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On the relationship between heat flux and water surface temperature in a
tropical hydroelectric reservoir
1
Enner Herenio Alcântara
1
José Luiz Stech
1
João Antônio Lorenzzetti
1
Evlyn Márcia Leão de Moraes Novo
1
Arcilan Trevenzoli Assireu
2
Marie Paule Bonnet
3
Xavier Casamitjana
1
Brazilian Institute for Space Research, Remote Sensing Division, Brazil.
E-mails: {enner, stech, loren, evlyn, arcilan}@dsr.inpe.br
2
Institut de Recherche pour le Développement.
E-mail: [email protected]
3
Environmental Physics Group, Physics Department, University of Girona, Spain
E-mail: [email protected]
Abstract
The water temperature plays an important role in the ecological functioning and controlling
the biogeochemical processes of a water body. Conventional water quality monitoring is
expensive and time consuming. Particularly problematic if the water bodies to be examined
are large. Conventional techniques also bring about a high probability of undersampling.
Conversely, remote sensing is a powerful tool to assess aquatic systems. Based on this, the
objective of this study was to map the surface water temperature and improve understanding
of spatiotemporal variations in a hydroelectric reservoir. In this work the MODIS land-surface
temperature (LST) level 2, 1-Km nominal resolution data (MOD11L2, version 5) was used.
All available clear-sky MODIS/Terra imagery between 2003 and 2008 were used, resulting in
a total of 786 daytime and 473 nighttime images. Descriptive statistics (mean, maximum and
minimum) was computed for the historical images, so as to build a time series of daytime and
nighttime monthly mean temperature. The thermal amplitude and the anomaly were also
computed. In-situ meteorological variables were used from 2003 to 2008 to help us
understand the spatiotemporal variability of the surface water temperature. The surface energy
budget and the depth the wind can distribute a given surface heat input were also measured. A
correlation between daytime and nighttime surface water temperature and the meteorological
parameters and a linear regression computed. These relationship and the causes of the
spatiotemporal variability was discussed.
Keywords: Water surface temperature; heat flux; mixed depth layer; thermal amplitude.
Introduction
Reservoirs, or man-made lakes, are usually built to store water for later use, water supply,
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flood control or power generation (Casamitjana et al., 2003). In Brazil, there are
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approximately 31 hydroelectric reservoir buildings by electric sector with volume more than 1
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billion of m3. The hydroelectric sector is responsible for 97% of energy generation and
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considered the largest hydroelectric park of the world (Kelman et al. 2002). The building of
3
these dams, however, causes greatest environmental, social and economics impacts (Tundisi,
4
1994). Over the time, the functioning of reservoirs affects its retention time. Ford (1990)
5
comparing lakes and reservoirs with the same morphometry concluded that inflow and
6
withdrawal lead to a decrease in the reservoir’s water retention time.
7
In accordance to Kimmel et al (1990) to understanding the performance and functioning of
8
reservoir ecosystems the water temperature distribution is fundamental. Surface water
9
temperature is a key parameter in the physics of aquatic system processes since it accounts for
10
surface-atmosphere interactions and energy fluxes between the atmosphere and the water
11
surface. As it influences water chemistry it also affects its biological processes (Lerman and
12
Imboden, 1995). Moreover, temperature differences between water and air control moisture
13
and heat exchange in the air/water boundary layer and as a consequence, are crucial for
14
understanding the hydrological cycle.
15
However, the study of the water temperature using the concept of conventional limnological
16
sampling is expensive and time consuming. Particularly problematic if the water bodies to be
17
examined are large. Conventional techniques also bring about a high probability of
18
undersampling. Conversely, remote sensing is a powerful tool to assess aquatic systems and is
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particularly useful in remote areas (Novo et al., 2006; Alcântara et al. 2009).
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Thermal infrared remote sensing applied to freshwater ecosystem has aimed to map surface
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temperature (Oesch et al., 2008; Reinart and Reinhold, 2008; Crosman and Horel, 2009), bulk
22
temperature (Thiemann and Schiller, 2003), circulation patterns (Schladow et al., 2004) and to
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characterize upwelling events (Steissberg et al., 2005). However, the application of thermal
24
infrared image to study surface water temperature in hydroelectric reservoir is scarce and, in
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Brazil it is being attempt for the first time.
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Several satellites have been launched with spatial, temporal and radiometric resolutions for
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study surface water temperature with relatively accuracy (Steissberg et al. 2005). However,
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most of them acquire data twice at every 16 days, as Landsat and ASTER (Advanced
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Spaceborne Thermal Emission and Reflection Radiometer) at a given location. And the
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Landsat satellite does not record data at night (unless by special request). The Moderate
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Resolution Imaging Spectroradiometer (MODIS) on board of Terra and Aqua satellites
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overcome these temporal resolution limitations. MODIS data can typically be acquired daily
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due to the large scan angle (Justice et al., 1998).
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Though, the objectives of this study are to map the annual cycle of surface water temperature
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in the Itumbiara hydroelectric reservoir and to identify their driven forces.
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Study Area
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The Itumbiara hydroelectric reservoir (18°25’S, 49°06’W) is located in a region stretched
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between Minas Gerais and Goiás States (Central Brazil) originally covered by tropical
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grassland savanna. Damming the Parnaiba River flooded backward its main tributaries:
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Araguari and Corumbá River. The basin geomorphology resulted in a lake with a dentritic
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pattern covering an area of approximately 814 Km² and volume of 17.03 billion m³ (Figure 1).
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(a)
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(b)
(c)
Figure 1: Localization of Itumbiara hydroelectric reservoir on Brazil’s central (a), on state
context (b) and on regional scale (c) with the bathymetric map. On regional scale is showing
the flooded area over a SRTM (Shuttle Radar Topography Mission) image.
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The reservoir was built in 1979 and started its operation in 1980. Figure 2 shows the reservoir
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area before the flooding (Figure 2-a) and after (Figure 2-b) flooding.
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(a)
(b)
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Figure 2: (a) MSS-Landsat-3 imagery from 11-08-1978 show the area before inundation; and
(b) TM-Landsat-5 imagery from 26-05-2007 actual period. The figure also shows the position
of dam on reservoir.
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The climate in the region is characterized by precipitation ranges from 2.0 mm in the dry
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season (May - September) to 315 mm in rainy season (October - April). In the rainy season
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the wind intensity ranges from 1.6 to 2.0 ms-1 and reaches up to 3.0 ms-1 in the dry season
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(Figure 3-a). The air temperature in the rainy season ranges from 25 to 26.5 ºC and breaks
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down to 21ºC in June as the dry season starts. The relative humidity has a pattern similar to
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that of the air temperature, but with a little shift of the minimum value towards September
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(47%). Moreover during the rainy season the humidity can reach 80% (see Figure 3-b).
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(a)
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(b)
Figure 3: Climate patterns on Itumbiara reservoir: mean monthly of (a) precipitation
(mm month-1) and wind intensity (m s-1), (b) air temperature (ºC) and humidity (%).
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These hydro-meteorological patterns and the operational routine for energy generation drive
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the water level fluctuations in the reservoir (Figure 4). The period when the water level starts
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to rising in December until May; from May to June the water level is high. Due to the use of
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water for power generation and evaporation rates the water level receding until November.
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From this month the water level reach the low water level condition until December.
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Figure 4: Daily average (from 2003 to 2008) water level fluctuation at Itumbiara reservoir.
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The following section will describe the methodology needed to explain the spatiotemporal
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variability in the water surface temperature.
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Methodological approach
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The methodological approach was developed using the concept of disturbing influences that
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the reservoirs is exposed and described by Fischer et al. (1979) as: (1) the meteorological
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conditions in the area will determine the strengths of any energy transfers across the air-water
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interface; (2) the water from the inflowing streams may impart kinetic and potential energy,
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and (3) some of the energy of the outflowing water may be transformed to kinetic energy of
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the reservoir water. So we hypothesized that the heat flux and meteorological data could
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explain the spatial-temporal water surface temperature variation in the Itumbiara reservoir.
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Satellite data
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MODIS land-surface temperature (LST) level 2, 1-km nominal resolution data (MOD11L2,
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version 5) was obtained from the National Aeronautics and Space Administration Land
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Processes Distributed Active Archive Center (Wan, 2008). All available clear-sky MODIS
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Terra imagery between 2003 and 2008 were used, resulting in a total of 786 daytime images
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and 473 nighttime images (Figure 5). The LST-MODIS data was extensively validated for
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inland waters and was considered accurate (Oesch et al., 2005; Oesch et al., 2008; Reinart and
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Reinhold, 2008; Crosman and Horel 2009).
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Figure 5: Acquisition date and time of all MODIS/Terra data for 2003-2008 used in this
study.
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Maps of monthly mean daytime and nighttime surface water temperature were produced for
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the period from 2003 to 2008. Descriptive statistics (global mean, maximum and minimum)
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was computed for the surface water temperature maps so as to build a time series of daytime
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and nighttime monthly mean temperature. The thermal amplitude was computed pixel-by-
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pixel by subtraction daytime and nighttime temperature.
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To obtain the anomaly the monthly mean temperature for the years spanning from 2003 to
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2004 was computed in a pixel bases and then subtracted from each month for the entire time
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interval. The seasonal thermal amplitude was also analyzed.
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In situ Data
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Daily mean air temperature (ºC), relative humidity (%), wind intensity (ms-1) and
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precipitation (mm) from 2003 to 2008 were used. These data was obtained from a
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meteorological station (see Figure 1 for location). The daily mean of each variable was
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converted into monthly mean to adequate it to the time scale of satellite data. The surface
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energy budget was also calculated to help the understanding the surface water temperature
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variability.
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Surface Energy Budget
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The study of exchanges of energy between lake and atmosphere is essential for the
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understanding the aquatic system behavior and its reaction to possible changes of
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environment and climatic conditions (Bonnet, Poulin and Devaux, 2000). The exchange of
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heat across the water surface was computed using the methodology described by Henderson-
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Sellers (1986) as:
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φ N = φ s (1 − AS ) + φ ri (1 − AL ) − φ ro − φ rad
(1)
where φ N the net energy available, φ s is the incident short-wave radiation, φ ri the incident
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long-wave radiation, AS and AL is short-wave and long-wave reflectivities (albedoes), φ ro
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the (blackbody) long-wave radiative loss, and φ rad the net non-radiative energy loss (sensible
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and latent heat flux). The units used for the terms in Eq. (1) are W m-2.
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The incident short-wave radiation φ s was calculated using the following equation:
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φ s = a1φ0 (sinh) b (1 − 0.65C 2 )
(2)
where a1 =0.79 and b1 =1.15 are two calibration parameters determined by comparison with
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the radiometer data, φ 0 =1390 Wm-2 is the solar constant, h is the hour angle and C is the
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cloud cover index.
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The Longwave radiation φ ri as given by Fu et al. (1984)
1
φ ri = εσTs4 (0.39 − 0.05ea2 )(1 − λC ) + 4εσTs3 (Ts − Ta )
(3)
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where ε=0.97 is the thermal infrared emissivity of the water, σ is the Stefan-Boltzmann
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constant, Ts = water surface temperature (ºC), Ta = surface air temperature (ºC), λ=0.8 is the
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Reed (1977) correction factor, ea = partial pressure of vapor (mb), which was calculated as:
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ea = resat (Ta )
(4)
is the saturation vapor pressure, that was calculated
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where r is the relative humidity and esat
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using the polynomial approximation of Lowe (1977);
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The non-radiative energy term φ rad which was divided into sensible heat flux was calculated
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as:
→
φ sf = ρ a c p c H V (Ts − Ta )
(5)
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where φ sf is the sensible heat flux (Wm-2), ρ a = 1.2 Kgm-3 is the air density; c p = 1.005x103
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JKg-1K-1 is the specific heat capacity of air c H =1.1x10-3 is the coefficient of turbulent
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exchange and V = surface wind speed (ms-1); and the latent heat flux as:
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→
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0.622
(6)
pa
where φ lf is the latent heat flux (Wm-2), c E =1.1x10-3 is a coefficient of turbulent exchange,
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L =2.501x106 JKg-1 is the vaporization latent heat and p a is the atmospheric surface pressure
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(mb).
φlf = ρ a c E L V [esat (Ts ) − resat (Ta )]
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Moreover, the energy exchange also occurs through precipitation, withdrawal of evaporated
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water, chemical and biological reactions in the water body, and conversion of kinetic to
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thermal energy. These energy terms are small enough to be omitted. Many researchers agree
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that omitting the energy budget components with small values does not significantly affect the
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results (Bolsenga, 1975; Sturrock et al., 1992; Winter et al., 2003). The sensible and latent
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heat flux will be calculated for daytime and nighttime using the monthly mean surface water
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temperature derived from MODIS data.
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Due to the complexity of these fluxes and the limitation about the atmospheric data available
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for the area of study some constraint was imposed. The air temperature ( Ta ), wind intensity
r
( V ), was considered the same for whole reservoir since just a one meteorological station are
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available. Also the incident solar radiation ( φ s ) was calculated through the equation (2) and
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considered a unique value reach the surface water.
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As pointed out by Ford and Johnson (1986), the wind is the major source of energy for many
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physical phenomena which both directly or indirectly cause mixing in the water system and
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also can alter the thermal patterns. So, the depth to which wind can mix the water reservoir
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will be calculated to help in the results discussion.
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Mixed Depth
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r
Using the wind intensity V from meteorological station and the net heat flux calculated by
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surface energy budget (Eq. 1) the depth ( Dt , m) to which wind can mix the reservoir is given
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by (Sundaram, 1973):
Dt =
w *3
B k αg
φN
ρC p
(7)
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where w * is the shear velocity of the wind (ms-1), Bk an empirical coefficient approximately
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equal to von Karman´s constant (0.4), α the volumetric coefficient of thermal expansion for
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water (1.8x10-4 ºC-1), φ N the surface heat flux (Wm-2), ρ the density of water ( ≈ 1000
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kgm-3), g is gravitational acceleration (9.8 ms-2), and C p the specific heat of water (4186 J
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kg-1 ºC-1).
15
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The physical significance of Dt is that it is a measure of the depth the wind can distribute a
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given surface heat input. If the aquatic systems have a depth greater than Dt and not
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dominated by advection, this system will probably stratify (Ford and Johnson, 1986).
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A correlation and multiple regression analysis were made to relate the surface water
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temperature (daytime and nighttime) variability with heat flux and meteorological parameters
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(Neter, 1996).
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23
Results and Discussion
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The figure 6 shows the monthly mean daytime and nighttime water surface temperature
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distributions at Itumbiara reservoir. In general way the daytime temperature decrease from
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boundary to center of the reservoir and for the nighttime the processes invert. This inversion
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at night was observed by Sturman et al. (1999) that attribute this phenomenon to turbulent
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convection due to differential cooling that induces an effective lateral transport, replacing the
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water from interior of the lake to the littoral zone (Imberger, 1985). The temperature, for a
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given heat flux out of the water surface, decreases more rapidly in the shallow water body due
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to the low thermal mass than in the deep regions (Wells and Sherman, 2001).
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Figure 6: Monthly mean of daytime and nighttime surface water temperature from 2003 to
2008.
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The daytime temperature in May presents low horizontal variations than the others and for
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nighttime these months are July and August. The daytime series shows that January is the
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month with the smallest Maximum temperature (26.5ºC), which starts to rise in February
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(30ºC). From March to July the maximum temperature rises and is kept stable around ± 28ºC.
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From August to October the temperature raises around 7ºC in relation to July. In November
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and December the temperature starts to drop. The mean temperature presents the same
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patterns observed in the maximum temperature.
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The daytime time series shows that the maximum temperature is coldest during January with
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a little rising in February (Figure 7-a). Between March and July the maximum temperature is
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little variable. Between August and October a rising of temperature occurs (~ 7ºC) in relation
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to July. The months of November and December presents a little down in maxima
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temperature. The mean temperature presents the same patters observed in the maxima
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temperatures. The minimum temperatures present an expressive down during March and May
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and after July the minimum temperature stats to rising.
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(a)
(b)
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14
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Figure 7: Monthly mean surface water temperature statistics from 2003-2008: (a) daytime and
(b) nighttime.
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The monthly mean nighttime temperature presents a small variability during the years than
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daytime (Figure 7-b). Their pattern of variation is well defined with highest temperature in
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January and May and October and December. The smallest temperature occurs between July
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and September. The comparison between daytime and nighttime temperatures reveals that the
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highest temperatures occur in September for daytime and January for nighttime whereas the
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lowest ones occur in May and July, respectively.
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The figure 8 shows the daytime and nighttime mean temperature difference on a monthly
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base. January has the smallest temperature difference from day to night (<1ºC). From January
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on the mean temperature difference increases and reaches its maximum in October (8.46ºC).
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Figure 8: Surface water mean temperature difference between daytime and nighttime from
2003 to 2008.
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The interanual temperature anomaly should be analyzed to show in each month the mean
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temperatures are outside these 6 years of water surface temperature.
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8
Interanual Temperature Anomaly
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The interanual temperature anomaly was analyzed and shows that the January presents the
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highest anomaly between 2003 and 2008 for daytime temperature; follow by September,
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November and December (Figure 9-a). The smallest anomaly was observed in June. The
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histogram of the anomaly for daytime shows the occurrence of the more frequently
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temperature anomaly of ± 2ºC (Figure 9-b).
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The same anomaly pattern was observed for daytime and nighttime water surface temperature,
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but with March presents the highest anomaly variability in the years of study (Figure 9-c). In
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this case the variability is small than observed during daytime. The histogram of the anomaly
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for nighttime shows the occurrence of the more frequently temperature anomaly of ± 0.5ºC
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(Figure 9-d).
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(a)
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(b)
(d)
(c)
Figure 9: Interanual-mean temperature anomaly and histogram distributions for daytime (a, b)
and nighttime (c, d) respectively.
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The spatial seasonal mean water surface amplitude was also mapped to show when and the
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location where, for example, the nighttime temperature is higher than daytime temperature.
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7
Seasonal water surface temperature
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The analysis of the seasonal changes of water surface temperature shows that the thermal
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amplitude between daytime and nighttime is negative for summer in great area of the
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reservoir (Figure 10). This means that the nighttime temperature is highest than daytime
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temperature during summer. This means that the nighttime temperature is higher than daytime
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temperature during the summer. The highest differences occur in the center of the reservoir
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(~-6ºC).
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In fall the thermal amplitude is near zero with t negative amplitudes occurring in the central
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portion of the reservoir. In winter this negative thermal amplitude does not occur and are
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replaced by patches of near zero amplitudes in the central portion of the reservoir. In the
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spring, these patches of near zero amplitude are smaller with the occurrence of positive
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differences (Figure 10).
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5
6
Figure 10: Mean-water surface temperature difference between daytime and nighttime of
stations of the year from 2003 to 2008.
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Thus, in general form it is possible to verify that a trend exist with positively differences from
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border to central water body of the reservoir from summer to spring. It is due to low depth in
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these areas, less than 1 m. During the spring highest positively temperature differences can
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occur (~ 6ºC). The nighttime temperature could be highest than daytime during summer and
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fall. However, during the summer this is more pronounced than fall. To understanding these
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variability observed in the results the energy fluxes was computed.
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Surface energy budget for daytime and nighttime
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The annual cycle of heat fluxes is shown in Figure 11, which gives monthly spatial means
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over Itumbiara reservoir of each type of heat flux, using meteorological and satellite data from
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2003 to 2008.
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Figure 11: Energy budget components for (a) daytime and (b) nighttime.
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The Table 1 shows the monthly means heat fluxes for daytime and nighttime and spatially
5
averaged over Itumbiara reservoir.
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7
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Table 1: Monthly mean heat fluxes (Wm-2) from 2003 to 2008 averaged over Itumbiara
reservoir.
Latent
Sensible
Longwave
Net
daytime nighttime daytime nighttime
daytime
nighttime daytime nighttime
Jan
10.88
4.47
-0.95
-2.58
51.28
47.91
285.47
-49.81
Feb
21.04
9.10
4.79
-0.14
72.39
61.41
242.26
-70.38
Mar
17.18
6.60
3.91
-2.05
69.02
54.92
223.29
-59.47
Apr
20.64
7.35
5.34
-2.24
78.56
59.80
161.20
-64.91
May
22.21
9.38
7.63
-0.99
95.94
73.40
103.20
-81.75
Jun
29.29
10.14
11.65
-1.91
102.83
74.24
64.28
-82.42
Jul
31.58
8.83
10.97
-6.70
103.36
69.44
69.00
-71.57
Aug
49.05
12.63
11.82
-12.13
110.84
66.07
75.08
-66.54
Sep
69.27
12.63
11.61
-20.37
106.36
53.50
100.59
-45.75
Oct
63.35
6.42
15.01
-12.34
96.12
48.10
137.86
-42.17
Nov
39.44
8.34
10.96
-4.52
91.13
56.16
200.20
-59.98
Dec
29.60
4.69
8.66
-4.41
84.14
51.74
228.00
-52.08
9
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Latent Heat Flux
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The latent heat flux was positive to all months during daytime and nighttime (Table 1). From
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January to June (from summer to fall) the latent flux is near zero, for both daytime and
4
nighttime. With the decrease of precipitation, rising of wind intensity and the high air
5
temperature (from January to March, see Figure 3) the water surface temperature tents do
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decrease until reach the minimum temperature in July (Figure 7). From August to October
7
(winter to spring) the latent flux for daytime are more pronounced than nighttime that
8
coincide with the highest temperature amplitude shown in Figure 8. This occurs because the
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formation of fog just above the surface that warm the water (see Figure 7) by precipitation
10
into it, as observed in the Figure 11-a (mainly in the beginning of the rainy season in
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September). In accordance to Lofgren and Zhu (2000) the positive latent flux generally occur
12
when the atmosphere above the water is stable, with a little turbulent mixing in the
13
atmospheric boundary layer. From November to December the latent flux decrease again and
14
the cycle recommences.
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16
Sensible Heat Flux
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The negative sensible heat flux occurs when the surface losses heat by convective and
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advective processes and as opposite is positive when surface gain heat. For daytime the
19
sensible heat flux is negative only in January (summer) indicate that the water surface is
20
colder than December and February (see Figure 7), and positive for the others months (see
21
Figure 11-a). A typical case of heat gain trough sensible flux occurs in October (spring) when
22
the highest value occur (15.01 Wm-2, see Table 1) and reach the highest values of water
23
surface temperature (see Figure 7). For nighttime the sensible flux is negative for all months
24
of the year with a peak in September (-20.37 Wm-2, see Table 1) that is due to advection
25
caused by high wind intensity (3.1 ms-1, see Figure 3). The lowest flux occur in February
26
(-0.14 Wm-2) when the wind is two times smallest than in September (1.7 ms-1). This pattern
27
of sensible heat distribution through the time was observed also by Serra et al. (2007) in a
28
reservoir of Spain.
29
30
Longwave Radiation
31
The Longwave radiation from daytime and nighttime is very close, but during the nighttime
32
the values of Longwave are smaller than daytime. From May (95.94 Wm-2) to September
33
(106.36Wm-2) occur the period when the values of Longwave are highest than from January
34
(51.28 Wm-2) to April (78.56 Wm-2) and from October (96.12 Wm-2) to December (84.14
16
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1
Wm-2) for daytime. The period of high flux of Longwave radiation occur during the fall-
2
winter in dry season, that is, when the cloud cover is very low and the lowest values when in
3
the rainy season with high cloud cover (spring-summer). The Longwave during nighttime
4
follows the same pattern observed during daytime but with lowest values (see Table 1).
5
6
Net Flux
7
The daytime net flux was always positive whereas the nighttime was always negative. This
8
happens because during daytime the primary source of the energy to warm up the water
9
surface is the incoming shortwave radiation and the main source of loss of heat is the
10
evaporation. During nighttime this source of short wave radiation does not exist and all
11
storage energy during the day will be exchanged through the atmosphere mainly by wind
12
action. The wind is a great source of energy that could modify the water surface temperature
13
through the water column mixing due to surface water wind action.
14
The highest net radiation for daytime occur from December (285.47 Wm-2) to January (228
15
Wm-2) and the lowest values from June to August (see Table 1). For nighttime during June
16
occurs the highest negatively net radiation (-82.42 Wm-2), that is represents the month when
17
the loss of radiation is very high during night that coincide with the lowest values of water
18
surface temperature (see Figure 7-b).
19
The influence of the shown heat flux patterns and meteorological conditions near the
20
Itumbiara reservoir in the depth of mixed layer will be investigated using the equation 7.
21
22
Daytime and nighttime mixed depth
23
The annual cycle evolutions of the mixed depth are show in the Figure 12 for daytime and
24
nighttime case. For daytime the highest mixed depth can occurs during September when the
25
mixed depth reach 2.71m and in February the small mixed depth (0.14m).
26
In September (winter) some meteorological characteristics should be evidenced to help us
27
understand what happens to have this peak of mixed depth. In this month starts the rainy
28
season, with a high value of wind intensity (~3 ms-1), an elevation of air temperature and a
29
decrease of air humidity (see Figure 3). In the other hand the latent flux is the highest of the
30
annual cycle for daytime and the sensible heat shown a little variation but is positive. Take in
31
consideration the equation 7 and the results present here shows that this peak is cause by the
32
high wind shear velocity and an increase in the incoming shortwave radiation.
33
17
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2
Figure 11: Annual wind mix depth (m) at Itumbiara reservoir.
3
4
For nighttime the highest mixed depth occurs also in September but with 5.98m (two times
5
higher than daytime) and the lowest the 0.66m in February (four times higher than in
6
daytime). The difference between September nighttime and daytime is due to the lake breeze
7
(Arrit, 1987) during afternoon that destroyed the surface thermal stratification formed during
8
daytime, deepened the mixed layer (Imberger, 1985).
9
Using the results present in the Figure 11 it is possible to classify the periods of stratification
10
and mixture of the water column. From January to June (along of rainy season and beginning
11
of dry season, from summer to fall) the water column stratifies. From June to September (dry
12
season, from fall to winter) the water column mixes (this is the winter turnover). This is
13
evidenced also by the increase of the air temperature (Figure 3-b) that warm up the water
14
surface and the density of the surface enter in equilibrium with the water from the bottom and
15
a very little wind intensity is needed to mix the water column, causing the turnover. The event
16
of turnover should be visualized in the Figure 6 where for daytime the centre of the reservoir
17
presents a cold water that probably arrive from the bottom.
18
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1
From September to December (end of dry season to rainy season, from the end of winter to
2
summer) the water column stratifies again. As described by Ford and Johnson (1986) if the
3
depth of the water body is greater than the depth of mixed layer and not dominated by
4
advection, this system will probably stratify. As we observe in Figure 1 all centre of the
5
reservoir have depths higher than 40 m, so from January to September the water do not
6
stratify due to advection processes.
7
A multiple regression analysis will be done to establish a relationship between the heat flux,
8
meteorological parameters and the water surface temperature to help us to understand the
9
spatiotemporal patterns (Figure 6).
10
11
Statistical model for daytime and nighttime water surface temperature
12
The Pearson correlation computed between daytime and nighttime water surface temperature
13
derived from the MODIS image against meteorological parameters are present at Table 2. For
14
the daytime temperature the significant correlated meteorological parameters are air
15
temperature, evaporation, short wave radiation and long wave radiation. For nighttime
16
temperature the meteorological correlated parameters are air temperature, humidity, wind
17
intensity, precipitation, evaporation, sensible heat flux and net heat flux.
18
19
20
21
Table 2: Pearson correlation coefficients for daytime and nighttime surface temperature
against air temperature (Tair), humidity (H) wind intensity (W), precipitation (P), evaporation
(Ev), short wave radiation (SW), long wave radiation (LW), sensible flux ( φ S ), latent flux ( φ L )
22
and net flux ( φ N ).
Daytime water temperature
Tair
23
Nighttime water temperature
0.82
0.73
H
-
0,78
W
-
-0.75
P
-
0.85
Ev
0.83
0.72
SW
0.65
-
LW
0.77
-
φS
-
0.82
φL
-
-
φN
-
-0.86
Only significant values at 95% significance level are shown.
19
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The multiple regression analysis shows that for daytime water surface temperature the
2
correlated
3
(RMS=0.62ºC, ρ = 0.0001 ). For nighttime the meteorological parameters explain 94%
4
(RMS=0.45ºC, ρ = 0.0006 ). The representative equations of these relationships are presented
5
in equations 3 and 4.
meteorological
parameters
explain
92%
of
the
annual
variation
6
Tdaytime = −137.49 − (3.2Tair ) + (4.33Ev) − (0.96 SW ) + (0.72 LW )
(8)
Tnighttime = 25.78 + (2.16Tair ) + (0,052 H ) − (0.26W ) +
(9)
(0.28 P) − (1.08 Ev) − (0.35φ N ) + (0.40φ S )
7
Where Tdaytime is the daytime water surface temperature (ºC), Tnighttime is the nighttime water
8
surface temperature (ºC), Tair is the air temperature (ºC), H is humidity (%), W is wind
9
intensity (ms-1), P the precipitation (mm), Ev is the evaporation (mm), SW is the short wave
10
radiation (W m-2), LW is the long wave radiation (W m-2), φ N is the net flux and φ S is the
11
sensible flux.
12
13
The daytime water surface temperature driven forces as shown in equation 8 is related to
14
heating processes though the short wave, and consequently heating of the air temperature.
15
Then the lake emits thermal radiation (outgoing long wave) and evaporates the water surface.
16
Because of this the daytime water surface temperature following the air temperature (see
17
Figure 3-b) and latent signals (see Figure 10-a).
18
The nighttime water surface temperature pattern is more complex than daytime because it
19
depends on multiple parameters. The air temperature continues important to explain the water
20
variability but the precipitation and latent and sensible flux is important also. The
21
precipitation is important because during the raining season the difference between daytime
22
and nighttime temperature is lower than during the dry season (see Figure 8).
23
The wind intensity explain the cooling phases of the surface temperature because during the
24
occurrence of a lake breezes (from land to water) the reservoir loss heat (Arrit, 1987;
25
Simpson, 1994); this is especially true during September when the wind intensity is higher
26
than others months of the year (see Figure 3-a). The equations 8 and 9 will help us to discuss
27
the results shown above.
28
As shown in the equation 8 and at Table 2 the temporal variability found in the daytime water
29
surface temperature is due mainly by evaporation and air temperature. In fact the water
20
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temperature (Figure 7-a) follows the same pattern found in the air temperature (Figure 3-b).
2
This is obviously due to heat transfer from atmosphere to the water. Moreover, the
3
evaporation processes is responsible for cooling the water surface, causing a differential heat
4
and cooling mechanisms.
5
This mechanism is responsible for the interanual anomaly observed for daytime (Figure 9-a).
6
That is, during January when the anomaly is higher than others month the sensible heat flux is
7
negative (heat losses) and this is variable from year to year. However the incoming short
8
wave radiation is high and consequently the air temperature also. The variability of the
9
precipitation should be a major source of the interanual anomaly observed in the daytime
10
water temperature. This is supported also due to the fact that when the precipitation breaks the
11
interanual anomaly drops down until ±1 ºC (see Figure 9-a).
12
For nighttime the precipitation (R²=0.85) and sensible heat flux (R²=0.82) are the two more
13
influential variables in controlling the water surface temperature; the net radiation (R²=-0.86)
14
is negatively correlated. In accordance to Becker and Daw (2005) at night, if the air column
15
temperature is near dew point, surface temperature is a function of sensible heat fluxes only;
16
this is not the case, because we have others variables as driven forces. The measured time of
17
MODIS nighttime is approximately 23:30 (Figure 5) and at this time the water surface still
18
losses heat by emitted shortwave radiation (evaporation) and add heat through precipitation.
19
That is, when the water losses heat generally the air/water boundary-layer stays more
20
humidity.
21
22
Summary and Conclusion
23
The objective of this study was to map the surface water temperature and improve
24
understanding of spatial and temporal variations in the Itumbiara hydroelectric reservoir. Our
25
hypothesis on how meteorological and heat flux would effect the water surface temperature
26
was developed and tested. The main conclusions are:
27
- The spatial variation of both daytime and nighttime surface water temperature follows the
28
air temperature signal;
29
- Surface temperature time variation during daytime is higher through the year as compared to
30
that of nighttime;
31
- The thermal amplitude is more pronounceable during September and October and the lowest
32
amplitude occurs in January;
33
- The interanual mean anomaly is larger during January and September and smaller during
34
June for both daytime and nighttime;
21
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- The negative amplitude occurs mainly in summer season and heating from land to the center
2
of the reservoir;
3
- September is the month when the latent flux is higher than the others months of the year and
4
the sensible flux is negative booth for daytime and nighttime;
5
- The highest depth mix caused by wind intensity in daytime occurs in September and in July
6
for nighttime;
7
- The driven forces for daytime surface temperature are air temperature, evaporation, short
8
and long wave radiation;
9
- For nighttime are the air temperature, humidity, wind intensity, precipitation, evaporation,
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
sensible and latent flux.
Acknowledgment
The authors would like to thank the FAPESP Project 2007/08103-2, INCT for Climate
Change project (grant 573797/2008-0 CNPq/FAPESP) and Enner Alcântara thanks CAPES
grant 0258059.
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