A STUDY ON EARTH CLOUD SPACE INFLUENCED BY CERTAIN DYNAMICS FACTORS

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1 A STUDY ON EAH COUD SPACE INFUENCED BY CEAIN DYNAMICS FACTORS Vivekanand Yadav and R. S. Yadav Deartment of Electronics and communication Engineering J K Institute for Alied Physics and Technology University of Allahabad, Allahabad ABSTRACT In this aer, dynamics factors and their influences in the formation of earth s cloud field have been studied. These influences are mainly based on heat and water-vaour flow equations in a turbulence atmoshere. The equations for cloud water content have been develoed, considering the influence of vertical movement and heat, cold advection and turbulence exchange. The conditions of formation and develoment of many form of cloud are observed in mesosheric region. I. INTRODUCTION The clouds are formed a result of the transformation of water vaour form a gaseous into a liquid or solid state. The otical roerties of clouds differ from the roerties of a cloudless atmoshere. The relationshis between atmosheric (air) temerature T and clouds exceed many times the relationshis between T and greenhouse gases and admixtures, rimarily carbon dioxide Matveev.et.al [1]. The formation of cyclones (including troical ones), tornados, strong winds, and floods is closely related to clouds Steven M. Smith [13], Matveev.et.al [9-10], Michael A.Persinger [11] and Stubenrauch.t.al [12]. Matveev.et.al [2 4] obtained formulas for changes in air temerature and cloud water content with time under the action of vertical movement. In this aer, other factors have been investigated which influence the formation and develoment of a cloud deending on the atmosheric temerature and water content. The accuracy of the results of this aer is obtained by the hel of MATAB Simulation setu. The aer has been devided into sections: Initial Equations, Vertical Movement, Turbulence, Cloud Formation and the Change in Water Content with Time, results and discussions, conclusion and future work. II. INITIA EQUATIONS Before any cloud forms, water vaor must achieve a state of saturation and the relative air humidity must attain a value of f = e 100%. Since the ressure of saturated water vaor E is a function of E temerature, to estimate change f, it is necessary to use the flow (balance) equation for water vaor and the heat flow (balance) equation. We write the heat balance equation in the form c + = ε T (1) Where T and P are air temerature and Pressure; R is the gas constant; c is the heat caacity of air; is the heat of vaor transformation (condensation); d = + u + v + w is the oerator of the total (individual)derivative; u, v and w are the airseed(wind seed) rojections along axes x, y and z(axis z is directed uward along the vertical0; t is time ; and ε T is the turbulent flow of heat(all quantity refer to 1kg of air). 945 Vol. 6, Issue 2,

2 The mass fraction of saturated water vaour q m entering into the third summand in the left-hand side of (1) is related to the saturation ressure E by the correlation. (T) q m (T)/ (2) ogarithmically differentiating it, we obtain the balance equation for water vaor in a saturated state (in a cloud): By (2) ogq m = log (0.622) +log E (T) log Differentiating w. r. t, t, we have 1 = 0+ 1 de (T) 1 q m E (T) de = = q m ( 1 E R v T 2 Where R v = 461.5J kg K de (T) 1 E (T) By (1) c = - [{q m( 1 E (T) ) +ε q (3) is the gas constant for water vaour. de (T) 1 c = +q m - q m de (T) -ε E (T) q +ε T c = + c = E (T) 0.622E (T) E (T) E )} + ε q] + ε T, by (3) E R v T E (T) 2 ε R v T 2 q+ε T -ε q+ε T by (4) (4) [c E (T) ] R v T 2 = ( 0.622E (T) + ) ε 2 q+ε T E (T) c [1 + ] c R v T E (T) c [1 + ] c R v T 2 = 1 2 (+0.622E (T)) ε q+ε T = (T) 2 ( E ) ε q+ε T = c 0.622E (T) (1+ ) ( E (T) + 1 (ε T ε q ) c ( E (T) = a c + 1 (ε T ε q ) c ( E (T) Where a = ( E (T) ) By (3), By (4), de E = ( E (T) = q m ( 1 E (T) R v T 2 (5) de (T) 1 ) +ε q Putting the value of de in (3), we have E (6) 946 Vol. 6, Issue 2,

3 = q m [ R v T2 (a c + 1 (ε T ε q ) c ( E (T) ) 1 ) +ε q] = q m { a R v T 2 c + 1 (ε T ε q ) c ( E (T) R v T 2) 1 }+ε q = q m { 1 ( a R v T 2 c -1) + 1 (ε T ε q ) c ( E (T) R v T 2}+ε q = q m { 1 ( ar ) R v Tc + 1 (ε T ε q ) c ( E (T) R v T 2} +ε q = q m ( a2 R v T 2 c - ) +q m (ε T ε q ) c ( E (T) ( a2 - ) E R v T 2 c 1 (ε T ε q ) c ( E (T) from (2) By (6) (1-a) = E/P E/R v T 2 c R R v Tc (a2 ) E 1 (ε T ε q ) RR v T 2 c c ( E (T) (7) (1 a) (R c R v T) R v T 2 c R(R v T 2 c E) (8) a = (+0.622E) (R v T 2 c E) R v T 2 c a = (+0.622E) R v Tc (R v T 2 c E) R Putting the value of a in (7), we have (9) (+0.622E) RvTc ( (RvT 2 c R R E) R v Tc RR v T 2 c ) E ( R R v Tc ) E 1 (ε T ε q ) R (R v T 2 c E) c ( E (T) 1 (ε T ε q ) c ( E (T) = 0.622E R ( R R v Tc ) E 1 (ε T ε q ) (R v T 2 c E) c ( E (T) a = ( E (T) ) ( E (T) = (1-a) E 1 (ε T ε q ) c ( E (T) (10) 947 Vol. 6, Issue 2,

4 a = γ ma (11) Where γ ma is moist-adiabatic gradient and is dry- adiabatic gradient. Since γ ma is always less than, in moist-saturated (cloud) air, arameter a is always less than unity (a< 1). < 0 in case of a article of air moving toward lower ressure. By (5) and (10), < 0 and dδ m < 0, In saturated air, q m decreases then cloud water content δ increases The increments of water content dδand temerature as ressure changes are, according to (5) and (10), related by the correlations = (1-a) = a c By eqs (10a) and (5a), we have (10a) (5a) = c (1 a) a (1 a) = dδ, dδ = c (12) a By equation (11), it is clear that for < 0 < 0 and dδ > 0, Also, when <0 Then dδ > 0. Thus, the increment dδ in large cyclone is significant in our study. For case of unsaturated (dry air) = 0, then (1) becomes c = ε T then (6) and (11) take the form; a=1; γ ma =1 Then equation (10) becomes Along the vertical, the correlation 1 (ε T ε q ) c ( E (T) = + u + v + w (13) Becomes = wgρ = wg = w (Static equation - = gρ) where ρ = is the air density; g is the increase in the seed of freefall From (5) and (13), we have = a ( wg ) + 1 (ε T ε q ) c c ( E (T) + u + v + w = awg + 1 (ε T ε q ) c c ( E (T) 948 Vol. 6, Issue 2,

5 = awg ( u + v + w ) + 1 (ε T ε q ) c c ( E (T) = awg { u + v + w( γ)} + 1 (ε T ε q ) c c ( = γ, vertical temt. gradient) ag = w(γ ) - ( u + v ) + 1 (ε T ε q ) c c ( E (T) ( E (T) ( a = γma ) = w(γ γ ma From (10) and (13), we have + u + v + w g ) - ( u + v ) + 1 (ε T ε q ) c c ( E (T) (14) = (1- γ ma )( wg ) E 1 (ε T ε q ) c ( E (T) III. + u + v + w = g (1- γ ma )w E = w[ g (γ γ ma ) + ] (u + v ) E a VEICA MOVEMENT (CONVECTION) From (3) = q m( 1 E (T) E (T) 1 E deends only on temerature and from (4), de = 1 (ε T ε q ) c ( E (T) 1 (ε T ε q ) c ( E (T) ( 15) ) (16) E R v T 2 E = ( de ) E = -γ (17) R v T 2 By Static equation (- = gρ) 1 = - g (ρ =, R=R R v T 2 vt) (18) By eqs. (17) and (18), eq. (16) becomes, By eqs. (15) and (19), = q m(-γ g R v T 2 R v T ( ) w = w[ g ( γ ma ) + ] 2) (19) ( ) w = w[ g (1 γ ma ) + ] ( ) w = w[ g (1 γ ma ) + q γ m (-γ a R v T 2 R v T 2)] Advective heat and water-vaor flows, according to eqs. (14) and (15), are written in the form g (19a) ( ) a = - ( u + v ), (20) ( ) a = (u + v ). (21) ogarithmically differentiating eq. (2) by x, we obtain 949 Vol. 6, Issue 2,

6 de = de dx dx = q m( 1 E E 1 ) (22) By eq. (4), By eq. (21), = q m( 1 E E 1 ) R v T 2 dx de = E R v T 2 de dx = E R v T 2 dx Similarly, By eq. (21), ( ) a ( ) a = q m q m R v T 2 = (u = - {u ( q m R v T 2 = q m q m R v T 2 + v ) q m ) + v ( q m R v T 2 ( ) a = - q m R v T2(u + v Multilying eq. (25) air density ρ,we rewrite it ρ cρ = -q mρ R v T2 (u + v ) + q mρ = - c q mρ R v T2 (u + v = c q m R v T2 (u = b(u + v )- c q m (u (u ) +c q mρ + v ) (u + v ) + v )- d(u + v q m )} ) + q m + v ) 950 Vol. 6, Issue 2, (23) (24) (u + v ) (25) ( = δ, δ = cδ) ) (26) Where b = q m, d = c q m (27) R v T 2 Multilier b in equation (26) coincides with the multilier in equation (19a) if we rewrite it for the rate of convective change in the bulk water content of the cloud, δ = cδ. ( δ ) w = cw[ g (1 γ ma ) + q γ m (-γ g a R v T 2 R v T2)] (28) IV. TURBUENCE According to Matveev.et.al [5], it was shown that turbulent exchange of heat and moisture lays a significant role in cloud formation and the change in water content. Turbulent heat and water-vaor flows, according to Matveev.et.al [6], have the form ε T = k c s ( 2 T + 2 T 2 2) + k z( + γ ma) (29) ε q = k s ( 2 q m q m ) + k 2 z( + C) (30) k s and k z are the coefficient of turbulence along the horizontal and vertical: C = c ( γ ma ) If we are correlation (23) and exression used in [6] ( + C) = q m R v T 2 ( + γ ma) (31)

7 From eqs (23), (24),(31) and (23) eq (30) takes the form, ε q = k s [ q m R v T 2 2 T q m q m 2 ( )2 + q m 2 T R v T q m 2 + q m ( 2 2 )2 ] + k z( + γ ma) ε q = q m [k R v T s( 2 T + 2 T ) + k z( + γ ma)] + k s 2{( )2 + ( )2 }- k sq m { } (32) V. COUD FORMATION AND THE CHANGE IN WATER CONTENT WITH TIME Comarison of Eqs. (20) and (25) and (27) and (32) for the temerature and mass fraction of water vaour shows that for all tyes of rocesses, the following equality may hold: = q m q m (33) R v T 2 Since = δ or = 1 c = (-c) = ( c)[ q m R v T 2 q m ] E = ( c)[ q m ] (34) R 2 v T 3 Multilying (26) by the time increment t, we write Eq. (34) for the increment in the bulk cloud water content Δδ* = δ in the form t Δδ*= -b ( T con + T adv + T turb ) (35) Where T con, T adv and T turb are the temerature increments for time t under the action of convection and turbulence? T con = w(γ γ ma ) t VI. VII. T turb = RESUT AND DISCUSSION T adv = (u + v ) t ε T ; b = E (36) c t R 2 v T 3 (i) When there is moisture-stable stratification (γ < γ ma ) at fixed levels (at oints), the air temerature decreases and cloud water content increases with time with uward movement (w > 0); the temerature increases and the cloud water content decreases with downward movement (w < 0). When there is non-moisture-stable stratification (γ >γ ma ), the signs of T con and Δδ*are the oosite of the signs for the case of (γ <γ ma ). (ii) When there is heat advection, at fixed oints, temerature increases with time ( T adv > 0) and the cloud water content decreases (Δδ* < 0). With cold advection, at oints with fixed coordinates, the temerature decreases ( T adv < 0) and cloud water content increases (Δδ* > 0). On the basis of Eq. (32) we can state that during cloud formation and develoment Stubenrauch et.al [12], the advective factor lays a role that is quite comarable to the convective factor. (iii) Under the action of turbulent heat and moisture exchange, the air temerature changes and, as a result, the mass fraction of water vaor also changes. The third equation of (33) is ositive only uon assage to turbulence along the horizontal in a closed cold region surrounded by a warm region. CONCUSIONS The heat and water vaor flow equations relate heat advection, vertical movement and turbulence exchange in some extent in our region. The role of cold air is more influensive in formation of cloud wall in a troical cyclone owing to heat flow that the cyclone draws from the ocean, the temerature in which (at distance of km from the earth s surface) increases by a few tens of degrees er day. This growth in comensated by advection of cold air at km from the cyclone. Due to 951 Vol. 6, Issue 2,

8 the action of this advection, owerful nimbocumulus clouds and heavy reciitation are formed in mesosheric region. In this aer, we focused on the fact that at the initial stage of the birth of a cloud, a significant role is layed by turbulent fluctuations in air temerature and humidity and the subsequent dislacement of volumes with different thermo hygrometric characteristics at which condensation of water vaor occurs. At the exense of heat condensation, the temerature of the mixture increases, which leads to the formation of vortex movement, in which colder air of the medium enters a article of the mixture and causes additional condensation sontaneous cloud growth arises. This rocess lays a determining role in the near-simultaneous formation of cumulus clouds over the largest art of the skydome following clear weather. VIII. FUTURE WORK (1) In our oinion, in the simultaneous formation of small cumulus clouds over the largest art of the skydome after clear weather, turbulent mixing of volumes of air at various values of temerature and relative humidity lays the main role. This is the future work. (2) Fluctuations in air temerature and humidity, which increase with increasing windseed and turbulent exchange, are well known not only from the results of secial measurements, but also, for instance, from televised weather data. This is the future work. ACKNOWEDGMENT Authors are grateful to the referee for his constructive criticism and valuable suggestions for the imrovement of this aer. REFERENCES [1].. T. Matveev and Yu.. Matveev, Oblaka i vikhri - osnova kolebanii ogody i klimata (Ross. Gos. Gidrometeorol. Univ., St. Petersburg, 2005) [in Russian]. [2].. T. Matveev and Yu.. Matveev, Dokl. Akad. Nauk 374 (5), 688 (2000). [3].. T. Matveev, Dinamicheskie faktory obrazovaniya oblakov i osadkov, Vorosy fiziki oblakov (Gidrometeoizdat, St. Petersburg, 2004) [in Russian]. [4]. Yu.. Matveev, Ob uravneniyakh ritoka tela i vodyanogo ara. Uchenye zaiski, no. 2 (Ross. Gos. Gidrometeorol. Univ., St. Petersburg, 2006) [in Russian]. [5].. T. Matveev, Dinamika oblakov (Gidrometeoizdat, eningrad, 1981) [in Russian]. [6].. T. Matveev, Osnovy obshchei meteorologii. Fizika atmosfery (Gidrometeoizdat, eningrad, 1965) [in Russian]. [7].. T. Matveev, Fizika atmosfery (Gidrometeoizdat, St. Petersburg, 2000) [in Russian]. [8]. Yu.. Matveev and. T. Matveev, Izv. Ross. Akad. Nauk, Fiz. Atmos. Okeana 36 (6), 760 (2000). [9].. T. Matveev, Yu.. Matveev and E.Yu.Nikolaeva Dynamic factors in the formation of the earth s cloud field Atmosheric and Oceanic otics, June 2009, Volume 22, Issue 3, [10]..T. Matveev, Yu.. Matveev Formation of reciitation hydrological cycle vol. II [11]. Michael A.Persinger The ossible role of dynamics ressure from the interlanetary magnetic field on global warming international journal of hysics science vol (1) , jan [12]. Stubenrauch, C. J., A. Chedin, G. Rädel, N. A. Scott, and S. Serrar Cloud roerties and their seasonal and diurnal variability from TOVS ath-b. J. Climate 19: [13]. Steven M. Smith, Seasonal variations in the correlation of mesosheric OH temerature and radiance at midlatitudes, Journal of Geohysical Research, vol. 117, a10308, 8., AUTHORS Vivekanand Yadav is currently ursuing D.Phil at University of Allahabad, Allahahbad (India) and obtained his B.E in ECE from Dr.B.R.A.University Agra, India. Obtained M.Tech(EC) at HBTI Kanur from UPTU, ucknow, India. Area of interest are Filter Design, Digital Signal Processing and Atmoshheric Dynamics. 952 Vol. 6, Issue 2,

9 R.S.Yadav is Presently working as Reader in the University of Allahabad,Allahabad ,India. Obtained D.Phil from University of Allahabad,Allahabad ,India.Area of interest are Digital Electronics and Atmoshheric Dynamics. 953 Vol. 6, Issue 2,