52
w. PuIs· T. Pohlmann· J. Siindermann
4.3
Temporal Variation of SPM Concentrations
The temporal variation of measured and computed depth averaged SPM concentrations c at each separate NSP station is determined from the same measured
or computed data which are the basis for the mean SPM concentrations shown
in Figs. 11 and 12. The evaluation is done in logarithmic terms log c, resulting in
a mean value mean (log c) and a standard deviation cr(log c). After having taken
the anti-logarithm, the final result, i.e. the temporal variation, is expressed as a
standard deviation factor lO cr (log c). The mean concentration is then (i) divided
by this factor and (ii) multiplied with this factor, resulting in a concentration
range which is somehow equivalent to a "normal" standard deviation. To give an
example: The original SPM concentration time series is {0.2, 2, 20} mg 1-1. In logarithmic terms, the data is {-0.70, 0.30, 1.30}. The mean and the standard deviation of the log-data is:
mean(logc) ± cr(logc) = 0.30± l.
Taking the anti-logarithm, the mean SPM concentration is 10°.30 = 2 mg 1-1,
the std. dev. factor is 10 1 = 10. The variability range of SPM concentrations is
thus from 2110 = 0.2 mg 1-1 to 2 x 10 = 20 mg 1-1.
There is a principal problem with the temporal variability of SPM concentrations. SPM concentrations are regarded on a logarithmic scale (see Sect. 4.2).
SPM erosion, however, rather acts on a linear scale, because the increase in the
SPM concentration in the water column by erosion does (of course) not depend
on the SPM background concentrations at the specific site. To give an example:
there are two SPM regimes with background concentrations of 1 mg 1-1 and 4 mg
1-1. The increase of the SPM concentration during an erosion event is 5 mg 1-1 in
both regimes. There are three measurements during non-erosion conditions
and one measurement during the erosion event. The time series of SPM concentrations are thus {l,1,1,6} and {4,4,4,9} for the two regimes. Now, in logarithmic
terms the std. dev. factors are 2.45 and 1.50, respectively, i.e. there is a substantial
difference. In linear terms the standard deviation is ± 2.5 mg 1-1 for each regime,
which is reasonable because the increase of the SPM is the same for each regime.
The example shows that processing SPM concentrations in linear terms is more
adequate for pure erosion events. For the sake of conformity, however, the temporal variability of SPM concentrations is calculated in logarithmic terms, as it
is done for the temporal-averaged SPM concentrations in Section 4.2. It must be
kept in mind that the use of a logarithmic scale means decreased std. dev. factors
in SPM regimes having high concentrations and increased standard deviations
in SPM regimes having low concentrations.
The distributions of std. dev. factors of measured and computed SPM concentrations are shown in Figs. 13 and 14, respectively. Just as in Figs. 11 and 12, the
space outside the stations is inter- or extrapolated. The spatial means of the factors (simple average of the 477 horizontal grid cells representing the model do-
w. PuIs· T. Pohlmann· J. Siindermann
4.3
Temporal Variation of SPM Concentrations
The temporal variation of measured and computed depth averaged SPM concentrations c at each separate NSP station is determined from the same measured
or computed data which are the basis for the mean SPM concentrations shown
in Figs. 11 and 12. The evaluation is done in logarithmic terms log c, resulting in
a mean value mean (log c) and a standard deviation cr(log c). After having taken
the anti-logarithm, the final result, i.e. the temporal variation, is expressed as a
standard deviation factor lO cr (log c). The mean concentration is then (i) divided
by this factor and (ii) multiplied with this factor, resulting in a concentration
range which is somehow equivalent to a "normal" standard deviation. To give an
example: The original SPM concentration time series is {0.2, 2, 20} mg 1-1. In logarithmic terms, the data is {-0.70, 0.30, 1.30}. The mean and the standard deviation of the log-data is:
mean(logc) ± cr(logc) = 0.30± l.
Taking the anti-logarithm, the mean SPM concentration is 10°.30 = 2 mg 1-1,
the std. dev. factor is 10 1 = 10. The variability range of SPM concentrations is
thus from 2110 = 0.2 mg 1-1 to 2 x 10 = 20 mg 1-1.
There is a principal problem with the temporal variability of SPM concentrations. SPM concentrations are regarded on a logarithmic scale (see Sect. 4.2).
SPM erosion, however, rather acts on a linear scale, because the increase in the
SPM concentration in the water column by erosion does (of course) not depend
on the SPM background concentrations at the specific site. To give an example:
there are two SPM regimes with background concentrations of 1 mg 1-1 and 4 mg
1-1. The increase of the SPM concentration during an erosion event is 5 mg 1-1 in
both regimes. There are three measurements during non-erosion conditions
and one measurement during the erosion event. The time series of SPM concentrations are thus {l,1,1,6} and {4,4,4,9} for the two regimes. Now, in logarithmic
terms the std. dev. factors are 2.45 and 1.50, respectively, i.e. there is a substantial
difference. In linear terms the standard deviation is ± 2.5 mg 1-1 for each regime,
which is reasonable because the increase of the SPM is the same for each regime.
The example shows that processing SPM concentrations in linear terms is more
adequate for pure erosion events. For the sake of conformity, however, the temporal variability of SPM concentrations is calculated in logarithmic terms, as it
is done for the temporal-averaged SPM concentrations in Section 4.2. It must be
kept in mind that the use of a logarithmic scale means decreased std. dev. factors
in SPM regimes having high concentrations and increased standard deviations
in SPM regimes having low concentrations.
The distributions of std. dev. factors of measured and computed SPM concentrations are shown in Figs. 13 and 14, respectively. Just as in Figs. 11 and 12, the
space outside the stations is inter- or extrapolated. The spatial means of the factors (simple average of the 477 horizontal grid cells representing the model do-