The blog castelodebode.blogspot.com conducted a study in order to get from a quick way the water temperature in Castelo do Bode reservoir, from the air temperature. For that daily measurements of water temperature were carried out on the reservoir and compared with air temperature during the year of 2012.The values of water temperature depend on many external factors that are not constant from day to day and therefore an estimate of water temperature has always an associated error. During 2012 the monthly average water temperature recorded at the beginning of the day on the reservoir ranged between 11.6ºC for February and 24.3ºC in August. On the other hand, the average monthly air temperature ranged between 6.9ºC for February and 22.3ºC in August.

1. Water Temperature Forecast in Castelo do Bode Reservoir
Paulo Marques
castelodebode@gmail.com
1. Introduction
1.2 1.2 Parameters Influencing Water
Temperature
1.1 Subject
The temperature of a lake or a reservoir has a great
impact on the biodiversity. The movements and
types of fish are closely related to water temperature
and to predict the behavior of these species, the
water temperature is a very important factor.
In the case of reservoirs or lakes which are intended
to capture water for human consumption, the water
temperature is also a great factor of influence on
their quality. A water at higher temperature has a
lower gas solubility containing, for example lower
dissolved oxygen compared to water with a lower
temperature. There are other factors such as toxic
compounds which are generally most abundant in
water at higher temperatures.
For leisure activities that are practiced in lakes and
reservoirs, knowing the water temperature is also an
advantage
to
add.
For
this
the
castelodebode.blogspot.com blog conducted a small
study to give reservoir users the possibility to know
an approximate value for the water temperature at
different stages of the year, from the air temperature.
There were several attempts to predict the water
temperature in reservoirs based on air temperature,
but all of them can only provide approximate values
due to the heterogeneity of water temperature in the
reservoir and the differences in air temperature along
the reservoir, differences that are not possible to
know. For the Castelo do Bode reservoir the goal has
always been to find a way, as close as possible to
reality, to obtain in an expeditious manner the water
temperature in the reservoir.
The water temperature at the reservoir surface is not
equal to the air temperature mainly because the
specific heat of water is different from the specific
heat of air. In this case, water needs about four times
more energy than air for heating the same mass in
one degree of temperature which indicates that the
water temperature follows with a delay relative to the
air temperature.
The water temperature depends on the solar
radiation of short wavelength and long wavelength
emitted by the surface of the water, the latent heat
and heat flow between water-air and ground-water.
These values are difficult to know and so the
temperature of the water is difficult to determine from
other variables. In addition to all these factors which
are dependent on the water temperature, it also
varies with the location of the reservoir and with
depth. In the latter case the temperature decreases
with depth, a very slight lowering at the surface
followed by a sudden reduction in a lower layer
maintaining the temperature in deeper zones. This
reduction in temperature with depth is related not
only to the parameters listed above but, also with an
increased water density that happens in depth.
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2. Fig.1 – Variation of water temperature in depth
2. Reservoir Features
Bode dam, approximately 110m. The average flow
of the river Zêzere is 42m3/s which means that the
reservoir carries 1.2 renewals of water per year.
The Castelo do Bode reservoir has an area of
32.9km2 and a water storage of 1.09 cubic
kilometers, over 59km, between the upstream dam
of Bouçã and Castelo do Bode dam. The maximum
depth of the reservoir is located near Castelo do
Where Castelo do Bode reservoir is located the
summer is hot and in winter the nights are cold.
3. Water Temperature in Castelo do Bode
Reservoir
In order to be able to find a quick way to provide the
water temperature in Castelo do Bode reservoir as
a function of air temperature it was necessary to
make measurements and records of the
temperature of water in the reservoir. These
measurements were performed throughout the year
of 2012, for a total of 165 records from January, 17
of 2012 until January, 16 of 2013. The
measurements were made with an HANNA
temperature probe at a depth of 10cm. The
measurement location was near the dam,
approximately 20m and the time of day that the
records were made was in the morning between
7am and 8am.
January February March April May June July August September October November Dezember
12.5
11.6
13.6
14.8
19.4
22.4
23.5
24.3
23.7
20.7
16.3
13.6
Table 1 – Average monthly water temperature recorded in Castelo do Bode reservoir in 2012.
For the average air temperatures, data were taken
from an amateur weather station, located in Tomar,
less than 10km from Castelo do Bode reservoir.
The
data
were
http://www.meteotomar.info.
taken
from
January February March April May June July August September October November Dezember
7.1
6.9
13.2
12.1
18.1
20.6
21.9
22.3
21.4
16.4
11.0
Table 2 – Average monthly temperatures of the air, for 2012, considered in this study.
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9.6

3. Before analyzing the data obtained, it is
necessary to take into account that water
temperature values obtained are measured in the
early morning hours where the water and air
temperature are at minimum values of the day. In
contrast, the values of air temperature are daily
average values and therefore do not correspond
to time measurement of water temperature. The
daily average water temperature in the reservoir,
which could be directly compared with the daily
average air temperature is higher than the
calculated values. Through only a measurement
of the water temperature of the reservoir
throughout the day, we found a high correlation
with the variation of air temperature throughout
the day, around 0.98. This result shows that the
difference between the average daily water
temperature and water temperature at the start of
the day depends largely on the daily air
temperature range.
Fig.2 – Registered water and air temperatures in Castelo do Bode reservoir throughout a day, where some values of
water temperature were obtained by interpolation.
The water temperature in the reservoir is not
dependent merely of air temperature but also
depends for instance from solar radiation, wind
speed, humidity, precipitation, or the number of
renovations of the reservoir per unit of time. As in
this document the objective is only to relate water
temperature with air temperature, all listed
parameters will not be considered and they will
enter in a final overall error.
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4. Fig.3 - Recorded water temperatures in the reservoir and average, maximum and minimum daily air temperatures.
4. Method for Water Temperature
Forecast
According to some studies, the average water
temperature usually exceeds the average air
temperature. (1) Other studies say that the water
temperature is related to the air temperature of the
day before and you can express it throughout a linear
equation. (1) Looking at Figure 3 it can be seen that
most of the time the water temperature at the start of
the day is higher than the average air temperature. If
instead of considering the water temperature at the
start of the day, consider the average water
temperature then this superiority becomes even
more evident.
we began by relating the average temperature of the
day before with the water temperature. As expected
beforehand that the best relationship of water
temperature could happen with the temperature of 2
days or 3 days before , we analyzed the correlations
between the values and pattern of water temperature
and mean air temperature of the day before , two
days before , three days before and four days before.
Since water requires more energy to raise its
temperature than air, it is expected that its
temperature has a time delay in relation to the air
temperature. This way the water temperature can be
related to the temperature of the air in a previous
day. To be able to find an expression that gives us
the water temperature in Castelo do Bode reservoir
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5. January February March April
May
June
July
August September October November Dezember
Day
0.645
-0.340
0.469 0.188 0.523 0.537 0.462
0.263
0.871
0.609
0.503
-0.165
Day (-1)
0.647
-0.391
0.552 0.290 0.607 0.685 0.593
0.441
0.914
0.648
0.520
-0.154
Day (-2)
0.645
-0.415
0.606 0.328 0.680 0.792 0.681
0.563
0.942
0.682
0.559
-0.174
Day (-3)
0.629
-0.402
0.635 0.356 0.742 0.857 0.736
0.630
0.942
0.696
0.583
-0.207
Day (-4) 0.527
-0.375
0.651 0.418 0.795 0.880 0.774 0.688
0.932
0.708
0.610
-0.271
Table 3 – Correlation factors between water temperature and daily mean air temperature of the day where water
temperature was recorded, the day before, the 2nd day before, the 3rd and 4th day before.
January February March April
May
June
July
August September
October
November Dezember
Day
3.036
3.165
2.333 1.705 3.051 2.251 1.804
1.514
2.047
3.314
3.549
3.147
Day (-1)
2.989
3.078
2.234 1.590 2.984 2.105 1.783
1.427
1.962
3.127
3.403
3.056
Day (-2)
2.906
2.992
2.155 1.501 2.931 1.953 1.725
1.361
1.905
3.007
3.247
2.974
Day (-3)
2.835
2.923
2.065 1.431 2.905 1.813 1.653
1.299
1.829
2.872
3.107
2.906
Day (-4)
2.784
2.874
1.979 1.396 2.876 1.709 1.571 1.243
1.748
2.736
2.977
2.837
Table 4 – Standard Deviation between water temperature and daily mean air temperature of the day where water
temperature was recorded, the previous day, the 2nd day before, the 3rd and 4th day before.
During the analysis of Table 2 and Table 3 it can be
seen that the correlation is higher the farther the
values of record date from the day of air temperature.
Although this situation occurs for most months, the
dispersion of large correlation values found did not
make possible to draw a conclusion about the data
regarding the date of air temperature used to
determine the water temperature. If data are
processed on an annual basis rather than on a
monthly basis, the verified correlation values
become quite near each other, being between 0.88
and 0.90, which shows that whatever the previous
day used from those listed in table 3 and 4, the
results achieved in water temperature will have very
small differences.
To determine an equation that its result is the water
temperature, using as variable the mean air
temperature of a previous day only, the first issue we
found was the type of equation, a linear equation,
second degree, third degree or a higher degree
equation. The equation aims to be used by most of
the people and so the simpler it becomes more
practical it is to use. Thus the equations used are
limited
to
the
third
degree.
Using MS Excel and its Solver tool an equation
dependent of air temperature was found, in which the
sum of the difference between their result and the
water temperature recorded in the reservoir was
minimal for the whole year. The best equation found
was a first degree equation which relates the mean
air temperature of the previous day with the water
temperature of the current day for the first few hours
of the day.
𝑇 𝑤 = 0.7𝑇 𝐴(−1) + 7.71
Eq.1
Tw – Water temperature at Castelo do Bode reservoir
in the early hours of the day
TA(-1) – Mean air temperature of the previous day in
Castelo do Bode reservoir area
Using equation 1 it is possible to get the water
temperature in the reservoir of Castelo do Bode
using only the mean air temperature of the previous
day. The equation, as an expected error compared
to the real values. The mean absolute error in
equation 1 is 1.72 ° C, the maximum error is 6.4 ° C
and the standard deviation of the values obtained by
the equation is 1.30 (values obtained by observing
only the data collected in 2012).
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6. Fig.4 – Real water temperature (blue) and water temperature obtained with equation 1 (red), during the year 2012.
The values obtained by equation 1 are values for the
first few hours of the day, between 7am and 8am,
when the air temperature is close to the daily
minimum. Thus, it is also expected that the water
temperature at that time is also near the daily
minimum, as can be seen in Figure 2. If the values
of equation 1 are near the daily minimum, throughout
the day the water temperature will be higher, as the
air temperature increases and thereby it is necessary
to add a value to equation 1 to get the temperature
at a different time of the day.
only of the air temperature that added to the equation
1 provides the temperature at a certain time of day.
By analyzing Figure 2 it can be seen that for a 1
degree change in air temperature the water
temperature varies between 0.07 and 0.13 degrees
Celsius, resulting in an average value of 0.1 degrees
Celsius. To equation 1 a new term can be added that
provides the water temperature at a different time
depending on the air temperature at that time
𝑇 𝑤 = 0.7𝑇 𝐴(−1) + 7.71 + 0.1∆ 𝑇𝐴
Eq.2
The water temperature during the day greatly
depends on many external factors such as air
temperature, air speed or the solar radiation and
others. Thus, it is difficult to obtain a value dependent
5. Problems and Improvements of the
Method
The values found using equation 1, despite being
close to the actual values of the water temperature
in the reservoir, can amount to more than 5 ° C of
error. This error, due to the absolute value of the
water temperature around 20 ° Celsius, is about 25
%, which is quite a high value. Although equation 1
is the equation found with minor error in the set of
ΔTA – Difference between the air temperature at the
time that want to know the water temperature and the
minimum air temperature of the day;
results throughout the year, still has a nonnegligible error.
The temperature along the reservoir is not
constant, depending on factors mentioned in
paragraph 1 of this document. Equation 1 was
obtained using basic measurements made near the
Castelo do Bode dam and therefore the
applicability of the equation in remote areas of the
reservoir can be questioned. The error values
found for the first equation, in the case of using it
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7. for zones far away from the dam, can rise above
the
previously
listed
values.
It is possible to improve the water temperature
obtained if the year is divided into several
segments and each segment as an equation to find
the temperature of the water. You can see in Figure
3 that the values given by equation 1 are closer to
the real values of water temperature from July until
the end of the year, while in the first part of the year
the error of the values obtained is larger, which
shows that the use of different equations for
different times of the year could reduce the global
error.
6. Conclusions
Through the water temperature records made in the
2012 and the air temperature in the area
surrounding the reservoir, it can be concluded that
the temperature of the water reservoir at the
beginning of the day exceeds in 85 % of the time the
average air temperature in the same day. When we
refer to the mean water temperature throughout the
day, the percentage of exceedance relative to the
average temperature of the air is 90 %.
The average water temperature shows a very close
correlation with the mean air temperature of the
previous four days, but were unable to find a day
that could have significantly better results than the
other. The expression built which shows an
approximation of the water temperature at the start
of the day has a mean absolute error of 1.72 ° C, a
value which is still somewhat high for the needs of
some users of the Castelo do Bode reservoir but,
already offers a very reasonable value for other
types of users, more recreational. If during the use
of the equation, if you have the notion that the
expression result shows a larger error at times of
year where the air temperature shows a wide
variation from one day to another, it is possible to
obtain results that are known in advance which have
a lower global error.
The use of the given expression is limited to the
Castelo do Bode reservoir and is not possible to
predict in advance whether their application can be
considered in other reservoirs.

7. Bibliography


Hobbs, E.H. Air-Water Temperature
Relations of Small Shallow Prairie
Reservoirs – Canadian Agricultural
Engineering. Canada, 1972.
Zhau, Liu, Min-quang, Feng, Shu-fang,
Fan, Simulation of Water Temperature
Distribution in Fenhe Reservoir. Water
Science and Engineering 2009. China,
2009.



http://castelodebode.blogspot.com
Temperatura da Água [Online] [Citação: 20
de
Maio
de
2013]
http://www.ufrrj.br/institutos/it/de/acidente
s/tem.htm
McCombie,
A.M.
Some
Relations
between Air Temperatures and the
Surface Water Temperature of the Lakes.
Ontário.
Deas, Michael L., Lowney Cindy L.
Water Temperature Modeling Review.
Central Valley, 2000.
www.meteotomar.info
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