Modeling algal growth in the Lake of Bled (LAI)
The task was to model algal biomass quantity in the Lake
of Bled, Slovenia. Eutrophication of the Lake of Bled progressed in big
steps this century, endangering the tourist economy of the region. Several
restoration measures have been undertaken to avoid the disturbing algal
blooms (Kompare and Rismal 1992). Modeling of the algal biomass quantity
could help understanding the mechanisms which influence the algal blooms
and choosing the measures to prevent them.
||Modeling algal growth in the Lake of Bled
||Contact Aram Karalic Aram.Karalic@ijs.si
||Eight data sets of approx. 60 examples each
Measurements were provided by the National Institute of
Biology, University of Ljubljana. During six years (1987-1992) several
quantities were measured in approximately monthly intervals. The measured
quantities, used as attributes in the learning process, include:
The measurements were taken at 2m depth intervals. The results
were then grouped to describe a situation in three water layers -- epilimnion
(top-most layer, depth from 0m to 4-8m), metalimnion (8m to 12m) and hypolimnion,
which consisted of the rest of the water. For every layer, two ways of
combining the measurements within the layer were employed:
Bio ... algal biomass [mg/l],
NH4 ... ammonia [mg/l],
NO2 ... nitrite [mg/l],
NO3 ... nitrate [mg/l],
OrtP ... orthophosphate PO [mg/l],
Ptot ... total phosphorus [mg/l],
Si ... silicon [mg/l],
TEMP ... temperature,
Additionally we took into account the fact, that the lake
is naturally divided in two basins -- east and west basin.
averaging the data points,
finding a data point with the maximal value.
We decided not to make any experiments concerning the
hypolimnion, since we were concerned primarily with modeling of biomass
which appears mainly in the upper two layers.
So, we were actually faced with 8 subproblems:
Eight kinds of models for biomass prediction were induced,
predicting average and maximal values, values for epilimnion and metalimnion,
and values in east and west basin.
The evaluation of the first series of models led to the
Due to conclusion (1) we reduced the problem from eight variants
to only one variant, suggested by the expert as the most interesting: prediction
of the maximal biomass quantity in the metalimnion of the east basin.
There is no particular difference between the variants.
From the initial set of attributes a few more attributes
could be generated, probably leading to induction of better models.
Literals which test Month appeared very often, indicating
that the time of the year is a factor with one of the strongest correlation
Expert suggested, that thresholds for certain ratios of
elements (e.g. ) may be important, therefore we introduced the inverse
values of the attributes PO4, NO3, and NH4,
as well as the inverse value of Ntot, where .
A background literal performing multiplication was introduced as well.
Since there were a lot of literals testing the value of
Month roughly corresponding to the time of season change, we also
defined background literals describing the seasons. This background knowledge
was used in subsequent experiments and, particularly in experiments using
the MDL pruning, it appeared very often in the induced models, while literals
directly testing the value of Month appeared less frequently.
Experiment with Additional Attributes
Experiment with additional attributes resulted in an excellent
(in experts opinion) model with the lowest error of all the models generated
in this domain, which also incorporated newly derived attributes and a
background knowledge literal defining autumn. Non-default values of parameters
were: minimal number of examples MinNoExs=10 and maximal number of linear
regression variables MaxLRVars=2.
Figure 4: Model of biomass quantity in the Lake
of Bled. BIM = maximal biomass quantity in the metalimnion of
the east basin, e = epilimnion, m = metalimnion. Unused
variables were removed from heads of the clauses for better readability.
The model was generated in 17 minutes of CPU time on Sun SPARCstation 10.
We present the model in Figure 4,
while the expert's comment on the model follows here.
The course of events, indicated by the model, agrees with
experts description of what is going on in the lake over one year: ``In
epiliminion a spring algal bloom takes place in March/April, after which
algae move into metalimnion, where the annual maximum occurs at the end
of spring or beginning of summer.
The first clause describes winter.
The second clause describes the phase of biomass decomposition.
This clause also makes use of one of the newly added attributes.
The third clause describes spring conditions of the algal
growth in months 2, 3, 4 (maybe 5). At this time the blue-green algae prevail.
For them the limiting factor of growth is phosphorus (enough P implies
plenty of algae). This comment was produced only after the expert took
a closer look at the examples, covered by the clause.
The fourth clause models the decomposition of biomass
in both, epilimnion and metalimnion.
The fifth clause covers some of the largest extremes in
biomass quantity. Phosphorus was consumed by the algae. The quantity of
NO2 is minimal or zero. That shows the phase of algal growth
(no decomposition, NH4). Besides P the algae also consumed N.
Term with Si shows the growth of Si algae.
The last clause shows preparation of Si algae in early
summer. At that time blue-green algae prevail which is indicated by both
terms in the linear expression.
In summary, the expert's opinion is that the induced models
describe the growth of algae quite well. The use of linear regression largely
increased the expressive power of the models, since it provided the expert
with additional information about the behavior of the biomass in a selected
region of the attribute space. The expert was also very satisfied with
the usage of additional attributes. Newly induced background literals defining
seasons helped in better comprehensibility of the induced models, but they
did not improve the performance of the models on the learning set.
A. Karalic, I. Bratko: First Order Regression. Machine Learning,
Kluwer (in press).
B. Kompare, S. Dzeroski, A. Karalic, I. Bratko, M. Sisko,
S.E. Jorgensen. Using machine learning techniques in the construction of
models, Part III: Learning systems with regression. Submitted to Ecological
B. Kompare and M. Rismal. Modelling the Lake of Bled. ISEM's
Eighth International Conference on the Stat-Of-The-Art in Ecological Modelling.
Kiel, Germany, 1992.
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