This work demonstrates the applicability of predictive analytics in the study of bioremediation by natural attenuation

1. Predictive Modeling of Natural Attenuation Processes in Soil
Orlu, R.N.a
, Stewart, D.I.a
, Bottrell, S.H.b
a
Institute of Public Health and Environmental Engineering, School of Civil Engineering,
b
Earth Surface Science Institute, School of Earth and Environment,
University of Leeds, Leeds, United Kingdom, LS2 9JT.
A two –level linear model for a sampling occasion i in a sampling period j is given below (where G and X represent the value on the level-2 and
level-1 predictors respectively):
§ The main aim of this study is to investigate the mechanisms of intrinsic, iron-mediated degradation of volatile petroleum hydrocarbons in
experimental analogues of subsurface regions (laboratory-constructed mesocosms).
§ Initial stages of experimentation involved the assessment of toluene removal in the presence and absence of a) extraneous sources of Fe3+
and b) differing soil matrices
§ The preceding stages involved analysis of the incubated material from the iron-amended (HM, GE, MT, FH, LP), soil-amended (S1, S2,
S3) and un-amended (SO, ST) mesocosms.
§ Statistical analysis using the mixed effects model approach was performed to produce a linear predictive model for toluene removal in the
un-amended and amended mesocosm groups over three sampling periods designated A, B, and C.
§ The analysis was performed using SPSS® software on a .05 alpha level with the data for total dissolved iron (Fe) and pH in the mesocosms
specified as level 2 and level 1 predictors respectively.
1. Atlas, R.M. and Philip, J. 2005. Bioremediation: Applied Microbial Solutions for Real world Environmental Cleanup. Washington, DC, : American society for Microbiology (ASM) Press.
2. Bagiella, E., Sloan, R.P. and Heitjan, D.F. 2000. Mixed-effects models in psychophysiology. Psychophysiology. 37(1), pp.13-20 Myers et al., 2013
3. Song, X.K. and Song, P.X.K. 2007. Correlated Data Analysis: Modeling, Analytics, and Applications. Springer.
4. Wang, L.A. and Goonewardene, Z. 2004. The use of MIXED models in the analysis of animal experiments with repeated measures data. Canadian Journal of Animal Science. 84(1), pp.1-11.
5. West, B.T., Welch, K.B. and Galecki, A.T. 2014. Linear Mixed Models: A Practical Guide Using Statistical Software, Second Edition. CRC Press.
6. Wu, L. 2009. Mixed Effects Models for Complex Data. CRC Press.
§ Repeatedly measured data from the mesocosm study showed toluene
concentrations, total dissolved iron and pH differed across the amended
and un-amended mesocosms.
§ Preliminary tests for correlation showed moderate (.30 < r < .50) to high
(.50 < r < 1.0) correlation in the time series data for mesocosm pH,
toluene, concentrations and total dissolved iron concentrations (Fe).
§ Tests for normality also indicated the data to be normally distributed.
§ The results of parameter estimation for the period A, B and C data
suggest the specified variables may not be suitable predictors of toluene
removal.
Linear model estimation for panel data is based on the classical general linear model (West et al., 2014). Classical general linear models include regression analysis, analysis of variance or ANOVA, and analysis of covariance or
ANCOVA. Classical general linear model or GLMs are used as statistical tools for experiments with continuous variables and are naturally studied in the framework of the multivariate normal distribution. Mixed effects models
are a rapidly growing application of basic multilevel modeling of longitudinal data. A mixed effect model incorporates the fixed effects assumption (i.e. that the individual specific effects are correlated with the individual
variables) as well as the random effects assumption (i.e. that the individual specific effects are uncorrelated with the independent variables). Data obtained from experimental or observational studies in which data is collected
over several points in time are referred to as repeated measures data (Taris, 2000; Verma, 2015; Nemec and Branch, 1996). The mixed effects model is considered a more appropriate method for analysing repeatedly measured
continuous data in comparison to classical GLMs as mixed models are based on less restrictive assumptions and provide a generally more flexible approach by allowing a wide variety of correlation patterns (or variance-
covariance structures) to be explicitly modeled (Bagiella et al., 2000; Wu, 2009). Monitored natural attenuation is a passive remedial approach which harnesses natural microbial processes to reduce the amount of contaminant in
soil or groundwater. Biodegradation studies assessing the fate of petroleum hydrocarbons in the unsaturated zone through a natural attenuation process may involve the collection of data over several time points. Mixed
effects models avoid violations due to missing data and unequal spacing making the approach particularly suitable for predictive modeling of repeatedly measured data from biodegradation studies.
Table 8.4 Parameter estimates for the level-2 mixed effects model of toluene removal with
predictors*
Parameter Period Estimate Value of test
statistic
p-value
FIXED EFFECTS PARAMETERS
ϒ00 Period A
Period B
Period C
1.610
1.773
15.2
t = -3.305
t = -1.028
t = -1.696
p = .001
p =.283
p = .096
ϒ10 Period A
Period B
Period C
.261
.309
2.23
t = 4.132
t = 1.415
t = 1.854
p = .0001
p =.160
p = .069
ϒ01 Period A
Period B
Period C
.259
.332
.985
t = 2.140
t = 1.865
t = 1.691
p = .035
p =.065
p = .097
ϒ11 Period A
Period B
Period C
.041
.048
.413
t = -2.615
t = -2.141
t = -1.810
p = .010
p =.035
p = .076
VARIANCE-COVARIANCE PARAMETERS
U0j Period A
Period B
Period C
.047
.294
.853
z = 3.368
z = 2.904
z = 2.269
p = .001
p =.004
p = .023
U1j Period A
Period B
Period C
.294
.003
.002
z = 2.904
z = 2.640
z = 2.093
p = .004
p =.008
p = .036
rij Period A
Period B
Period C
.008
.012
.008
z = 7.612
z = 7.000
z = 5.049
p = .0001
p =.0001
p = .0001
*All tests were performed at the .05 alpha level
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
6 7 8 9 10 11
0.0
0.2
0.4
0.6
0.8
1.0
12 13 14 15 16 17
0.0
0.2
0.4
0.6
0.8
1.0
BA C
Toluene(mM)
Period
SO
ST
HM
GE
MT
FH
LP
S1
S2
S3
Toluene(mM)
Period
SO
ST
HM
GE
MT
FH
LP
S1
S2
S3
Toluene(mM)
Period
SO
ST
HM
GE
MT
FH
LP
S1
S2
S3
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
6 7 8 9 10 11
0.0
0.2
0.4
0.6
0.8
1.0
12 13 14 15 16 17
0.0
0.2
0.4
0.6
0.8
1.0
BA C
Toluene(mM)
Period
SO
ST
HM
GE
MT
FH
LP
S1
S2
S3
Toluene(mM)
Period
SO
ST
HM
GE
MT
FH
LP
S1
S2
S3
Toluene(mM)
Period
SO
ST
HM
GE
MT
FH
LP
S1
S2
S3
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
6 7 8 9 10 11
0.0
0.2
0.4
0.6
0.8
1.0
12 13 14 15 16 17
0.0
0.2
0.4
0.6
0.8
1.0
BA C
Toluene(mM)
Period
SO
ST
HM
GE
MT
FH
LP
S1
S2
S3
Toluene(mM)
Period
SO
ST
HM
GE
MT
FH
LP
S1
S2
S3
Toluene(mM)
Period
SO
ST
HM
GE
MT
FH
LP
S1
S2
S3
Background
Analytical approach Preliminary findings
References