and stoichiometric parameters) for the ASM
(Activated Sludge model) were adopted from Jeppsson et al. (2007), see Table 2. Details on
parameters related to settlement tanks can be found in the studies Jeppsson et al. (2007) and Takács
et al. (1991). Additional parameters which are reported in other studies as being sensitive but
dependent on the operational philosophy of the plant for example oxygen transfer rate are not
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assessed in the sensitivity analysis. Instead, they were manually adjusted and calibrated based on
available information.
Table 2: Parameters used for sensitivity analysis
Para-
meters Description
Literature
average
Lower
bound
Upper
bound Remark/ References
mu_H Maximum specific growth rate for
heterotrophic biomass [d-1]
8.000 3.000 13 a, b, e
K_S Half-saturation coefficient for heterotrophic
biomass
[g COD.m-3]
95.000 10.000 180 Ks (mg/L) value varies from 50 - 120 for domestic waste
(g, b, a)
K_OH Oxygen Half Saturation Coefficient for
heterotrophic biomass
[g (-COD).m-3]
1.150 0.300 2 K_OH value was reported
1mg/L (g, h, a)
K_NO Nitrate NO3-N half saturation coefficient for
heterotrophic biomass [g NO3-N.m-3]
0.150 0.100 0.2 a
b_H Decay coefficient for heterotrophic biomass
[d-1]
0.825 0.050 1.6 b_H without recycling was found to vary from 0.05 day-1 to 1.6 day-1 for some food-
processing wastes (a)
mu_A Maximum specific growth rate for autotrophic
biomass [d-1]
0.495 0.340 0.65 This parameter is strongly associated with the removal
of ammonia nitrogen (a)
K_NH Ammonia half-saturation coefficient for
autotrophic biomass
[g NH3-N.m-3]
1.000 0.500 1.5
c
K_OA Oxygen Half Saturation Coefficient for
autotrophic biomass
[g (-COD).m-3]
1.350 1.200 1.5
a, f
b_A Decay coefficient for autotrophic biomass [d-
1]
0.100 0.050 0.15 a
ny_g Correction factor for mu_H under anoxic
condition [dimensionless]
0.800 0.600 1 b, a
k_a* ammonification rate [m3.(gCOD.d)-1] 0.050 0.025 0.075 b, c
k_h* Maximum specific hydrolysis rate [g SBCOD.
(g cell COD. d)-1]
3.000 1.500 4.5 b, c, d
K_X* Half-saturation coefficient for hydrolysis of
slowly biodegradable substrate [g SBCOD.
(g cell COD)-1]
0.100 0.050 0.15
b, d
ny_h* Correction factor for hydrolysis under anoxic
condition [dimensionless]
0.800 0.400 1.2 b, d
Y_H Yield for heterotrophic biomass
[g cell COD formed. (g COD oxidized)-1]
0.575 0.460 0.69 a
Y_A Yield for autotrophic biomass
[g cell COD formed. (g COD oxidized)-1]
0.150 0.020 0.28 a
f_P* Fraction of biomass leading to particulate
products [dimensionless]
0.080 0.040 0.12 b, c
i_XB* Mass of nitrogen per mass of COD in biomass
[g N.(g COD)-1 in biomass]
0.080 0.040 0.12 b, c
i_XP* Mass of nitrogen per mass of COD in
products from biomass
[g N.(g COD)-1 in biomass]
0.06 0.030 0.09
b, c
v0* Secondary settlement maximum settling
velocity [m.d-1]
250 125 375 b, c
v0_max
*
Secondary clarifier maximum visilind velocity
[m.d-1]
474 237 711 b, c
r_h* Secondary settlement hindered zone settling
parameter [m3.(gSS)-1]
0.0006 0.0003 0.0009 b, c
r_p* secondary settlement flocculants zone settling
parameter [m3.(gSS)-1]
0.00286 0.00143 0.00429 b, c
f_ns* Secondary clarifier non-settleable fraction
[dimensionless]
0.00228 0.00114 0.00342 b, c
Henze et al (2002) argues that most kinetic parameters value varies widely and very dependent on the nature of the wastewater being treated.
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*Parameters whose upper bound (UB) and lower bound (LB) were taken ±50% of the average literature value.
a - Henze (2002), b - Benedetti et al. (2008), c - Jeppsson et al. (2007), d - Sweetapple et al. (2013), e - Dold (1986), f - Picioreanu et al. (1997)
g - Horan (1990), h - Henze (2008)
The model was run twice for each parameter with its lower and upper bounds values while keeping
the rest of the parameters’ value to the literature average. The six parameters to which the model was
sensitive, in terms of model performance measures (RMSE and R2), were selected for model
calibration purposes. In this study the term model performance is used to refer to how well the model
output is close to the observed dataset.
Four different values for the top six most sensitive parameters were used for model calibration; the
average value from literature, the lower/upper bound of the parameter and two more values in
between. The choice between lower and upper bounds was based on which limit (upper or lower) of
the parameter gave the highest percentage change in model calibration accuracy indicators, R2 and
RMSE. 4096 different combinations were created and the WwTW model ran 4096 times.
In order to assess the impact of having different levels of dataset on model performance, it is
necessary to follow the same calibration procedure in all the scenarios. This can avoid the
introduction of model performance increase/decrease due to inconsistent calibration levels. For this
reason, the same calibration procedure was carried out for each scenario.
Results and Discussion
The OAT sensitivity analysis results are presented in 4 and 5, showing the percentage change in
model performance indicator with respect to the base case (literature average value) when each
parameter was set to its respective upper and lower bounds. The variation of parameter values within
the feasible range can have a significant effect in model performance. The OAT sensitivity result
showed that the model performance indicators R2 and RMSE are highly sensitive to; b_H, r_h, Y_H,
Y_A, V0, f_ns, f_P, i_XB, K_S and K_OH which were also identified as sensitive parameters by
Benedetti et al. (2008) and Sweetapple et al. (2013). However, the model was not sensitive to
changes in b_A and to changes to V0_max at its upper bound.
The parameters to which the model is highly sensitive were selected in such a way that the first four
parameters that impact TSS R2 and RMSE were selected first. Second, the top four parameters that
highly affect NH3-N R2 and RMSE were selected and further assessed for calibration, see Error!
Reference source not found..
Unlike TSS, the NH3-N model performance indicators R2 and RMSE were always positively
correlated, i.e. parameter value change that results in increase of NH3-N R2 were also observed to
increase the of NH3-N RMSE. This is because parameter changes that result in NH3-N pattern similar
to the measured one but their values are far from the measure NH3-N. As a result, in the selection of
parameters for calibration more emphasis was given to NH3-N RMSE than R2.
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Figure 3: Percentage change in R2 and RMSE in simulating TSS
Figure 4: Percentage change in RMSE and R2 in simulating NH3-N
Since b_H was the most sensitive in all the measures at its lower bound, its lower bound range was
selected for calibration purposes. K_OH and K_S at their upper bound significantly increased model
performance indicators in simulating both TSS and NH3-N except they reduced R2 in simulating NH3-
N. Since the upper bound of these parameter improved model performance in most aspects, at a
higher degree, their upper bound range was selected for model calibration.
The maximum settling velocity in the secondary settlement tank (V0) at its upper bound and r_h at its
lower bound increases the model performance in simulating TSS but their impact on model
performance in simulating NH3-N is negative, especially the r_h. Due to their significant impact on
model performance in simulating TSS, these parameters were used for further calibration.
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Y_A at its lower bound reduced the RMSE in simulating NH3-N and TSS, and increased the R2 in
simulation of NH3_N and TSS. Y_H increased model performance in simulating TSS and NH3-N as
demonstrated by the R2 but it reduces the model performance due to a considerable increase in
RMSE at its lower bound. Since more emphasis was given to RMSE than R2 in analysing model
performance in simulating NH3-N, Y_A was selected for model calibration.
Selected parameters for model calibration and their respective four different values are listed in Table
3. The model has run for each unique combination of these parameters, which is discussed in the
next section.
Table 3: Most sensitive parameters selected for model calibration
Parameters used for calibration Values used for model calibration
b_H [d-1] 0.05 0.308 0.566 0.825
r_h [m3.(gSS)-1] 0.0003 0.0004 0.0005 0.0006
K_OH [g (-COD).m-3] 1.15 1.43 1.72 2.0
V0 [m.d-1] 474 553 632 711
K_S [g COD.m-3] 95 38.33 66.66 10
Y_A [g cell COD formed. (g COD oxidized)-1] 0.15 0.106 0.063 0.02
Calibration result for baseline model
The baseline model was calibrated using a semi-automated approach with the different combinations
of parameter values listed in Table 3. The model was run 4096 times to identify the best fit model
parameter combinations under calibration. Figure 5 shows that the model performance for the
baseline is not high with a maximum R2 value of 0.016 in simulating NH3-N and 0.015 in simulating
TSS. The parameter combinations which gave the highest R2 are not the ones which gave the lowest
RMSE, see Figure 6. The points with the same colour in figure 6 and 7 represents a simulation with
the same parameter values combinations. There were five combinations of parameters which gave R2
to be above 0.013 both for NH3-N and TSS. These combinations have RMSE between 3.6 – 3.8 for
NH3-N and 10 – 10.7 for TSS.
In absolute terms, the calibration accuracy indicators have low values. Since there is no consensus
on how to apply these performance measures nor has been their applicability over different value
ranges been established (Belia et al. 2009), it has not been possible to compare them with a
standard. Most often visual comparison is used as the only form of model performance assessment.
Ahnert et al. (2007) discussed the difficulties in finding a common basis for a standardised evaluation
of goodness-of-fit measures in wastewater treatment works modelling but unfortunately a benchmark
to compare model performance was not proposed.
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Figure 5: Calibration result baseline: model performance indicator R2 in simulating TSS
and NH3-N
Figure 6: Calibration result baseline: model performance indicator RMSE in simulating
TSS and NH3-N
Calibration result MLSS and DO scenario
Similarly this scenario was run 4096 times using the same parameter combinations. This scenario
resulted in more simulation runs having higher R2 values both in simulating NH3-N and TSS. There
were 55 simulations with R2 higher than 0.013 both for NH3-N and R2, see Figure 7. These
simulations also had the lowest RMSE ranging between 8.5 – 11mg/L for TSS and 2.6 – 2.85 for NH3-
N, see Figure 8. Higher numbers of accurate models were observed in this scenario than the baseline
scenario both in terms of R2 and RMSE.
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Figure 7: Calibration result MLSS and DO scenario: model performance indicator R2 in
simulating TSS and NH3-N
Figure 8: Calibration result MLSS and DO scenario: model performance indicator RMSE
in simulating TSS and NH3-N
Calibration results for the phenomenological influent generator scenario
In this scenario the model performance in simulating the NH3-N increased significantly but its
performance in simulating TSS did not change significantly. The R2 in simulating the NH3-N were
observed to be as high as 0.3 and 0.02 in simulating TSS, see Figure 9.
The parameter combinations which gave high R2 in simulated NH3-N were not the ones which
resulted in the highest R2 in simulating TSS, unlike the above two scenarios. One of the reasons for
this is the use of the same sensitivity analysis result that was used in the above two scenarios which
were built using different influent concentration inputs. Since a different input was used in this
scenario it would have been useful to run another sensitivity analysis and identify the most sensitive
parameter and define whether it is the upper bound or the lower bound which increases model
performance etc. However, model performance in simulating NH3-N increased much more than the
model performance in simulating TSS.
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Figure 9: Calibration result phenomenological influent generator scenario: model
performance indicator R2 in simulating TSS and NH3-N
Figure 10: Calibration result phenomenological influent generator scenario: model
performance indicator RMSE in simulating TSS and NH3-N
Conclusions
This paper investigated the performance of a WwTWs model that is potentially be used for active
control. The preliminary results obtained from the case study show the changes in model performance
under three scenarios of different levels of data availability in the model setup and calibration process.
The second scenario that uses measured MLSS and DO dataset in the calibration process shows a
slight model performance improvement.
The study showed that not all measured data increase model performance at equal level. The use of
a phenomenological influent generator achieved a higher improvement in model performance than the
use of MLSS/DO dataset. This is because a number of assumptions have to be made in the baseline
scenario in characterising the influent wastewater, due to lack of detailed influent quality data. The
low absolute model performance indicator values show a need for further model calibration and data
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monitoring, especially in characterising the influent wastewater. Thus, monitoring the influent quality at
a finer time scale and fractionating COD and total nitrogen can help modellers by avoiding
unnecessary data matching efforts in order to improve model performance.
Acknowledgments
This project is sponsored by EPSRC and Scottish Water as part of the STREAM Programme.
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