Estimation of Algal Growth Parameters from Vertical Primary Production Profiles

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Estimation of Algal Growth
Parameters from Vertical
Primary Production Profiles
Straten, G. van and Herodek, S.

IIASA Collaborative Paper
June 1981
Straten, G. van and Herodek, S. (1981) Estimation of Algal Growth Parameters from Vertical Primary Production
Profiles. IIASA Collaborative Paper. IIASA, Laxenburg, Austria, CP-81-019 Copyright © June 1981 by the
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ESTIMATION OF ALGAL GROWTH
PARAMETERS FROM VERTICAL
PRIMARY PRODUCTION PROFILES
G e r r i t van Straten
Sandor Herodek
June 1981
CP-81-19
CoZZaboratiue Papers report work which has not been
performed solely a t the International Institute for
Applied Systems Analysis and which has received only
limited review. Views or opinions expressed herein
do not necessarily represent those of the Institute,
its National Member Organizations, or other organi-
zations supporting the work.
INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS
A-2361 Laxenburg, Austria
AUTHORS
G. van Straten is with the Department of Chemical Technology,
Twente University of Technology, Enschede, The Netherlands.
Formerly, he was a research scholar and leader of the Lake
Balaton Case Study a t IIASA from April 1978-December 1979.
Sandor Herodek is a research scientist a t the Biological Research
Institute of the Hungarian Academy of Sciences, Tihany, Hungary.
PREFACE
One of the principal themes of the Task on Environmental
Quality Control and Management i n IIASA's Resources and
Environment Area is a case study of eutrophication management
for Lake Balaton, Hungary. The case study is a collaborative
project involving a number of scientists from several Hungarian
institutions and IIASA (for details see WP-80-187).
As part of the case study three different biochemical
models of the lake's behavior are under development (results
for two of these models have already been described i n earlier
working papers WP-80-139 and WP-80-149). In a l l these models
the maximum algal growth rate plays an important role. This
paper illustrates how t h i s parameter can be estimated from
measured vertical profiles of primary production. The
procedure suggested provides not only a better understanding
and explanation of the particularly high growth rate, compared
to values quoted i n the literature, but also decreases the
number of parameters t o be estimated i n terms of the complex
biochemical models.
This paper was originally prepared under the t i t l e "Modelling
for Management" for presentation a t a Nater Research Centre
(U.K. ) Conference on "River Pollution Control", Oxford,
9-11 A s r i l , 1979.
ABSTRACT
Phytoplankton maximum growth r a t e and the saturation l i g h t
intensity, Is, can be estimated from vertical profiles of primary
production by non-linear least-squares estimation. Solution through
the normal equations leads t o formula which a r e relatively simple
and easy t o implement. The computation of confidence contours is
demonstrated, and the results are contrasted to the confidence
l i m i t s on the parameters individually. These can be quite mis-
leading due to model non-linearity and c ~ r r e l a t i o nb etween para-
meter estimation.
The procedure has been applied t o primary production data
from Lake Baiaton, a shallow lake i n Hungary. The growth rate-
temperature relation is analyzed by separating the parameter set
into two groups characteristic for 'warm' and 'cold' water phyto-
plankton, respectively. A bell-shaped curve is found for 'cold'
-
water communities, with an optimum a t about 7 g°C, whereas
the 'warm' water phytoplankton exhibits a strong exponential depen-
dancy i n the temperature range of interest (up t o 2 5 ' ~ ) . Is
appears also t o be related to essentially constant. However, a
roughly linear relation with considerably less scatter is obtained
when Is is plotted directly versus day-averaged solar radiation.
This apparent f a s t adaptation is attributed t o the extremely short
overtime i n Lake Bslaton. Maximum growth r a t e s of 10-20 day''
have been found for temperatures between 20' and 2 5 ' ~ . These
results and a c r i t i c a l appraisal of available literature suggest
that the common notion of maximum growth r a t e s being i n the order
of 1-3 day'l needs revision, a t l e a s t for lakes with relatively
high summer temperatures.

CONTENTS
INTRODUCTION
LAKE BALATON
PRIMARY PRODUCTION EXPERIMENTS
METHOD
ASSUMPTIONS
ESTIMATION PROCEDURE
CONFIDENCE REGIONS
VARIANCE-COVARIANCE MATRIX
EXAMPLE
RESULTS
ANALYSIS
BIOMASS COMPOSITION
-
RELATION GROWTH RATE TEMPERATURE
OPTIMAL LIGHT INTENSITY
DISCUSSION AND CONCLUSION
REFERENCES