tion Systems, Waltham, MA generated an isosurface connecting the surface voxels. The generated isosurface had an associated list of coordinates of vertices of a
polyhedron with triangular facets which are determined by the tessellation of values of the surrounding 26 voxels Montemagno and Gray, 1995. Summation of these
triangular areas was a measure of biofilm surface area.
2
.
5
. Statistical analysis Analysis of variances ANOVA was used to detect differences in biofilm
structure due to sand sizes 0.23 versus 0.60 mm and physical location within the reactor vessel high versus low. The biofilm characteristics of interest were volume
per unit sand area, surface area per unit sand area, and surface area per biofilm volume. Analysis of variances were performed on all three parameters to detect
significance due to reactor variability and depth for a particular sand size. Data from reactors of the same sand size was grouped and additional ANOVA tests were
performed to detect significance of sand size on measured parameters. All tests of significance were performed at an alpha level of 0.05.
Stabilized variance is a necessary requirement for ANOVA tests. However, residual versus fitted plots of biofilm volume per unit sand area and biofilm surface
area per unit sand area revealed increasing variance with increasing measurement values. Similar patterns were observed by Gjaltema et al. 1997. Snedecor and
Cochran 1989 suggest using a natural log transformation as an appropriate method to stabilize variance in these cases for ANOVA tests. Residual versus fitted
plots and linear normality plots of transformed data confirmed stabilized variance. No transformation was necessary with biofilm surface area per biofilm volume since
raw data was normally distributed with a stabilized variance.
3. Results
The means and standard errors of biofilm volume per unit sand area, biofilm surface area per unit sand area, and biofilm surface area per biofilm volume
according to reactor, sand size, and sampling location are given in Table 2.
3
.
1
. Effect of sand size ANOVA tests, which grouped data of all reactors with the same sand size,
showed a very significant effect of sand size on biofilm volume per unit sand area P-value 0.000 and biofilm surface area per unit sand area P-value 0.000.
Statistically, effect of sand size on biofilm surface area per biofilm volume was also significant P-value 0.006. However, the magnitude of the two means were
numerically similar 0.49 per mm, se = 0.27 and 0.55 per mm, se = 0.20 for small and large sand reactors, respectively. Therefore, we do not consider these films to
be practically different from the other, but essentially being similar from a structural perspective. This is a very important finding.
219 T
.K .
Nam et
al .
Aquacultural
Engineering
22 2000
213 –
224
Table 2 Means and standard errors of biofilm volume per projected sand area, biofilm surface area per projected sand area, and biofilm surface area per biofilm
volume for small and big sand reactors at low and high column depths Reactor
Biofilm volume per projected Depth in reac-
Biofilm surface area per pro- Effective sand
Biofilm surface area per biofilm volume per mm
jected sand area tor cm
sand area mm diameter mm
0.23 0.46 9 0.20
i
20.5 12.18 9 0.65
a
S1 5.11 9 0.40
e
0.23 0.58 9 0.36
i
S1 70.5
11.26 9 0.39
f
21.97 9 0.49
b
0.48 9 0.19
i
0.23 20.5
16.71 9 0.38
a
7.98 9 0.43
e
S2 7.94 9 0.55
f
0.42 9 0.19
i
0.23 S2
70.5 19.38 9 0.51
b
0.54 9 0.24
i
0.23 20.5
7.53 9 0.48
a
3.73 9 0.39
e
S3 S3
0.44 9 0.25
i
8.04 9 0.52
f
0.23 19.89 9 0.57
b
70.5 0.49 9 0.18
j
0.60 20.5
7.73 9 0.27
c
3.71 9 0.20
g
B1 0.55 9 0.20
j
0.60 70.5
6.44 9 0.38
c
3.39 9 0.35
g
B1 3.12 9 0.69
h
0.54 9 0.15
j
6.09 9 0.74
d
B2 20.5
0.60 1.94 9 0.40
h
0.57 9 0.26
j
70.5 B2
3.50 9 0.42
d
0.60 B3
0.58 9 0.09
j
0.60 2.47 9 0.38
h
20.5 4.26 9 0.35
d
B3 0.60
70.5 4.50 9 0.41
d
2.41 9 0.44
h
0.55 9 0.24
j a
: means and standard deviations marked with the same letter are not statistically different.
3
.
2
. Effect of sampling location Biofilm volume per unit sand area P-value 0.004 and biofilm surface area per
unit sand area P-value 0.004 were statistically different at low locations than high locations for small sand reactors. In large sand reactors, depth had no effect on
biofilm volume per unit sand area P-value 0.149 or biofilm surface area per unit sand area P-value 0.150. Biofilm surface area per biofilm volume was not affected
by sampling depth for either small P-value 0.572 or large P-value 0.521 sand reactors.
3
.
3
. Effect of reactor 6ariability For small sand reactors, biofilm volume per unit sand area P-value 0.105,
biofilm surface area per unit sand area P-value 0.065, and biofilm surface area per biofilm volume P-value 0.248 did not significantly vary from one replicate reactor
to another. In large sand reactors, biofilm volume per unit sand area P-value 0.002 and biofilm surface area per unit sand area P-value 0.003 were statistically
different within replicate reactors. Of the large sand reactors, samples from one reactor had slightly higher biofilm volume and surface area per unit sand area 7.09,
se = 0.32 versus 4.79, se = 0.73 and 4.38, se = 0.38 mm for biofilm volume per unit sand area and 3.55, se = 0.28 versus 2.53, se = 0.67 and 2.44, se = 0.40 for biofilm
surface area per unit sand area, thereby causing a significant effect due to reactor variability. Despite these slight variations in large sand reactors, it is interesting to
note that biofilm surface area per biofilm volume P-value 0.356 did not vary significantly within replicates of large sand reactors.
4. Discussion
