Indian Journal of Geo-Marine Science
Vol. 44(11), November 2015, pp. 1684-1689
Heat exchange at the air-sea interface in the Red Sea by equilibrium
temperature method
Moaath Hamed Ghanem*; Fazal Ahmad and Abdullah Mohammed Al-subhi
Department of Marine Physics, Faculty of Marine Sciences, King Abdulaziz University
Jeddah, Saudi Arabia
[E-mail: [email protected]]
Received 18 June 2014; revised 29 August 2014
For estimating the net heat flux by equilibrium temperature method, the Red Sea is divided into five regions (South, South Central, Central,
North Central and North) each extending 3o latitude from near Bab-el-Mandab (13 o N) to Suez Canal (≈28oN). Monthly averages of
oceanographic and meteorological data 1995-2012 (1ox1o grid) over the Red Sea are from Comprehension Ocean Atmosphere Data Sets
(COADS) and National Oceanic and Atmospheric Administration (NOAA). On an annual basis sea gains heat of 8 and 10 Wm-2 respectively
in the South and South Central region. In the Central, North Central and North regions the loss of heat is about 22, 30 and 75 Wm-2
respectively. As a whole the annual average loss of heat from the Red Sea is 22Wm-2. Earlier studies also conclude a net loss of heat at the
surface which is compensated by advective heat flux through Bab-el-Mandab varying from 7 to 19 Wm-2.
[Keywords: Red Sea, Equilibrium Temperature, Heat Exchange.]
Introduction
The exchange of heat between a water body
and the atmosphere includes heat loss from the
water by back radiation, evaporation, convection
and heat gain primarily through solar radiation
and long wave atmosphere radiation. Thus the
total downward flux of heat across the water
surface is the sum of the downward solar
radiation Qs minus the net upward flux of
longwave radiation Qb, latent heat Qe and
sensible heat Qh.
The estimation of the terms is through
paramitrization1-6. However large errors can be
introduced
by
the
application
of
4,7,8
and a single bulk formula
parameterization
with constant numerical coefficients is unable to
reproduce the fluxes at the surface for all
seasons and all climate regions9.
Assuming that the ocean is in contact with an
atmospheric equilibrium state, a heat flux
formulation;
QT= K(te - ts )
has been suggested, where te is the apparent
atmospheric equilibrium temperature, and ts is
the sea surface temperature in oc. If the
equilibrium temperature is higher than sea
surface temperature, the sea surface gains heat
and if the equilibrium temperature is less than
sea surface temperature, the sea surface loses
heat. K is a bulk coefficient which depends on
water temperature, wind speed and other
meteorological parameters such as saturation
vapor pressure10,11. In spite of its variation the
parameter is usually between 10-50 Wm-2oc -112,
13
.
Some investigators have replaced te by ta
where ta is the surface air temperature as the
equilibrium temperature has often been related
to air temperature14,15,16,17. Air temperature is
however insufficient to quantity all heat transfer
process through the water surface i,e solar
radiation and evaporative cooling. This
deficiency is removed when equilibrium
temperature is used instead of air temperature
because equilibrium temperature accounts for all
heat transfer processes; radiative, latent and
sensible across the air-sea interface.
GHANEM et al.: HEAT EXCHANGE AT THE AIR-SEA INTERFACE IN THE RES SEA
Methods
Equilibrium temperature is the temperature that
a water body will reach when the sum of the heat
fluxes across the air-sea interface is zero11,18. For
moderately long periods of averaging (weekly or
monthly) the difference between equilibrium
temperature and water temperature is relatively
small18.
Considering the empirical relations for net back
radiation, evaporative and sensible heat fluxes, an
equation can be written as
QT= Qs – [εσ(∆+ts)4 + ρa L(0.622/p) Ce (es-ea) w +
ρa Cp Ch (ts-ta) w] …. 1
∆ is 273; absolute temperature constant.
ε is the emissivity of sea surface.
σ is Stefan-Boltzman constant.
ρa is air density.
L is latent heat of evaporation (2500.8 – 2.3 ts
KJ/Kg)
P is atmospheric pressure.
Ce is transfer coefficient for latent heat flux.
es is saturation vapour pressure at sea surface
temperature.
ea is vapour pressure at air temperature.
Cp is specific heat of air.
Ch is transfer coefficient for sensible heat flux.
ta is air temperature in oc.
ts is sea surface temperature in oc.
.
W is wind speed
Introducing constant C1 in Bowen's ratio
C1 = ρa Cp Ch / ρa L Ce (0.622/p)
QT=Qs-[εσ(∆+ts)4 + ρa L Ce 0.622/p (es-ea)w + C1
ρa L Ce 0.622/p (ts-ta)w] …. 2
Considering
f(w) =ρa L Ce(0.622/p) w
the equation becomes
QT= Qs –[ εσ(∆+ts)4 + (es-ea) f(w)+ C1 (ts-ta)
f(w)]….3
Introducing a relation between saturation vapour
pressure and water temperature βw = (es-ea)/(ts-td)
where td is the dew point temperature. Binomial
expansion of relation for Qb and retaining linear
and quadric terms;
QT=Qs – (εσ∆4 + 4εσ∆3 ts + 6 εσ∆2 ts2) – βw(ts-td)
f(w) – C1 (ts-ta) f(w) …. 4
At equilibrium temperature te, the net exchange of
heat at the surface is zero.
Substituting te for ts and βe for βw
1685
1685
0= Qs - (εσ∆4 + 4 εσ∆3te + 6 εσ∆2 t2e) – βe (te-td)
f(w) – C1 (te – ta) f(w) …. 5
Subtracting equation (5) from equation (4) and
with βw=βe=β
QT=[4 εσ∆3 + 6 εσ∆2 (te+ts) + (C1+β) f(w)] (tets)....6
Or
QT= K(te-ts)
Where
K = 4 εσ∆3 + 6 εσ∆2 (te+ts)+(C1+β) f(w)
Over longer period of time: average te≈ average
ts
Therefore
K = 4εσ∆3+12σ∆2ts+(C1+β) f(w)
Many empirical relations have been suggested
for the estimation of β, one of which is11;
β = 0.35 + 0.015 tm + 0.0012 tm2
where tm is the average of sea surface and dew
point temperatures.
The commonly used relation for te is
te = td + Qs/K 11,19
Qs is in W m-2
Red Sea is a semi-enclosed basin which
stretches from about 12о 30' N to 30о N. (fig1).
The only significant opening is at
Bab.el.Mandab connecting the south of the Red
Sea to the Gulf of Aden. The climate is arid and
evaporation highly exceeds precipitation2,4,20-25.
The estimates of evaporation20 (≈ 200cm a-1) are
considerably higher than the annual evaporation
amounts from corresponding latitudes of the
other oceans which range from 120-130 cm a-1.
Fig. 1. Red sea map showing the study areas.
1686 1686
INDIAN J. MAR. SCI., VOL. 44, NO. 11 NOVEMBER 2015
The hydrological budget is negative because
of the excessive evaporation causing a two layer
system of flow from October to May and a three
layer system from June to September. Based on
the in and outflows at Bab-el-Mandab various
estimates of the net surface heat flux to the Red
Sea have been made which include, 7Wm-226; 19
Wm-223; 8±2 Wm-24; 11±5 Wm-224; 17 Wm-227.
The surface heat fluxes for the Red Sea region
have been calculated before2,4,21,22. These studies
conclude that there is a net lose of heat at the sea
surface which is compensated by a net advective
heat flux through Bab.el.Mandab.
Over the last few decades there has been
growing interest in the meteorology and
oceanography of the Red Sea. The
understanding of the net heat flux over the Red
Sea is necessary for input to climate models; and
study prediction and changes over days, weeks
and years. The equilibrium temperature method
is a direct and simple method to calculate net
heat flux at the air-sea interface.
Data Sources and Analysis
For this study the Red Sea was divided into
five regions: Southern region which extends
from near Bab.el.Mandab to 16oN latitude;
South Central region that lies between 16o to
19o; Central region between 19o and 22o latitude;
North Central from 220 to 25o latitude whereas
Northern region extends from 25o to entrance of
Suez Canal.
From the monthly values of International
Comprehensive Ocean Atmosphere Data Set
(ICOADS) (http://icoads.noaa.gov) and the
National
Oceanic
and
Atmospheric
Administration (NOAA) Live Access Server
(LAS)
(http://data.nodc.noaa.gov/las/getUI.do) data (1o
x 1o box) from 1995-2012 for the Red Sea figure
(1), the average monthly values of sea surface
temperature, air temperature, wind speed,
relative humidity and solar radiation were
derived for each grid points (1ox1o box).
From data at each grid point (1o x1o box), the
average values were derived for a region based
on the number of grids in that region.
The plots for monthly means (1995-2012) of
sea surface temperature, air temperature, wind
speed, relative humidity and solar radiation for
five regions are shown respectively in figures (26).
Fig. 2. Average monthly values of SST for five regions of
the Red Sea
Fig. 3. Average monthly values of Air Temperature for five
regions of the Red Sea
Fig. 4. Average monthly values of Wind Speed for five
regions of the Red Sea
Fig. 5. Average monthly values of Relative Humidity for
five regions of the Red Sea
Fig. 6. Average monthly values of Solar Radiation for five
regions of the Red Sea
GHANEM et al.: HEAT EXCHANGE AT THE AIR-SEA INTERFACE IN THE RES SEA
Sea surface temperature is minimum in
February and maximum in August in all the
regions figure (2). Generally, it decreases from
South to North as expected. Although the
general pattern of mean sea surface temperature
throughout the year is decreasing temperature
from south to north, there is an area of
temperature maximum in the southern Red Sea,
the position of which shows seasonal variation.
However, the averaging of the temperature from
all the grids in the South and South Central
regions evens out this variation. Air temperature
almost follows the same trend as that of sea
surface temperature figure (3).
The wind speed is slightly higher towards the
north and lower towards the south figure (4).
Relative humidity is generally higher towards
the south and lower towards north figure (5)
with a variation of about 10 percent in a region.
The highest relative humidity is about 78% and
lowest is about 62%.
The solar radiation decrease from south to
north during winter with a reverse trend in
summer months figure (6). The dew point
temperature is derived from the relation
td= (Rh/100) ^ (1/8)*(112+0.9* ta) + (0.1 * ta) –
112
and plotted in figure (7). Rh is relative humidity.
The dew point temperature is generally higher in
the south and decreases towards north with
higher values in summer and lower in winter.
Fig. 7. Average monthly values of dew point temperature
for five regions of the Red Sea
The value of thermal exchange coefficient K
depends on sea surface temperature; β, the
relation between saturation vapour pressure and
water temperature; f(w) the wind speed function;
constant C1 in Bown's ratio and indirectly on
transfer coefficients Ch for sensible heat flux and
Ce for latent heat flux. The calculated values of
1687
1687
K are plotted in figure (8). Variation of K is
between 35 and 55 Wm-2 oc-1.
Fig. 8. Average monthly values of K for five regions of the
Red Sea
Conventional equations to determine sensible
heat flux Qh; and latent heat flux Qe depend on
the choice of the values for transfer coefficients.
These coefficients depend on the wind speed,
sea-air temperature difference and relative
humidity. The coefficient Ch varies with stable
and unstable conditions over the sea, being
lower in stable condition (ta>ts) and higher in
unstable condition (ts>ta).
Over the Red Sea the air temperature is
generally higher than the sea surface
temperature in the southern regions and lower
than sea surface temperature in the northern
regions. An average value of the coefficient2,28
Ch = 1.2x10-3is considered. The evaporation over
the Red Sea is much higher than the
corresponding oceans at the same latitude.
Ahmad and Sultan22 used a value of 1.7x10-3 for
Ce with sea surface and meteorological data over
the Central Red Sea from Saudi Sudanese
commission for the exploitation of the Red Sea
resources. In the present study the above values
of Ch and Ce are considered for the wind
function f(w) and constant C1.
The equilibrium temperature te is calculated
from the solar radiation, coefficient K, the dew
point temperature and given in figure (9). te
varies from about 17 to 33 oc.
Fig. 9. Average monthly values of te for five regions of the
Red Sea
INDIAN J. MAR. SCI., VOL. 44, NO. 11 NOVEMBER 2015
1688 1688
The value of equilibrium temperature te is
lower in the winter months and higher in the
summer months. Generally the sea gains heat in
summer and loses heat in winter.
From the difference in equilibrium and sea
surface temperature and the relevant value of K,
the net heat exchange at the sea surface is
calculated and shown in figure (10).
Fig. 10. Average monthly values of Qt for five regions of
the Red Sea
For comparison QT values are also calculated
based on the monthly data for each year from
1995-2012 and the annual averages are made for
a particular year. The mean of annual averages
(1995-2012) and standard deviation are given in
Table (1). This table also shows the values of QT
based on 18 years (1995-2012) monthly
averages of data.
Table 1: Values of QT based on: 18 years monthly averages
of data and monthly data for each year.
Region
South
South Central
Central
North Central
North
Qt based on
monthly averages
of 18 years (19952012) data
-2
8 Wm
10 Wm-2
-22 Wm-2
-30 Wm-2
-75 Wm-2
Qt based on each
year's monthly
data (1995-2012)
In the Southern region the higher heat gain is
during May and higher loss of heat in
November. Net annual gain is 8 Wm-2. South
central region follows similar trend with higher
heat gain in April-May and higher loss during
November-January. The annual average gain
is10 Wm-2. The Central region has higher gain
during May to July and higher loss in November
to February. Annual average loss is 22 Wm-2.
North central region follows the same pattern
with annual average loss of 30 Wm-2. In the
Northern region the heat gain during summer
months is comparatively less and the heat loss is
higher compared to other regions. Annual
average loss is 75 Wm-2. For the Red Sea as a
whole the heat loss is 22 Wm-2 at the sea
surface. Previous studies by conventional
methods also indicate that the sea loses heat at
the surface which is compensated by the
advective heat flux at Bab-el-Mandab3,4,23.
QT values based on monthly data for a
particular year give heat gain of 6 ± 19 Wm-2; 11
± 11 Wm-2for South and South Central regions;
and heat loss of 21 ± 13 Wm-2; 29 ± 18 Wm-2
and 77 ± 17 Wm-2 respectively for Central,
North Central and North regions of the Red Sea.
The equilibrium temperature method is an easier
approach to calculate net heat flux at the surface
of a water body.
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6±19 Wm
11±11 Wm-2
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2.
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Results and Discussion
Generally the sea gains heat in summer and
loses heat during winter. On an annual basis the
Southern and South central regions gain heat.
The other three regions Central, Northcentral
and North lose heat and the loss of heat
increases towards the north. There is a
considerable monthly variation in the heat loss
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