107
Net Heat Flux at the Air-Sea Interface by Equilibrium Temperature Method in the Central Red Sea and
Comparison with Conventional Approach
Moaath Hamed Ghanem, Fazal Ahmad and Abdullah Mohammed Alsubhi
Department of Marine Physics, Faculty of Marine Sciences, King Abdulaziz University, Jeddah, Saudi Arabia
Abstract. Earlier studies by researchers estimate the net heat balance at the air-sea interface in the Red sea by conventional methods and conclude that the sea loses heat at the water surface which is compensated by an advective heat flow at Bab-al-Mandab. Here we apply a simple method based on equilibrium temperature concept to calculate the balance of heat at the air-sea interface in the central Red Sea. The method gives almost same results as those from conventional methods. The results show that central Red Sea gains heat from April to October and loses heat from November to March. The annual average heat loss at the air-sea interface is 28 Wm-2.
Introduction
The Red Sea extends from 12о 30' N to about 30o N and has a link with the Indian Ocean via Gulf of Aden. It is a semienclosed basin and the only significant opening is at Bab al. Mandab to the south (Fig.1).
The prevailing winds in the northern half (northward of about latitude 20o N) are NNW throughout the year. To the south of latitude 20oN the winds blow from the same direction as in the northern Red Sea from May to September. In October the winds start to change to SSE and retain this direction until April. An intermediate region occurs in the winter months between the NNW winds of the northern half and SSE winds of the southern half. The region varies in size and oscillates in position (Edwards, 1987).
Fig. 1. Red sea map showing the study area.
During the past few decades there has been a considerable research effort to understand the role of the air-sea interaction. The atmosphere and the ocean form a coupled system exchanging heat, momentum and water. The understanding to which extent the atmosphere and ocean interact with each other are closely related to the climate variation.
Meteorological air-sea interaction studies mainly concentrate on vertical fluxes of heat, water vapor and momentum. The investigation of these processes demands the recording of various independent environmental information such as routine hourly meteorological and oceanographic data, cloud cover and incoming solar radiation. The methods of determining fluxes are summarized by Kraus (1972).
Changes in the heat stored in the upper layers of the sea surface can be described by the imbalance between solar radiation, the net long wave radiation, latent and sensible heat fluxes as;
QT = Qs – Qb – Qe – Qh
Many different empirical, semi-empirical and deterministic relationships for the terms have been developed. However their accuracy highly depends on the determination of the transfer coefficients and each of the coefficients reveal a strong dependence on sea state, wind speed, stability and measurement height of the meteorological parameters (Taylor 1984).
Some studies (Ahmad and Sultan 1987;1989; Ahmad et al., 1989;
Al-Madani 2002; Bunker et al., 1982; Matsoukas et al., 2007; Sofianos et al., 2002 and Tragou et al., 1999) have been undertaken to estimate the heat fluxes in the Red Sea by conventional methods with meteorological data. These studies show that there is a net loss of heat at the air-sea interface in the Red Sea. From these studies Ahmad and Al-Barakati (2013) also conclude that there is net loss of heat at the air-sea interface for the whole Red Sea as well. This loss of heat at the surface is balanced by advective heat flow at Bab-al-Mandab.
Equilibrium Temperature Method
The equilibrium temperature approach is a simple method which encompasses the empirical relations of the individual terms of the above conventional equation so that,
QT = Qs-εσ(∆+tw)4-(ew-ea) f(w) – C1(tw-ta) f(w)
The 2nd, 3rd and 4th terms are general empirical relations for Qb, Qe
and Qh respectively. Here ∆ is the absolute temperature constant; ε is coefficient of emissivity; σ is Stefen-Boltzman constant; tw and ta are sea surface and air temperatures; ew and ea are saturation vapor pressure at sea surface temperature and vapor pressure at air temperature; C1is a numerical constant in Bowen's ratio and f(w) is function of wind speed.
The binomial expansion of the relation for Qb and retaining linear and quadratic terms only gives;
QT= Qs – (εσ∆4+ 4εσ∆3tw+6 εσ∆2tw2)-(ew-ea) f(w)- C1(tw-ta) f(w) Introducing a relation between saturation vapor pressure and water temperature by a linear relationship of the form with slope βw which is;
βw = (ew-ea)/(tw-td) where td is the dew point temperature.
Therefore
QT=Qs-(εσ∆4+4 εσ∆3 tw +6 εσ∆2tw2) - βw(tw-td) f(w) – C1(tw-ta) f(w) At equilibrium temperature te, the net rate of heat exchange at the surface would be zero, therefore substituting te for tw and βe for βw equation becomes.
0 = Qs – (εσ∆4+4 εσ∆3te + 6 εσ∆2te2) – βe (te-td) f(w) – C1(te-ta) f(w) Subtracting this equation from the above equation
QT= 4 εσ∆3(te-tw) + 6 εσ∆2 (te2-tw2) + (βw-βe) td f(w) + [(C1+βe) te – (C1+βw) tw] f(w)
The 2nd term on the right hand side is usually small. Also the difference between equilibrium temperature and the surface water temperature is relatively small for moderately long period of averaging, so the slopes of vapor pressure approximation βw and βe will be approximately equal;
βw = βe = β The equation becomes
QT = [ 4 εσ∆3+ 6 εσ∆2 (te2 – tw2) + (C1+ β) f(w)] (te-tw)
Or QT = K (te-tw)
where
K ≈ 4 εσ∆3 + 6 εσ∆2 (te + tw) + (C1 + β) f(w)
It follows from the equation that, for a given set of meteorological conditions, a body of water that has a temperature below equilibrium temperature will approach equilibrium temperature by gaining heat and a body of water above equilibrium temperature will approach equilibrium temperature by losing heat. The method is simple and encompasses all the terms of the heat balance equation into a simple relation.
Also K can be approximated as;
K= 4 εσ∆3 + 12 εσ∆2 tw + (0.47 +β) f(w) Where
C1 = 0.47 (Edinger et al 1974) and over longer duration te ≈ tw
ε ≈ 0.98 and σ = 5.67*10-8 Wm-2 deg-4
Various formulations have been suggested for the estimation of β which relate it with the average of sea surface and dew point temperatures (Thomann and Mueller, 1987).
β = 0.35 + 0.015 tm + 0.0012 tm2
tm is average of tw and td and f(w) is a function that depends on wind speed. With C1= 0.47 f(w) is 3.3w when w is in m/sec (Edinger et al., 1974).
Brady et al. (1969) have shown empirically that a good approximation to te is
te = td + Qs/K Where Qs is the solar radiation in W m-2
The thermal exchange coefficient enters in two places one directly as the proportionality coefficient and the other indirectly as the divider of the solar radiation in the approximation of te.
Materials and Methods
This study is undertaken to demonstrate the capability of the equilibrium temperature method to estimate net surface heat flux at the air sea interface in the central Red Sea and compare it with the conventional methods. The comprehensive ocean-atmosphere data set (COADS) are the complete surface marine observation 1o latitude x 1o longitude boxes mainly from merchant ships (woodruff et al., 1993).
However the COADS data have serious spatial and temporal sampling problems as measurements are along the shipping lanes with fair weather bias.
The satellite observations can also provide important parameters such as SST, air temperature, surface wind speed and relative humidity.
Based on the available data from COADS and satellite observations (1ox1o box) from 1995 to 2012 for the central Red Sea between 19o to 22o latitude Fig 1, the average monthly values of SST, air temperature, wind speed and relative humidity were derived and are plotted in Fig.2.
Fig. 2. Average monthly values of (a) SST ▬▬▬, air temperature - - - -, (b) wind speed - - - - and relative humidity ▬▬▬ based on 1995 to 2012 meteorological data.
The dew point temperature is derived from the air temperature and the relative humidity from the equation (Wanielista et al., 1997)
Td= (Rh/100) ^ (1/8) * (112+0.9* Ta) + (0.1 * Ta) – 112 and is plotted in Fig.3.
Fig. 3. Monthly variation of dew point temperature - - - and monthly estimates of solar radiation Qs ▬▬▬ absorbed at the sea surface (after Ahmad and sultan, 1989).
The monthly values of solar radiation incident at the sea surface are from Ahmad and sultan (1989) and are also given in Fig.3. The computed
values of K and equilibrium temperature te are given in Fig.4. Based on these data the monthly values of net surface heat flux at the air-sea interface are computed and plotted in Fig.5.
Fig. 4. Monthly estimates of constant K - - - - and monthly variation of equilibrium temperature te ▬▬▬.
Fig. 5. Monthly variation of net surface heat flux QT at the air-sea interface in the central Red sea.
Results and discussion
Monthly estimates of the net heat flux at the air-sea interface QT in the central Red Sea show that the sea gains heat from April to October and loses heat from November to March. The annual mean of QT is -48 Wm-2, meaning that the Red Sea may gain heat by advective heat transport through Bab al Mandab to balance the net negative annual heat balance at the air sea interface. This is in-agreement with previous studies (Patzert, 1974; Tragou et al., 1999; Sofianos et al 2002;
Abualnaja et al., 2011 and Albarakati 2005) where the authors conclude that the Red Sea gains heat by advective heat flow at Bab Al-Mandab, to
compensate the heat loss at the air-sea interface. Ahmed and Sultan (1989) show that the net annual heat loss from the central Red Sea is -34 Wm-2, this is almost in agreement with our results.
It can be concluded that the equilibrium temperature method can be safely applied to find the net heat flux at the air-sea interface in the Red Sea. The method is simple compared to the conventional methods.
References
Abualnaja, Y.O., Ahmad, F. and Almutairi, N.A. (2011) Balance of surface, advective and upwelling heat fluxes in the Gulf of Aden, Indian Journal of Geomarine Sciences, 40: 42- 47.
Ahmad, F. and Al Barakati, A.M.A. (2013) Heat balance of the Red Sea. Workshop on the "Red Sea, its origin, structure and Environment" 2-5 February 2013; Saudi geological survey.
Jeddah.
Ahmad, F. and Sultan, S.A.R. (1987) A note on the heat balance in the central region of the red sea. Deep-Sea Research, 34(10): 1757-1760.
Ahmad, F. and Sultan, S.A.R. (1989) Surface heat fluxes and their comparison with the oceanic heat flow in the Red Sea. Oceanologica Acta, 12(1): 33-36.
Ahmad, F., Sultan, S.A.R. and Moammer, M.O. (1989) Monthly Variations of Net Heat Flux at the Air-Sea Interface in Coastal Waters Near Jeddah, Red Sea. Atmosphere – Ocean., 27:
406-413.
Al-Barakati, A.M.A. (2005) Advective heat transport to the strait of Bab el.mandab. JKAU. Mar.
Sci., 16: 133-140.
Al-Madani, S.A. (2002) Variations of heat flux at the air-sea interface in the Red Sea MSc thesis, King Abdulaziz University, 84.
Brady, D.K., Graves, W.L. and Geyer, J.C. (1969) Surface heat exchange at power plant cooling lakes. Cooling water discharge. Project report No. 5, Electrical Institute Publication, No. 69-901, New York, USA.
Bunker, A.F., Charnock, H. and Goldsmith, R.A. (1982) A note on the heat balance of the Mediterranean and Red Seas. Journal of Marine Research, 40 (supp.) 73-84.
Edinger J.E., Brady D.K. and Geyer J.C. (1974) Heat exchange and transport in the environment: Cooling water discharge project report No 14. Electrical Power Research institution publication No 74-049-003 Polo Alto.
Edwards, F.J. (1987) Climate and Oceanography. In: Edwards, A.J. and Head, S.M. (Eds.), Key Environments Red Sea. First edition, Pergamon Books Ltd., 45-68.
Kraus, E.B. (1972) Atmosphere-Ocean Interaction, Claredon Press, Oxford, UK, 275 p.
Matsoukas, C., Banks, A.C., Pavlakis, K.G., Hatzianastassiou, N., Stackhouse P.W. Jr. and Varfavas, I. (2007) Seasonal heat budgets of the Red and Black seas. Journal of Geophysical Research, 112: 1-15.
Patzert, W.C. (1974) Wind-induced reversal in Red Sea circulation. Deep-Sea Res., 21(2): 109- 121.
Sofianos, S.S., Johns W.E. and Murray S.P. (2002) Heat and freshwater budgets in the Red Sea from direct observations at Bab el Mandeb. Deep-Sea Research II, 49: 1323-1340.
Taylor, P.K. (1984) The determination of surface fluxes of heat and water by satellite microwave radiometry and in situ measurements. In: C. Gautier and M. Fieux (ed.), Large-Scale Oceanographic Experiments and Satellites, D. Reidel Publishing Company.
Thomann, R. and Mueller J. (1987) Principles of surface water quality modeling and concept.
Harper Collins New York.
Tragou, E., Garrett C., Outerbridge R. and Gilman C. (1999) The heat and freshwater budgets of the Red Sea. Journal of Physical Oceanography, 29: 2504-2522.
Wanielista, M., Kersten, R. and Eaglin, R. (1997) Hydrography water quality and quality control. John Wiley and Sons 2nd edition.
Woodruff, S.D., Lubker S.J., Wolter K., Worley, S.J. and Elms J.D. (1993) Comprehensive Ocean-Atmosphere Data Set (COADS) Release la: 1980-92, Earth System Monitor, 4(1): l- S.
ﻲﻓ رﺣﺑﻟا ﺢطﺳ دﻧﻋ ءﺎﻣﻟاو ءاوﻬﻟا نﻳﺑ يرارﺣﻟا قﻓدﺗﻟا ﻲﻓﺎﺻ ﻷا رﺣﺑﻠﻟ ﻰطﺳوﻟا ﺔﻘطﻧﻣﻟا يرارﺣﻟا نازﺗﻻا ﺔﻘﻳرط مادﺧﺗﺳﺎﺑ رﻣﺣ
ﺔﻳدﻳﻠﻘﺗﻟا قرطﻟﺎﺑ ﺎﻬﺗﻧرﺎﻘﻣو
و ،مﻧﺎﻏ دﻳﻣﺣ ذﺎﻌﻣ
،دﻣﺣأ ﻝﺿﻓ
و ﻲﺣﺑﺻﻟا دﻣﺣﻣ ﷲادﺑﻋ
رﺎﺣﺑﻟا موﻠﻋ ﺔﻳﻠﻛ
، زﻳزﻌﻟادﺑﻋ كﻠﻣﻟا ﺔﻌﻣﺎﺟ
ﺟـ ةد - ﺔﻳدوﻌﺳﻟا ﺔﻳﺑرﻌﻟا ﺔﻛﻠﻣﻣﻟا
صﻠﺧﺗـــﺳﻣﻟا .
أ ﻲـــﺗﻟا ﺔﻘﺑﺎـــﺳﻟا تﺎـــﺳاردﻟا تـــﺗﺑﺛ أ
رﻳدـــﻘﺗﻟ نوﺛﺣﺎـــﺑﻟا ﺎـــﻫارﺟ
ا ﺢطــﺳ دــﻧﻋ يرارــﺣﻟا قﻓدــﺗﻟا ﻲﻓﺎــﺻ مادﺧﺗــﺳﺎﺑ رــﻣﺣﻷا رــﺣﺑﻟا ﻲــﻓ ءﺎــﻣﻟ
ﻷا رـــﺣﺑﻟا نأ ﺔـــﻳدﻳﻠﻘﺗﻟا قرـــطﻟا ﺔـــﻳرارﺣﻟا ﺔـــﻗﺎطﻟا نـــﻣ ﺔـــﻳﻣﻛ دـــﻘﻔﻳ رـــﻣﺣ
ًﻳوﻧﺳ ءاوﻬﻟا ﻩﺎﺟﺗﺎﺑ نـﻋ ةدوـﻘﻔﻣﻟا ةرارـﺣﻟا نـﻣ ﺔﻳﻣﻛﻟا ﻩذﻫ ضﻳوﻌﺗ مﺗﻳو ﺎ
ﻷا ﻩﺎـﻳﻣﻟا تارﺎـﻳﺗ قﻓدﺗ قﻳرط ﻲـﻘﻓ
رـﺑﻋ بدـﻧﻣﻟا بﺎـﺑ
، ﺔـﺳاردﻟا ﻩذـﻫ ﻲـﻓ
ﺎـــﻧﻣﻗ ﺑ يرارـــﺣﻟا نازـــﺗﻻا ﺔـــﻘﻳرط مادﺧﺗـــﺳﺎﺑ ﺔـــﻳرارﺣﻟا ﺔـــﻗﺎطﻟا ﺔـــﻳﻣﻛ رﻳدـــﻘﺗ
ءﺎـــﻣﻟا ﺢطـــﺳ دـــﻧﻋ رـــﺣﺑﻟاو ءاوـــﻬﻟا نﻳـــﺑ ﺔـــﻘﻓدﺗﻣﻟا ﻰطـــﺳوﻟا ﺔـــﻘطﻧﻣﻟا ﻲـــﻓ
ﻷا رﺣﺑﻠﻟ رﻣﺣ أ دﻗو ﺎﺑﻳرﻘﺗ ﺞﺋﺎﺗﻧﻟا سﻔﻧ ﺔﻘﻳرطﻟا ﻩذﻫ تطﻋ ﺔﻧرﺎﻘﻣ
ﺑ كﻠﺗ
مادﺧﺗـــﺳﺎﺑ ﺎـــﻬﻳﻟا ﻝـــﺻوﺗﻟا مـــﺗ ﻲـــﺗﻟا ىرـــﺧﻷا قرـــطﻟا
، أ دـــﻗو ﻩذـــﻫ ترـــﻬظ
ﺞﺋﺎﺗﻧﻟا ﻷا رﺣﺑﻠﻟ ﻰطﺳوﻟا ﺔﻘطﻧﻣﻟا نأ ﺎط بﺳﺗﻛﺗ رﻣﺣ
ﻝﻼﺧ ﺔﻳرارﺣ ﺔﻗ
أ ﻰــﻟإ ﻝــﻳرﺑإ نــﻣ ةرــﺗﻔﻟا نــﻣ ةرــﺗﻔﻟا ﻝﻼــﺧ ﺔــﻳرارﺣﻟا ﺔــﻗﺎطﻟا دــﻘﻔﺗو رﺑوــﺗﻛ
رﺑﻣﻓوــﻧ إ ــﻳﻣﻛ ردــﻘﺗو سرﺎــﻣ ﻰــﻟ قــﻳرط نــﻋ ةدوــﻘﻔﻣﻟا ﺔــﻳرارﺣﻟا ﺔــﻗﺎطﻟا ﺔ
ًﻳوﻧـــﺳ ءﺎـــﻣﻟاو ءاوـــﻬﻟا نﻳـــﺑ يرارـــﺣﻟا قﻓدـــﺗﻟا ﻝدـــﻌﻣﺑ ﺎ
رـــﺗﻣ ﻝـــﻛﻟ تاو28
ﻊﺑرﻣ .
