12
F. Berger and W. Schmitz
c
= specific heat of water at TW
GLR = global radiation (solar + diffuse skylight radiation)
EBR = effective long wave radiation of water at TW
EV = heat exchange by evaporation (-) or by condensation (+)
HCA = heat exchange by (turbulent) heat conduction with air
HCS = heat exchange by heat conduction with soil of the river bed.
The dimensions used in the calculations of ATW are:
[cal . cm"
2 . h"
1 ] . [h]
= 0 p
[cm] [g . cm"
3 ] [cal. g
_I . °C
_1 ]
This equation may be simplified for gradual solution:
1) p and c are made unity;
2) HCS is neglected, since it is not relevant to short-time fluctuations of water
temperature;
3) dt is replaced by At = 1 hour. dTW hence will become temperature deviation ATW after
1 hour;
4) R is a coefficient of GLR, which considers the losses of GLR at the water surface by
reflection and by incomplete absorption;
5) H is considered as the average depth of that particular range of the stream through
which the river water flows during the corresponding At.
The equation used for the calculation is hence:
ATW = pj (R . GLR - EBR ± EV ± HCA) . At
NUMERICAL CALCULATIONS
1) The calculations are started with the arbitrarily fixed initial temperature TWA.
2) H (in cm) is obtained for each hour step from a longitudinal stream profile in
connection with hour step nomograms (Fig.l). Nomograms have been developed for
different well defined cases of run-off. This information is generally taken from
studies, tracing the flow by use of rhodamine WT technique or by calculations from
known geometric data of the river bed.
3) GLR (in cal.cm"
2 .h"
1 ) is obtained as the average ordinate of single hour steps taken
from global radiation diagrams (Fig.2). The information de.rives from actual
observations with pyranometers.
4) R is either used as a constant R = 0.85 or it may be individually fixed for each daily
hour on the basis of sun angle-reflection tables and data for reflection of scattered
skylight as published by Sauberer and Ruttner (4).
5) EBR = 60 (BRW - BRA) . b (in cal.cm"
2 .h"
1 ), whereas BRW is long-wave
back-radiation of the water and BRA long-wave counter-radiation of the atmosphere.
BRW is calculated according to Stefan-Boltzmann as
BRW = 0.95 σ . (TW + 273)
4 (in cal.cm"
2 .min"
1 ),
F. Berger and W. Schmitz
c
= specific heat of water at TW
GLR = global radiation (solar + diffuse skylight radiation)
EBR = effective long wave radiation of water at TW
EV = heat exchange by evaporation (-) or by condensation (+)
HCA = heat exchange by (turbulent) heat conduction with air
HCS = heat exchange by heat conduction with soil of the river bed.
The dimensions used in the calculations of ATW are:
[cal . cm"
2 . h"
1 ] . [h]
= 0 p
[cm] [g . cm"
3 ] [cal. g
_I . °C
_1 ]
This equation may be simplified for gradual solution:
1) p and c are made unity;
2) HCS is neglected, since it is not relevant to short-time fluctuations of water
temperature;
3) dt is replaced by At = 1 hour. dTW hence will become temperature deviation ATW after
1 hour;
4) R is a coefficient of GLR, which considers the losses of GLR at the water surface by
reflection and by incomplete absorption;
5) H is considered as the average depth of that particular range of the stream through
which the river water flows during the corresponding At.
The equation used for the calculation is hence:
ATW = pj (R . GLR - EBR ± EV ± HCA) . At
NUMERICAL CALCULATIONS
1) The calculations are started with the arbitrarily fixed initial temperature TWA.
2) H (in cm) is obtained for each hour step from a longitudinal stream profile in
connection with hour step nomograms (Fig.l). Nomograms have been developed for
different well defined cases of run-off. This information is generally taken from
studies, tracing the flow by use of rhodamine WT technique or by calculations from
known geometric data of the river bed.
3) GLR (in cal.cm"
2 .h"
1 ) is obtained as the average ordinate of single hour steps taken
from global radiation diagrams (Fig.2). The information de.rives from actual
observations with pyranometers.
4) R is either used as a constant R = 0.85 or it may be individually fixed for each daily
hour on the basis of sun angle-reflection tables and data for reflection of scattered
skylight as published by Sauberer and Ruttner (4).
5) EBR = 60 (BRW - BRA) . b (in cal.cm"
2 .h"
1 ), whereas BRW is long-wave
back-radiation of the water and BRA long-wave counter-radiation of the atmosphere.
BRW is calculated according to Stefan-Boltzmann as
BRW = 0.95 σ . (TW + 273)
4 (in cal.cm"
2 .min"
1 ),