PREDICTIONS OF TEMPERATURE
IN STREAMS RECEIVING THERMAL
DISCHARGES BY USING A DETERMINISTIC
MODEL AND COMPUTER TECHNIQUE
FRANZ BERGER, Biologische Station Lunz der Osterreichischen Akademie der Wissenschaften,
Lunz am See, Osterreich.
WOLFGANG SCHMITZ, Landesstelle fur Gewasserkunde und wasserwirtschaftliche Planung BadenWürttemberg, 75 Karlsruhe, Hebelstr. 2, B. R. Deutschland.
INTRODUCTION
The effect of a thermal discharge into a river on the temperature of the water is not
only due to mixing, but to interference with the natural heat budget of the flowing water.
The elements of the heat budget are subject to considerable diurnal and seasonal
fluctuations and are dependent on the temperature of the water itself. Therefore
calculations of the resulting temperatures are laborious and require the aid of a computer
technique. The principle of including the heat budget into the calculations was applied by
the authors in a study to predict temperature changes expected to occur in the River
Rhine between the mouth of the tributary Aare and the city of Basel (Switzerland) after
installation of power plants in future. Detailed results were laid down in an internal
report prepared by Berger (1) in 1966, which has not been published. Further use has
been made from the experiences of this study in the development of a general plan to
manage thermal discharges into the Rhine river between Aare confluence and the
Dutch-German border. This plan was prepared by. Landesstelle für Gewässerkunde
Baden-Württemberg and has been approved and edited by the joint Commission of the
German States on Sanitation of the River Rhine in 1971 (2).
DETERMINISTIC MODEL OF THERMAL SITUATION IN STREAMS
The deterministic model used is based on the proposals of Eckel and Reuter (3). In
this procedure the calculations of temperatures are made in the form of a
one-dimensional deterministic model assuming some simplification of the natural events.
The assumptions are as follows:
a) the water is homothermic in the cross-section of the stream;
b) the cooling water is totally mixed with the water of the receiving river immediately;
c) the distortion of bodies of flowing water by longitudinal dispersion during their
transport downstream is neglected.
Under these conditions the temperature of the water TW will undergo a deviation of
temperature dTW according to the following equation during each small period of
flowtime dt.
1
dTW =
(GLR ± EBR ± EV ± HCA ± HCS) . dt
H . p . c
where:
H
= depth of water during interval of flow time dt
p
= density of water at TW
11
IN STREAMS RECEIVING THERMAL
DISCHARGES BY USING A DETERMINISTIC
MODEL AND COMPUTER TECHNIQUE
FRANZ BERGER, Biologische Station Lunz der Osterreichischen Akademie der Wissenschaften,
Lunz am See, Osterreich.
WOLFGANG SCHMITZ, Landesstelle fur Gewasserkunde und wasserwirtschaftliche Planung BadenWürttemberg, 75 Karlsruhe, Hebelstr. 2, B. R. Deutschland.
INTRODUCTION
The effect of a thermal discharge into a river on the temperature of the water is not
only due to mixing, but to interference with the natural heat budget of the flowing water.
The elements of the heat budget are subject to considerable diurnal and seasonal
fluctuations and are dependent on the temperature of the water itself. Therefore
calculations of the resulting temperatures are laborious and require the aid of a computer
technique. The principle of including the heat budget into the calculations was applied by
the authors in a study to predict temperature changes expected to occur in the River
Rhine between the mouth of the tributary Aare and the city of Basel (Switzerland) after
installation of power plants in future. Detailed results were laid down in an internal
report prepared by Berger (1) in 1966, which has not been published. Further use has
been made from the experiences of this study in the development of a general plan to
manage thermal discharges into the Rhine river between Aare confluence and the
Dutch-German border. This plan was prepared by. Landesstelle für Gewässerkunde
Baden-Württemberg and has been approved and edited by the joint Commission of the
German States on Sanitation of the River Rhine in 1971 (2).
DETERMINISTIC MODEL OF THERMAL SITUATION IN STREAMS
The deterministic model used is based on the proposals of Eckel and Reuter (3). In
this procedure the calculations of temperatures are made in the form of a
one-dimensional deterministic model assuming some simplification of the natural events.
The assumptions are as follows:
a) the water is homothermic in the cross-section of the stream;
b) the cooling water is totally mixed with the water of the receiving river immediately;
c) the distortion of bodies of flowing water by longitudinal dispersion during their
transport downstream is neglected.
Under these conditions the temperature of the water TW will undergo a deviation of
temperature dTW according to the following equation during each small period of
flowtime dt.
1
dTW =
(GLR ± EBR ± EV ± HCA ± HCS) . dt
H . p . c
where:
H
= depth of water during interval of flow time dt
p
= density of water at TW
11