CHAPTER IV
DYNAMICS OF OROGRAPHIC RAINFALL
Page
Summary 132
4 .1 In troduc tion 133
4.2 Region of our study 135
4.2.1 Rainfall distributions in these
r eg ions 138
4.3 The model of orographic rainfall 145
4.3.1 Model for vertical velocity 146
4.3.1.1 Solution for Western Ghats 148
4.3.2 Numerical evaluation 157
4.4 Computation of rainfall 158
4.4.1 Modification for unsaturation 160
4.5 Downwind drift of precipitation 163
4.6 Discussion and results 164
4.7 Conclusion 188 132
CHAPTER IV
DYNAMICS OF OROGRAPHIC RAINFALL
SUMMARY
In this chapter, an attempt has been made to study the dynamic influence of orography on rainfall distribution. Some sections in the Western Ghats and in the Khasi and Jaintia hills in India have been considered for this purpose.
A two-dimensional model for orographic rainfall was deve loped by Sarker (1)66, 1967) and applied by him along the Western
Ghats and later applied by De (1973) for the Khasi-Jaintia hills.
The same model has been applied here for a number of cases in the Western Ghats and the Khasi-Jaintia hills. Vertical velocities have been computed by the model. Rainfall has been computed from the vertical velocities using the principal of conservation of mass and moisture. The computed rainfall distributions agree well with the observed rainfall distribution both for the Western Ghats and the
Khasi and Jaintia hills during the active monsoon situations. The peak in rainfall distribution is seen to be purely an orographic effect.
However, the performance of the model is not good for weak monsoon cases when the atmosphere is not saturated. Some modifica tions have been made in the model to take into account unsaturated conditions. The results of such cases have been presented. 133
CHAPTER IV
DYNAMICS OF OROGRAPHIC RAINFALL
4 . 1 Introduction :
The rainfall of a place is believed to be influenced by the presence of orographic barriers. The effect of topography is fairly well known at least in qualitative term in the sense that rainfall increases with height and is greater on the slopes facing the prevailing wind than on the lee slopes. The precipitation occurs due to lifting of saturated air as a result of perturbations caused in it by the orography. However, the precipitation in mountainous regions may also be due to several other causes viz., horizontal convergences and convective instability.
Qualitative evaluation of rainfall in mountainous regions is a complex problem as it involves different physical and dynamical aspects of the process on different scales.
First,there are synoptic scale factors which determine the characteristics of the airstream which crosses the mountain, its speed, direction, thermal stability and moisture content.
Second aspect is the microphysics of the rain and cloud forming process. Third aspect is the dynamics of the airflow over and around the hill which determines the distribution of vertical velocity and the displacement of the airstream at each level and along the entire path. 134
These important aspects of the problem have been studied by several investigators. Mention may be made of the studies by Douglas and Glasspoole (1947), Ludlam (1955,
1956) and Sawyer (1956); although the list is not quite ex haustive. An empirical model for computation of orographic rainfall is also available in the Hydrometeorological Report
No.36, U.S. Weather Bureau (l96l).
The monsoon rainfall over the Western Ghats and in
Assam particularly over the Khasi and Jaintia hills is believed to be strongly orographic in character. During the southwest monsoon, the windward slopes of the mountains almost in the direct path of monsoon winds, get copious rainfall and heavy clouding, the rainfall decreasing on the lee ward side. For the first time Sarker (1966, 1967) proposed a sound dynamical model of orographic rainfall based on the theories of airflow for the Western Ghats. The model gives the amount of rainfall due to lifting caused by orographic forcing and also accounts for the variation of rainfall along the slopes. The agreement between the observed and computed rainfall during monsoon season over the Western
Ghats is remarkable. This model was successfully applied by
De (1973) for the Khasi and Jaintia hills in northeast India.
We apply the same model for a number of cases in
some sections of the Western Ghats and the Khasi-Jaintia hills. 13 5
This model is based on the assumption that the
atmosphere is saturated. We found that there is good agree
ment between observed and computed rainfall during active
monsoon cases when the atmosphere is saturated. However,
during weak monsoon cases the performance of the model is
not satisfactory. Accordingly we made some modifications
in the model to take into account unsaturation during weak monsoon cases. Some results are also presented for a few
cases of this type.
4.2 Region of our study :
We shall be considering orographic rainfall in the Western
Ghats and the Khasi-Jaintia hills. The topography is shown in
Fig. 4.1 or two sections (marked by rectangles) of the Western
Ghats and in Fig. 4.2 for the Khasi and Jaintia hills and its
neighbourhood (marked 2). The Western Ghats run approximately
in the north-south direction with average height 1 km. The
prevailing wind during southwest monsoon season is westerly
in the lower levels and easterly in the higher levels. The
Assam hills run approximately in a north-south direction with
a westward extension along the Khasi and Jaintia hills; the
height of the hills varies between 1-2 km. The prevailing
wind over the Khasi and Jaintia hills is southerly. Hence in
case of the Western Ghats as well as the Khasi and Jaintia
hills, the prevailing wind is perpendicular to the barrier. 136
IBOMAi¥J.n j\ ! <; \
KHANMlA^~-».VADGAON^
"' -^POONA
Fig. 4-1 137
1 BRAHMPUTRA VALLEY 5 KUMONRANGE a NORTH BURMA HILLS 2 KHASI a JAINTIA HILLS 6 IRRAWADY VALLEY 3 MANIPUR & NAGA HILLS 7 YUNNAN PLATEAU 4 CHINDWIN VALLEY 8 GREAT SNOWY MOUNTAINS
>3 kmI 2-3 kmll-2 krr. [5CO m IzOOrr. Fig. 4-2 138
4.2.1 Rainfall distribution in these regions :
Before proceeding to the actual model of orographic rainfall it is of interest to examine the observed features of rainfall over the Khasi and Jaintia hills and the Western
Ghats in a broad sense. The normal rainfall daring southwest monsoon (June to September) is found to increase from south to north as we proceed along a profile from the plains of the
Khasi and Jaintia hills on the westward slopes (Fig. 4.3(a)).
Rainfall is maximum over Cherrapunji (25 15'N and 91 44'E) which is situated on the windward side at about 20 km from the crest of the hill. Rainfall decreases sharply between Cherra punji and Mawphlang which is at a distance of 20 km only.
Further northwards Shillong and Gauhati have much lesser amount of rainfall.
The rainfall distribution along two sections of the
Western Ghats eastward from the coast is shown in Fig. 4.3(b) and (c). The strong orographic effect is also seen here.
The rainfall of Khandala and Agumbe on the windward side are the highest with low lee side values over Pune and Chikmagalur.
The rainfall distributions during different months of the southwest monsoon for three sections are shown in
Figs. 4.4, 4.5 and 4.6. Strong orographic effects are noticed in all these months over Agartala - Gauhati section of the Khasi and Jaintia hills (Fig. 4.4) and Mangalore - Chikmagalur section 139
o _c/> I- o if LiJ C/) o
< a 5 1 2 « • _. -3 < « tt < z i= x < ? £ < a: 3 < E ~o cc " I ft:w d^ J r1> ^> CD w fO o> OOO 0 0 OOO 0 0 O 00 en ^r CM ~ y3awaid3S 01 3Nnr 1H9I3H (oio) HVJNIVy 1VN0SV3S 140 Western Ghats ( Bombay - Pune Section) B- BOMBAY, Pe-PEN, R - ROHA, K-KHANDALA, L-LONAVLA, V-VAOGAON, P-PUNE . 600 E 400k *•• a. a» CO 200 k c I Km 40 50 DISTANCE (Km) Fig, 4-3 (b) 141 < o < < o ce a. < a. cc CD o a. CO i CO •*: < < cc i < CD o JQ X E CO XL < _J cc < cc < _J UJ < CO I co CD I I CD z: < i_ cc o CO o I CO cc c UJ z> O o cr 2! i 2! X o UJ O _J CD o < X o ID UJ 2: _J < < < i i CD < I CO (uiQ) ITVdNIViJ 1VN0SV3S J.H9I3H 142 KHASI - JAINTIA HILLS ( AGARTALA-GAUHATI SECTION) JUNE JULY AUGUST SEPTEMBER AGARTALA. KAILASHAHAR. SILCHAR. CHERRAPUNJI. MAWPHLANG. SHILLONG. GAUHATI. -160 -160 -140 -120 100 -80 -60 -4-0 -20 HORIZONTAL DISTANCE (km) Fig. 4-4 143 WESTERN GHATS (BOMBAY-PUNE SECTION) OO-J HORIZONTAL ..DISTANCE (km) Fig.4-5 144 WESTERN GHATS ( MANGALORE-AGUMBE SECTION ) JUNE - JULY AUGUST SEPTEMBER M :MANGALORE. Mu :MULKI. KA iKARKAL. A iAGUMBE. S :SRINGERI. KO :KOPPA. B :BALEHONNUR. N :NARSIMHARAJPURA. CH :CHIKMAGALUR. -100 -80 + 60 HORIZONTAL DISTANCE (km) Fig. 4-6 145 (Fig. 4.6) of the Western Ghats. However, in case of Bombay - Pune section (Fig. 4.5) of the Western Ghats#orographic effects are more prominent in the month of July and August. 4.3 The model of orographic rainfall : The model of orographic rainfall consists of two parts. First, a model of airflow to compute the vertical velocities due to orographic forcing and a second part, a physical model to compute the rainfall caused due to lifting of saturated or partially saturated airmass at different vertical levels. We consider in this model how far the moist air is lifted by the orographic barriers. The air current during the southwest monsoon season does not have a stable thermal stratification and the lapse rate can be taken as moist adiabatic at least during strong monsoon situations upto the level of tropospheric westerlies. In this chapter our dynamical model for orographic rainfall for a saturated atmosphere is similar to Sarker (1966, 1967). During the weak monsoon situations the thermodynamic structure is somewhat different and it has been shown by Srinivasan and Sadasivan (1975) that upto about 850 mb the air is fully saturated. Above 850 mb, the air generally partially saturated during weak monsoon spells. In the second part we have modified the model suitably by taking into consi deration lack of saturation beyond 850 mb level during weak 146 monsoon situations. Over the Western Ghats there is predominently westerly winds in the lower troposphere at least upto 5-6 km during the strong monsoon season. The wind speed decreases upward and changes over to easterly at a height of about 6-7 km. On the other hand the wind has a southerly component over the Khasi and Jaintia hills region. The wind has a maximum southerly component between 1-2 km and there after decreases and becomes zonal at a height of about 6-7 km. However, with these conditions, it is possible to use the linearised perturbation equation to compute the vertical velocity induced by orography; since the upper level flow pattern does not significantly affect the results at low levels (Corby and Sawyer, 1958). 4.3.1 Model for vertical velocity - Dynamical Model : We consider a rectangular cartesian coordinate system with X axis pointing towards east, Y axis towards north and Z axis vertical considered positive upwards. For the Western Ghats we also consider an undisturbed westerly current blowing perpendicular to the mountain ridge. The mountain ridge is considered to have an infinite exten sion in the Y direction so that the motion is assumed to be two-dimensional in the vertical X-Z plane. For the Khasi and Jaintia hills, which has an east-west orientation, we consider 147 an undisturbed southerly current blowing perpendicular to the mountain ridge. The mountain ridge is considered to have an infinite extension in the X direction so that the motion is assumed to be two-dimensional in vertical Y-Z plane . Linearised equation for perturbation vertical velo city was already obtained in Chapter II for a two-dimensional steady state adiabatic frictionless flow, and is as follows : ^ + a!wL + f(z)W| = 0 1 ax< az (4.1) g (y -V) i d2u Where f(Z) = U2T u dz' r*-r I dU OCRT u dz - 2 dU g- RV aRT \ dZ J \ 2RTf ) / (4.2) (See equations (2.20), (2.2l), (2.19) of chapter II). Equation k.l is the perturbation equation in terms of vertical velocity. For the perturbation equation of the two-dimensional section of the Khasi and Jaintia hills we have to replace X by Y and U by V in the above equations. In Chapter II,Y* was the dry-adiabatic lapse rate. In this chapter, Y* i-s tne pseudo-adiabatic lapse rate and 148 for a saturated atmosphere (i.e., strong monsoon case) we shall have Y= V . The atmosphere is thus statically neutral. 4.3.1.1 Solution for the Western Ghats : Now we solve equation (4.l) with suitable boundary conditions for two sections of the Western Ghats by quasi-numeri cal method. If W1 (x,z) is resolved into its harmonic components by Fourier transform we get,as in Chapter II, CO kx w, ( X ,z) =Ji/ (Z ,k) ei dk (4.3) Substitution of (4.3) in (4.l) leads to Cz k) 2 ^ ' +]f(z)-k w C z ,k ) = 0 (4.4) dz oo r ikx and W (x,z) = e xP(^S z)Re/w (z,k)e dk (4.5) \2RT / «^o Equation (4.5) gives the vertical velocity for a sinusoidal ground profile of wave number k. From this we can get the vertical velocity for any mountain by proper integration. 149 The profile for the Western Ghats is given by 1sM = i-V aW -I- 00 ==/eak(ab coskx-f a' sin^] dk (4.6) where "$<- ( X ) is the elevation of the ground surface at the level z = - h. The numerical values for the two sections are : h = 0.2 5 km a = 18.00 km For E-W Western Ghat section b = 0.52 km along Bombay-Khandala-Pune. 2 a ' = -— x 0.35 and h = 0 a = 70.00 km ) For E-W Western Ghat section ) • b = 0.88 km along Mangalore-Agumbe-Chikmagalur, 2 x 0.45 7T Boundary condition : Equation (4.4) can be solved subject to two boundary conditions. Lower boundary condition : At the lower boundary the flow is tangential to the 150 surface. This is given by dx U[>s(x)]+u[x^s(x)] In view of the restriction to mountain having a shallow slope a good approximation to the condition (4.7) is dts = w[x,o ] (4 8) dx U[^s(x)] ' For a mountain profile at z = 0 condition (4.8) is somewhat inconsistent. We should have taken W [ x *~f H instead of w (x, 0) but in that case it would have been difficult to solve. If again the wind shear near the earth's surface is not large,the linearised lower boundary condition can be fur- (j ^a e W ( y O ) ther approximated to 2_ — —*_^x ?v '. dx U(o) This is called "linearised lower boundary condition". However, we take into account the wind shear in the lower levels near the ground and thus the lower boundary conditions for the present investigation are the following : w (x -h) »TJ(^c) dts(x) For the Western Ghats' y d x Bombay-Pune section / \ 77 /— x d^tCx) For the Western Ghats, 5 W ( X,0 ) = U (^s) —T- dx Mangalore-Agumbe section 151 e h 2 Qk J This gives W (~ h , k ) = - -^ DCSs)e (ab f')ik (*.9) where g-Rf "_h \2 exp =— z 2RT The upper boundary condition : The solution of (4.4) is strictly indeterminate unless the values of f(z) are specified at great heights. However, it is physically unlikely that the computed patterns in the lower troposphere will be greatly affected by the temperature and wind in the upper boundary condition. We have assumed that f(z) = 0 above the level where the wind direction changes to easterly i.e., about 6-8 km in each case. The choice of f(z) has only very small effect at low levels as shown by Palm and Foldvik (i960), Corby and Sawyer (1958) and Sawyer (i960). The appropriate solution of equa tion (4.4) in the region of constant f(z) = 0 is of the form, w (z ,k) == A exp (-kz) (4.10) Since, the pressure and vertical velocity are conti nuous , W(z, k) and are continuous function of Z, 152 Equation (4.10) can, therefore, be used to provide boundary- condition at the level z = z. W 8 km which is the upper limit for the numerical solution of equation V4.4), The cond it ion is -~ w ( z ,k) = - kw (z ,k ) at z = z, (4.11) o Z I To solve equation (4.4) numerically we specify a function I (Z,k) satisfying equation (4.4) and the boundary condi tion (4.1l) at z = z km. p (z k) 4 12 Thus JL^ > +[f(z)_k2]Y(z ,k) = 0 ( - ) and ^Z,k) = k Y(z,k ) at z=z. (4.13) 62 We als o assume for convenience Y (2 k ) = I Qt Z — Zi (4.14) Then W(z, k) is a simple multiple of Y ( Z } k ) which satisfies the lower boundary condition (4.9). Thus for the Western Ghat profile, the vertical velo city is given by r _ i. 00 C 2 w(x,z)=Re< ( ^-) U(ts)^ (ab-ig^ik • L qk ik nz,k) e- e * (4.15) Y(-h,k) dk 153 Integration of (4.15) is difficult when the integrand has a singularity in ^ / _ h k )=0 for some values of k in the range of integration. These singularities correspond to the lee waves and are of special importance. To remove the singularity, we subtract from the integrand a function which has a similar behaviour near the singular point. Such a function is Y{z , kr) exp (-ak + ikx ) i a' ab - (4.16) y*(-h,kr) (k-kr ) where k = k is a singular point and y(-h,kr)-[-|Y(-h,k)]k.kr The expressions (4.16) has a simple pole at ^ _ k with the same residue as the integrand in (4.15). We thus write equa tion (4.15) in the form D( w(x,z) = Re *z wr(T (4-17) 154 The integrand in the first integral of (4.17) is now free from singularities and the second integral is evaluated in the complex K-plane. The path of integration is shown in Fig. 4.7. The path is chosen such that the singularity is confined to the upper quadrant only, thereby allowing only waves down stream of the barrier. Performing the integration and making the radii of indentations tend to zero and the radius of circular arc tends to infinity we get the second integral in (4.17) as 00 a C( K ' ' \ -i exp (-ak + ikx ) ab lk dk = J( -— ) u-kr) 00 1 exp[{-(a+x)-h'(x-a)}k] i(l + i) fkjab- a'i (1-i) dk 2k k (I -f i)- kr + 2TTi ikr fab-L^!.^ exp (-akr + ikr x ) for X >0 i)l e^p[{-Ca-X) + i(x+a)[kJ = i(I-i) J k- ab- Jo . 2k ~ k(l-l)-kr for X < 0 (4-18) 155 PATH OF INTEGRATION Fig 4-7 156 It is seen that a term of the form 2 TT i e xp (-akr + ikrX ) appears for X ^ 0. This represents a lee wave. For simplicity^ we choose f(z) = L = 0 above z-H (km). With this choice,k happens to be real and the lee wave term represents a simple harmonic wave train extending infinitely down stream. The complete solution for vertical velocity can be written as W(X,Z) =U(?S)(^2 Re(X,-fX2+X3) (4.19) fr N where x,= r(z,k) r(z ;kr) Y(-h k )(k-k ) k *6 ir(-h,k) ; r r r=l •ik exp (-ak + ikx ) dk for all x-(4i9a) We have for region X ^0 y - V Tt z , kr a'i (l-i ) 2k r=l '0 exp[{-(a + x) + i(x-a)}k] dk (4 19 b) k (I -4- i ) - kr N 3 r z r(-h;kr) v kry r=l .exp (-akr+ikrx) (419c) 157 For X < 0 N x =2 Ylz^A :(|_i)2 2 r(-h,k ) r= r fJ _ q'i(i+i)l exp[{-(q-x) + i(x+q)}k] Qb dk(4-i9d) o . 2k J. kCl-i ) -W-K- X3 = 0 (4l9e) 4.3-2 Numerical evaluation : Numerical integration of (4.4) was carried out following Sarker (1967) for 32 values of k for the range 0 to 5 km- . The method has already been described in sections 2.3.1 and 2.3-2 of Chapter II. Evaluation of the integrals in 4.19 (a,b,c,d,e) has been done by considering the integrand in the expression 4.19 to be a product of A(k) and exp(ikx); that in 4.19(b) in the form of A(k) . expf ik(x-a)| and in the expression 4.19(c) in the form A(k) . exp J ik( x+a)J where A(k) is a slowly varying function of k. The integral between two successive pair of ordinates k. and k^ is k2 ' A(k) exp(ikx)dk ^2.Ln(*z±ll%±^ J 2 k|4_k2 (k2-k,) > - ~tcos - • (k2-ki> Sin X x(k2-k.) 2 '(k«+k ) •(A2-A,) exp IX 2 Y (4 • 20 ) 158 This formula has been obtained on the assumption that A(k) varies very slowly with k so that its derivative is constant in the range k. and k9 • Having obtained the values of Y(z, k) and Y (0, k) and having obtained the integral for X1 , X0, X_ by using formula (4.20) for successive pairs of values of k in 4.19 (a, b, c, d, e) we get vertical veloc ity. 4.4 Computation of rainfall : To compute rainfall intensity from vertical velocity we first derive the formula for rainfall on the principle of conservation of mass and conservation of moisture. This is similar to Sarker (1966, 1967). We consider a column of air of unit cross-section, let ZAz be the thickness of the column, its top being at z = Zn and bottom at z = z. . Let ^oan(i ^.1 , W„ and W and q2 and q.. be the densities of dry air, the vertical velocities and humidity mixing ratios respectively at these two levels. If at a point (x, z) within this column ^ be the density of air, q its mixing ratio and u and w be the compo nents of horizontal and vertical velocity then the net inflow of moisture within this column is H - < (Cuq) + — ( ewq) dz (4-21) ax oZ 1 159 We now assume that the rate of precipitation is equal to the rate of condensation. Therefore, the rate of precipitation I = JLUuq) + !_Uwq) Hz (4.22) For a steady state flow, the equation of continuity of mass is -^-(eu)+ -£• (€w) = 0 (4.23) Substituting (4.23) in (4.22), we get Su43.+ewJ4>dz (4.24) 5X ' "" h Z -;. zl - ^ Assuming further that humidity mixing ratio does not vary in x - direction, equation (4.24) reduces to (ewq)- q-— (ew)fdz -n Bz dZ (4.25) ,z2 ( ew)dz - -r— (ewq)dz dZ T>Z = S\W, (q,-q)-f e2w2(q-q ) 160 where q is the mean mixing ratio of the column. -3 If density is expressed as kg m , humidity mixing ratio as gm/kg and vertical velocity as cm sec then the rainfall intensity is 4 26 I-O-OSS^Wjlq, -q) + e2w2(q-q2)] mm.hr. ( - ) We have used this formula to compute rainfall intensity from surface to a height upto which the model for vertical velocity is assumed to be valid and assuming that the atmosphere is saturated. We call this model I. 4.4.1 Modification for unsaturation : It has been observed from earlier computations of Sarker (1967) that the model of orographic rainfall for a saturated atmosphere does not work satisfactorily during the situation of a weak monsoon over the West coast. As a first step we examined the thermodynamic structure of the air- stream on those occasions and found that above 1 to 1.5 km the air is not fully saturated. This fact has been also pointed out by Srinivasan and Sadasivan (1975) in an extensive study on the structure of the southwest monsoon. Therefore, we con sider a modified model of the atmosphere which is partially saturated. The atmospheric layer above 1.5 km is taken to be unsaturated and the values of f(z) are computed by using actual temperature values instead of pseudo-adiabatic approximation. 161 However, below 1.5 km the pseudo-adiabatic approximation is maintained. Using the temperature distribution thus obtained and observed winds, the values of f(z) are calculated for the modified model. These values are then utilised to compute the vertical velocities as was done in the earlier model. It is needless to say that the values of vertical velocities in the lower levels are essentially the same. The difference in vertical velocities appears above 1.5 km only. The modification in the rainfall intensity du2 to initially unsaturated condition has been discussed by Thomson and Collins (1953). Essentially, the method assumes that in an unsaturated environment a part of the total vertical velocity is effective in producing actual condensation and precipitation. Let us consider a layer of thickness C~^ z within a mean vertical velocity W. Then the amount of precipitation M from the layer in time /At will be M = I w Az At' C».27) where, I is the rate of precipitation from layer of unit thick ness per unit vertical speed and At- is the part of At during which the air is saturated. At' can be computed from the vertical velocity and moisture available. It is more convenient for computing purposes to change the equation (4.27) to form M = I w'A Z A t 162 where W 'At = W At1 (4.28) This new effective speed W has been calculated by assuming that the computed vertical velocities at any level are steady and can be taken as t-he mean vertical speed for time interval of several hours. The total ascent of a layer in time At is given by i = wAt (4'29) This total ascent is the sum of the lift (z ) needed to reach saturation and the lift (zp) which produced precipitation. Z = Z, + Z2 .(4.30) The lift needed to reach saturation is To-Tdo (4>31) dT _drA_ dz dz where T, is the dew point temperature of the layer. The lift (z„) which produces precipitation is equal to Z2 = WAt'= W'At (4.32) Substituting (4.30), (4.31), (4.32) in (4.29) we get T T T Td0 wAt=_ o ~ do + wiAt or w'At=wAt+ °~ dT dTd dT dTd dz dz dz dz To " Tdo or w' = w 4- dZ d2/ (4.33) 163 Substituting in this equation At= 24 hrs,-^- = -S-^Ckm"1 dTd . o , -I = — 1- a6 r C-km dz and making use of the vertical velocities computed earlier by using equation 4.19 (a, b, c, d, e), the effective verti cal velocities are computed from equation (4.33) and these are used to determine the contribution to rainfall intensity for levels above 1.5 km during the weak monsoon situation. Below 1.5 km the vertical velocities computed earlier for the saturated atmospheric conditions are used. We call this model II. 4.5 Downwind drift of precipitation :. It is well known that precipitation falling from diffe rent heights drift in the downwind direction with the velocity of airstream at that level. This effect has been studied by various workers using radar observation (Marshall, 1953; Langleben, 1954; Gunn and Marshall, 1955; Mason and Andrews, i960). Their discussions have dealt mainly with the generating cells moving with the wind velocity at the level of the generating cell. We consider here the horizontal extension along the wind in the case of fixed generating ce lis (Sarker, 1966). For the present model, we assume that the rate of descent 164 of the precipitation element is constant and equal to the terminal velocity depending upon its drop size and that the precipitation element is drifted horizontally with speed of wind at a particular level. Consequently, if U(z) is the horizontal wind speed at a level z and UT is the terminal velocity of the precipi tation element then the horizontal distance E travelled x by the precipitation element created at an anchored generat ing cell at the level z in falling to the level z is given by Ex = ~~ \ U(z) dz (4.34)' The integral (4.34) is equivalent to the area bounded by the graph U(z) and the Z-axis at the level z and z, divided by the terminal velocity. The precipitation element above the freezing level is snow flake and water droplet below. The terminal velocities accordingly are different above and below the freezing level. It . is seen that the orographic precipitation has an inten sity 2-8 mm/hr for which the most probable drop diameter is 1.00 - 1.25 (Kelkar, 1959). The corresponding terminal velo city is 4.5 m sec in the liquid phase and 1.00 m sec in the snow phase (Langleben, 1954; Gunn and Kinzer, 1949 repro duced by List, 195l). 4.6 Discussion and Results : Using the above model the vertical velocities were 165 computed and then rainfall computed for five situations over Bombay-Pune section of the Western Ghats, four situations over the Mangalore-Agumbe section of the Western Ghats and four situations over the Khasi and Jaintia hills. Some of the situations were for active monsoon case and some for weak monsoon case. We discuss these cases below briefly. For Bomhay-Pune section of the Western Ghats, the wind distribution has been taken from the upper air radio sonde ascent of Santacruz (19 07'N, 72 51'E). The average vertical distribution has been worked out by considering the average eastward component of 00Z and 12Z wind speed of the date. Five different situations over this section have been studied. For Mangalore-Agumbe section of the Western Ghats average radiosonde ascent of Mangalore-Bajpe (12 55'N, 74 53'E), 00Z and 12Z of the date has been considered. Four different situations have been studied over this section. The wind distribution for Agartala-Cherrapunji section of the Khasi and Jaintia hills has been taken from upper air rawin ascent of Agartala. The average vertical distribution was worked out considering northward component of 00Z and 12Z wind speed. Four different situations have been studied over this sec tion . A summary of the results given in Table 4.1 and 4.2 166 Table 4.1 SI. Date Wave Maximum Distance of Height of No. leng- vertical maximum W maximum W ths velocity W from the (km) (km) (cm sec ) crest (km) WESTERN GHATS : BOMBAY-PUNE SECTION 1. 22 July 1968 19.6 12.0 -10 1 2. 7 July 1970 36.9 15.4 -10 1 3. 15 July 1970 (Model I) 14.2 15.5 -10 1 (Model II) 8.3 7.1 -10 Surface WESTERN GHATS : MANGALORE-AGUMBE SECTION 4. 17 June 1973 36.9 23.2 -20 1 5. 9 July 1974 30.9 40.6 -20 1 6. 12 July 1974 26.5 9.2 -20 1 KHASI - JAINTIA HILLS 7. 4 July 1975 37.5 15.4 -15 1 8. 19-20 July 23.1 17.9 -15 1 1979 9. 23 July 1979 31.0 25.7 -15 1 167 Table 4.2 SI. Date Maximum rainfall Maximum rainfall inten- No. intensity in mm/hr sity in mm/hr (observed) (computed) WESTERN GHATS : BOMBAY-PUNE SECTION 1. 22 July 1968 3.1 at Khandala 2.7 at X = - 5 km 2. 7 July 1970 5.8 at Khandala 3.9 at X = - 5 km 3 15 July 1970 1.0 at Khandala 4.2 at X = - 5 km (Model i) 0.8 at X = -10 km (Model II) WESTERN GHATS : MANGALORE-AGUMBE SECTION 4. 17 June 1973 9.2 at Agumbe 6.1 at X = -15 km 5. 9 July 1974 6.0 at Agumbe 10.6 at X = -15 km (Model i) 6.8 at X = -15 km (Model II) 6. 12 July 1974 3.0 at Agumbe 2.7 at X = -15 km KHASI-JAINTIA HILLS 7. 4 July 1975 5.5 at Cherrapunji 4.7 at X = -15 km 8. 19-20 July 1979 6.5 at Cherrapunji 6.5 at X = -15 km 9. 23 July 1979 7.2 at Cherrapunji 6.9 at X = -15 km 168 showing the computed wavelength, maximum computed vertical velocities, maximum computed and observed rainfall intensi ties. We now discuss the various cases : Lee waves : In all these cases the lee waves are present. The wavelength varies between 8 to 40 km. The wavelengths are shorter during weak monsoon situations i.e., 15 July, 1970; 9 July, 1974; and 25 July, 1974 (Table 4.1). The existence of lee waves in neutral static stability is due to variation of wind speed and wind shear with height. Sarker (1967) has reported similar findings earlier over the Western Ghats. Vertical velocities : The maximum vertical velocities and their location with respect to the origin in different sections are given in Table 4.1. Distributions of vertical velocities are also given for some cases in Figs. 4.8(a), (b) to 4.11(a), (b). Detailed examination of these and the rest of the cases show that vertical velocities are in general positive on the wind ward side at least in the lower levels. The values increase as one proceeds along the mountain towards the peak. The increase of vertical velocities continues upto a distance of 10 to 20 km on the windward side of the peak, thereafter the magnitude decreases. In the vertical plane the vertical velocity shows cellular pattern i.e., it shows ascending motion in the 169 *~~ o •—• z: 1^ | o 92 _l t- t LU Hco- O < oUJ ri- O X ID en — S o " '*—' UJ Z z: 2 o (X ID o UJ Q_ CO t- z: co o UJ 2 5 MBA Y < UJ CoO co UJM Nl 1H 170 01 =X - 0Z= X s}- ro m NI "IH 171 -iCO 172 WESTERN GHATS ( BOMBAY-PUNE SECTION) 15-7-1970 WEAK MONSOON (MODEL-n) -2 -10 I VERTICAL VELOCITY IN cm/sec Fig. 4-9 (b) 173 H oo _ < O to O x LU o to in 'w* Nl 1H9I3H 174 m OI=X H <* H ro OJ cm/se c — •z. >- J3 \- O 0£ = X o . o o ^r L_Ul d> 01? = X- > u. _J I- o O VERTIC A O - 2 1 CD .2 00 O CD s ro a: >L 0} 1 UJ LU CD in ^j- ro CM w>1 Nl 1H9I3H 175 O CO UJ O I— co O < CO x UJ o QQ a: o cr> < I- i co UJ UJ n w u o _J o < a> to u >- O UJ 2 > u. < o h- CE UJ > OI- = X 09-=X OS-=X 02-=X 0fr-=X 0£-=X Is- 10 ^ ro OJ 'UJ>i Nl 1H9I3H 176 EC T CO CO 0l7=X 0£=X 02 =X 0I=X 0=X g = x N The vertical velocity is positive in the lower level for both model I and model II, though the values of vertical velocities obtained by model II is lesser than that obtained by model I. In the upper level on the windward side above 4 km vertical velocity is negative for model I while for model II the vertical velocity is negative between 2 to 4 km above which the vertical velocities are positive. On the lee ward side the vertical velocities are negative in the lower levels upto 4 km above which the vertical velocities are posi tive for model I. In case of model II on the leeward side vertical velocities are negative upto 2 km height and then it is positive between 2 and 4 km height above which it is 178 n egat ive. Computed Rainfal 1 : We have computed rainfall by model I for strong monsoon cases and by model II for weak monsoon cases. The computed and observed rainfall distributions for all the cases are given in Figs.4.12-4.20.The maximum rainfall intensity and its location of occurrence are also given in Table 4.2. Detailed examination shows that the computed rainfall pattern shows a pronounced orographic effect. However, the computed rainfall intensities are similar than the observed values. This is partly due to the fact that all the three areas are affected by presence of synoptic systems during the south west monsoon. The intensity of orographic rainfall during normal and active monsoon situation due to orographic effect varies between 3 mm/hour to 11 mm/hr for the Western Ghats and bet ween 5.0 mm/hr to 8.0 mm/hr for Khasi and Jaintia hills. The maximum observed as well as computed rainfall intensity is at a distance of 10-15 km from the crest. For the weak monsoon cases as mentioned earlier, computations has been made with a modified rainfall model taking into account unsaturated initial conditions. The modification resulted in a better approximation of observed rainfall. 179 WESTERN GHATS ( BOMBAY-PUNE SECTION) 22-7-1968 ACTIVE MONSOON OBSERVED RAINFALL -60 -40 -20 0 20 40 DISTANCE IN km Fig.-412 180 WESTERN GHATS ( BOMBAY-PUNE SECTION) 7.7.1970 ACTIVE MONSOON OBSERVED RAINFALL COMPUTED RAINFALL •20 0 20 40 50 DISTANCE IN km. Fig. 4-13 181 WESTERN GHATS ( BOMBAY-PUNE SECTION) 15-7-1970 WEAK MONSOON COMPUTED RAINFALL / ^BY MODEL I OBSERVED RAINFALL DISTANCE IN km. Fig. 4-14 182 2 o h- o LL! < LLJ ynoH / ww NI TIVJNIVH- 183 s I - <£) '-O tj- rO CM "UJij 184 RAINf i _I Q _l UJ 1- 2 a. < S o o SERVE D R ^—^ CD / o f "Z. \ L o t- X( \ o \ ' «2K \ < UJ X CD O ^ _ 3 ~ o Z ct < O UJ , o ^ UJ in w cc -z. o £y -oJ < 2 IV E < h- h- :E ou < rO CM — O jnoM/ujuj MI HVJNIVy -UJ>H 185 o ^^—v — m ^~ _l oo 1 SE C (MOD E in 00 N CO Q Q UJ \ UJ 1 o o 1 o _) CM O sr i i i 1 1 1 1 1 CO o O O o o o o O CD N CO \C> CO _! _J o LU _J UJ Q CO O X -z. 01 o E H O Q Q < < 5 CO UJ LU *» H X 2 i C UJ Q- < D 2 w 2 < CO m o 1 o UJ ° ° 1 CM > < i _I 0) i CO 1- 1 < < o I X < 1 •XL < **"" ^* < 9 o f fl W - U-UJM2 1H0I3H H jnoq / WUJ Ml A1ISN31NI TlVdNltfy 187 o ^ « o o o o o o o _ [^-UJX 2 1H0I3H-H cb N tb & <$ n °° jnoq / UJOJ Nl A1ISN31NI 11VJNIV8 188 4.7 Conelusions: We can draw the following conclusions from the present investigation : (i) The orographic rainfall, computed from this model increases from the plains along the slope and reaches a maximum before the crest of the mountain is reached, after which it falls off sharply. The normal rainfall during the south west monsoon and also during the individual months of June to September is seen to have a similar distribution along all the sections cons idered. (ii) The position of the maximum rainfall observed and computed are in good agreement and generally occur at 5-15 km before the crest of the barrier, (iii) The observed rainfall is higher so that the only a part of it is explained by orography. The peak in rainfall is, however, purely an orogra phic effect, where the computed values are nearly 90$ or more of the observed values, (iv) By studying the orographic effect in three different sections it may be said that height alone is not the criteria for maximum rainfall. Slope and airstream characteristics are also 189 important. (v) It is seen that during weak monsoon the rainfall distribution is explained better by the modified model which takes into account the unsaturated conditions, (vi) The ascending motion in the present model on the windward side and on the lee ward side suggests that rainfall on the wind ward side originates at low levels below 5 km and that on the lee side has high level origin above 5 km. These observa tions show that precipitation on the wind ward side comes from the cloud tops which are below the freezing level and only condensation coa lescence process is involved in the initiation of rain in this region. On the lee ward side most of the rain is from above the freezing level and is initiated by Bergeron process through ice nucleation. This is evidenced by the "Bright Bands" of rain echoes and is supported by the study of Pisharoty (1962) and Mani et al (1962). However, while noting that the model of orographic rain fall explains the observed rainfall distribution quite satis factorily, it is not free from limitations. And the discre pancies between the observed rainfall and rainfall computed 190 from the model can be attributed to the following reasons : (a) The choice of a linear model and taking a smoothed profile for the terrain. (b) Microphysical processes of rainfall have been incorporated in the model, and (c) Synoptic scale convergence and instability have not been included in the model, which may be significant contributors to vertical velocity in some cases. cr 1 > LU as 1 CO / AU H ,INT I 3 CD o 1