Chapter 4

MIXING HEIGHT CALCULATION OVER NCT OF DELHI

4.1 Introduction

Transport and diffusion of pollutants in the lower atmosphere is dependent largely on the

structure of the planetary boundary layer (PBL), one important nature of which is the height of

the well-mixed layer. Massive quantities such as particles and gases are mixed nearly uniformly

throughout this layer by turbulence which results partially from strong surface heating during the

daytime hours. The mixing layer is capped by a temperature inversion thereby limiting the height

of the mixing. The variation of this height due to diurnal variations of solar radiation, synoptic

conditions and local terrain strongly affects pollutant concentrations.

4.2 AtmosplzericIPlanetary Boundary Layer

The height of the atmospheric boundary layer essentially governs vertical mixing of

atmospheric pollutants, which is expressed by the synonym "mixing height" with respect to

applications in environmental meteorology. It therefore plays an important role in air pollution

monitoring and assessment and serves as a basic input parameter to all classes of dispersion and

transport models.

In dispersion models, the mixing height is a key parameter needed to determine the

turbulent domain in which dispersion takes place. Air pollution climatology is concerned with

the aggregate of weather as it may affect the atmospheric concentrations of pollutants.

The mixing layer is the depth of the atmospheric layer which is characterized by strong

turbulent and convective mixing. Accurate representation of mixing depth plays an essential role

in the ability of models to predict pollutant concentrations (Vimont and Scire, 1994, Rao et aI.,

1994). There are several methods currently available for the estimation of mixing heights

(Holzworth, 1972; Garrett, 1981; Maughan et al., 1982; Myrick et al., 1994). They include those

using temperature profiles measured by sondes or by a fixed tower, and the remote sensing

techniques such as lidar and sodar (Coulter, 1979; Marsik et al., 1995). Each method has its own

advantages and limitations, and different methodologies give rise to differences in mixing

heights. These differences are the results of the physical limitations of each method and the

48

assumptions used as to which variable most accurately defines the depth of the mixed layer.

Among the most commonly methods of calculating mixing height from temperature profiles

are the Holzworth method (Holzworth, 1967), the capping method (Dayan et al., 1988), the

Heffter method (Heffter, 1980) and the Kink method (Goldman, 1980). The conventional

Holzworth mixing height is calculated as the intersection point of the dry adiabatic from the

surface temperature and the morning temperature sounding. It neither includes the effect of

horizontal temperature advection nor of moisture content and is sensitive to surface temperature.

Benkley and Schulman (1979) proposed an operational model based on Holzworth's met~od

including the effect of temperature advection. The daytime mixing height is normally identified

with the base of an elevated inversion or stable layer, capping the well-mixed convective

boundary layer. The capping mixing height is determined assuming that turbulent mixing caused

by convective and mechanical turbulence extends to the base of the elevated inversion. In Heffter

method, potential temperature profiles computed for each sounding are analyzed for the existence

of a critical inversion. The inversion is defined following the criteria that recognize the likelihood

of mixing to overshoot the base of the critical inversion. It does not inc~ude the effects of wind

shear within the critical inversion. The kink method estimates mixing height from vertical

temperature soundings with higher resolution than synoptic soundings. It assumes that vertical

mixing is limited at the base of the first significantly stable layer defined by imposed operational

conditions.

Remote ground-based observing systems, such as radar, sodar and lidar, have an advantage

over in situ measurements, their ability to obtain volume and continuous averages which are

more representative than point and instantaneous values. Radar and sodar see clearly the

convective boundary layer structure through the detection of small-scale variations in the

atmosphere's refractive index structure due to temperature and water-vapor fluctuations at the top

of the convective boundary layer. This result in a maximum backscatter signal intensity (Beyrich,

1995, Marsik et al., 1995). Radar systematically overestimates the depth of the mixed layer

during the early morning hours, and its measurements are affected by the presence of fog, clouds,

rain and persistent shear layers aloft (Marsik et aI., 1995). Sodar sends short pulses of sound, and

the attenuation of sound in the atmosphere causes difficulty in the detection of structures beyond

a range of about 1 km. This is an important limitation for operational application, specially in

summer, when many mixed layers grow to heights above that value in the afternoon (Stull, 1988;

Beyrich, 1995). When a neutral boundary layer exists, or no inversion layering is detected, no

49

information can be obtained. When multiple layers are observed, mixing height is taken to be the

height of the base of the lowest layer, but this could not be the strongest in terms of being a

barrier to vertical dispersion. The operation of a sodar is limited to relatively noise-free locations

and measurements are affected by wind and rain interface (Maughan et aI., 1982). Lidar transmits

laser light, which is scattered by air molecules, cloud droplets and aerosols in the boundary layer.

This method of mixing height determination measures the depth to which particles have become

mixed in the atmosphere (Stull, 1988; Maughan et al., 1982). The Lidar is less range limited in

the near field than other systems, and thus can detect the shallow, developing mixed layers during

the early morning hours. Lidar measurements are affected by clouds, lifting fog and elevated

plumes of aerosols and it does not operate during periods of precipitation (Marsik et aI., 1995).

Air pollution climatology is usually described in terms of statistics of wind, temperature,

stability, mixing height, ventilation coefficient, etc.

The climatological model CALMET applied in the present study gives the mixing height

along with visibility, stability, velocity and temperature fields for the study region. In the present

case, the mixing height determination uses an energy balance approach to estimate the surface

heat flux in driving the growth of the mixed layer (Scire et al., 1995) and the prameterizations

used in the energy budget are based primarily on Holtslag and van Ulden's (1993).

During the daytime, CALMET calculates the mixing height as the maximum of the

convective and mechanical mixing heights. ·The convective mixing height at time (t+l) is

estimated from time (t) in a stepwise manner as a function of sensible heat flux (Maul, 1980).

The mechanical mixing height is estimated from Venkatram's (1980a) relationship h= (BuJ ,

where u. is the friction velocity, f is the Coriolis parameter, and NB is the BruntWis~a frequency in the stable air above.

During the nighttime, CALMET uses the minimum of the two niixing heights. The first

mixing height is estimated by Venkatram's (1980b) relationship h= B2 u.3n., where

B2 = 2400 (constant). The second formula from Zilintinkevich (1972) is given as h= 0.4 (u.LIj) In. ,

where L is the Monin-Obukhov length.

In this chapter, the assimilative capacity (or carrying capacity, as often used

interchangeably) of the atmosphere is estimated. The assimilative capacity of the atmosphere is

the maximum amount of pollution load that can be discharged without violating the best designed

use of the air resources in the planning region. The phenomenon governing the assimilative

50

capacity of atmosphere includes dilution, dispersion, phase transformation, . deposition and

absorption.

The air pollution assimilation potential of an air shed, primarily for a plain terrain, can be

estimated as the ventilation coefficient which is an indicator of horizontal as well as vertical

mixing potential.

The ventilation coefficient over a region of atmosphere is the product of mixing height and

transport winds averaged over the entire mixing layer.

For the main purposes of the present study, the climatology of air pollution potential, the

non-precipitation data are considered to be adequately representative of all cases.

Estimation of assimilative capacity of the atmosphere involves:

• Delineation of air shed based on topography of the area and identification of micro-

climatic zones depending upon sources, topography and wind field data.

• Preparation of inventory of point, area, and line sources, and quantification of pollution

loads.

• Establishment of temporal and special variations of micro-meteorological parameters.

• Prediction of temporal and special variations in air pollutant concentrations for existing

sources using multiple source-receptor model to establish source- receptor relationship.

• Estimation of available assimilative capacity in critical micro-climatic zones for various

pollutants vis-it-vis air quality standards for sensitive receptors.

• Establishment of upper limits of pollution load in critical pockets.

51

4.3 Model Description

4.3.1 Introduction

CALMET is a meteorological model which includes a diagnostic wind field generator

containing objective analysis and parameterized treatments of slope flows, kinematic terrain

effects, terrain blocking effects, and a divergence minimization procedure, and a

micrometeorological model for overland and overwater boundary layers.

The CALMET model contains Boundary Layer Model for application to overland grid cells,

over land surfaces, the energy balance method of Holtslag and van Ulden (1983) is used to

compute hourly gridded fields of the sensible heat flux, surface friction velocity, Monin-Obukhov

length, and convective velocity scale. Mixing heights are determined from the computed hourly

surface heat fluxes and observed temperature soundings using a modified Carson (1973) method

based on Maul (1980). Gridded fields of PGT stability class is also determined by the model. An

upwind-looking spatial averaging scheme is optionally applied to the mixing height and 3-

dimensional temperature fields in order to account for important advective effects.

4.3.2 Technical Description

The CALMET model uses a grid system consisting of NZ layers of NX by NY square

horizontal grid cells. Figure 4-1 illustrates one layer of grid cells for a 11 x 12 grid. The" grid

point" rerers to the center of the grid cell in both the horizontal and vertical dimensions. The

"cell face" refers to either the horizontal or vertical boundary between two adjacent cells. In

CALMET, the horizontal wind components (u and v) are defined at each grid point. The vertical

wind component (w) is defined at the vertical cell faces.

52

Y

G

R

I

D

C

E

L

L

I

N

D

Grid Cell

E (XORIGKM, YORIGKM)

X X GRID CELL INDEX

Fig. 4.1. Schematic illustration of the CALMET horizontal grid system for a l1X12 grid showing

the grid origin (XORIGKM, YORIGKM) and grid point location (.)

The position of the meteorological grid in real space is detemlined by the reference

coordinates (XORIGKM, YORIGKM) of the southwest comer of grid cell (1,1). Thus, grid point

(1,1) is located at (XORIGKM + DGRIDKMl2., YORIGKM + DGRIDKMl2.), where

DGRIDKM is the length of one side of the grid square.

It is assumed that the orientation of the X and Y axes of the CALMET grid are west-east

and south-north, respectively. In this way, the grid system is compatible with the usual definition

53

of the u and v horizontal wind components as the easterly and northerly components of the wind,

respectively. One commonly-used grid system compatible with CALMET is the Universal

Transverse Mercator (UTM) Grid.

The CALMET model operates in a terrain-following vertical coordinate system.

(4.1)

where

Z is the terrain-following vertical coordinate (m),

z is the Cartesian vertical coordinate (m), and

hI is the terrain height (m).

The vertical velocity, W, in the terrain-following coordinate system is defined as:

(4.2)

where

w is the physical vertical wind component (m/s) in Cartesian coordinates, and

u,v are the horizontal wind components (m/s).

4.3.3 Divergence Minimization Procedure

Three-dimensional divergence in the wind field is minimized by a procedure (Goodin et

aI.1980), which iteratively adjusts the horizontal wind components (u,v) for a fixed vertical

velocity field so that at each grid point, the divergence is less than a user-specified maximum

value.

du dv dw -+-+-<e dx dy dz

(4.3)

where

u,v are the horizontal wind components,

w is the vertical velocity in ten'ain following coordinates, and

E is the maximum allowable divergence.

In CALMET, the horizontal wind components are defined at the grid points. Vertical

velocities are defined at the vertical grid cell faces. Therefore, the divergence, D, at grid point

54

(i, j, k) is:

(4.4)

where Llx and Lly are the sizes of the grid cell in the x and y directions, respectively. For each

grid point, divergence is computed. The u and v wind components at the surrounding cells are

adjusted so that the divergence at the grid point is zero.The adjustments are:

'1/ \ • 1/. • 1/ . . ~ new/i.IJ.k ,.IJ.k ad]

(4.5)

'1/ \ • u. I . k - U d· ~ new/i_IJ.k ,- J. a Y (4.6)

(V l . v .. I k + V J. new IJ.I.k 'J' • a Y (4.7)

(V l . v .. I k - V J. new iJ-I.k 'J- • a Y (4.8)

where the adjustment velocities (uadj , vadj ) are:

-Dijkt::.X U .--

aJ) 2 (4.9)

(4.1 0)

Each time the divergence is eliminated at a particular grid point, divergence is created at

surrounding points. However, by applying the procedure iteratively, the divergence is gradually

reduced below the threshold value, E, throughout the grid.

4.3.4 Micrometeorological Model

4.3.4.1 Surface Heat and Momentum Flux Parameters

Significant advances have been made in recent years In the understanding and

characterization of the structure of the planetary boundary layer (PBL) (Weil, 1985; Briggs,

55

1985). According to van Ulden and Holtslag (1985) and others, the use of the appropriate

boundary layer scaling parameters can improve the quality of dispersion predictions. The major

parameters needed to describe the boundary layer structure are the surface heat flux (Qh)' surface

momentum flux (p u/), and the boundary layer height (h). Several additional parameters,

including the friction velocity (u.), convective velocity scale (w.), and the Monin-Obukhov

length (L), are derived from these.

Hanna et al. (1986) have evaluated several models for the prediction of these boundary

layer parameters from routinely available meteorological observations. Two basic methods are

commonly used to estimate the surface heat and momentum fluxes. The first method known as

the profile method, requires at a minimum the measurement of the wind speed at one height and

the temperature difference between two heights in the surface layer, as well as knowledge of the

air temperature and roughness characteristics of the surface. Monin-Obukhov similarity theory

is then used to solve for the surface fluxes by iteration. The second approach, known as the

energy budget method, computes the surface heat flux by parameterizing the unknown terms of

the surface energy budget equation.

4.3.4.2 Overland Boundary Layer

An energy budget method, based primarily on Holtslag and van Ulden (1983), is used over

land surfaces in the CALMET micrometeorological model. The energy balance at the surface can

be written as:

(4.11 )

where

Q. is the net radiation (W/m2),

Qf is the anthropogenic heat flux (W/m2),

Qh is the sensible heat flux (W/m2),

Qe is the latent heat flux (W/m2), and,

Qg is the storage/soil heat flux term (W/m2).

The ratio of the sensible heat flux to the latent heat flux is defined as the Bowen ratio.

(4.12)

56

The model will require gridded values of the Bowen ratio. The Bowen ratio is important

in determining the degree of convective turbulence because it reflects the partitioning of the

available energy into sensible and latent heat flux. Typical values of B range from'" 0.1 over

water bodies to ~ 10 for deserts.

The flux of heat into the soil or building materials, Qg' is usually parameterized during the

daytime in terms of the net radiation (Oke, 1978; Holtslag and van Ulden, 1983).

Qg • cg Q. (4.13)

where the constant cg is a function of the properties of the surface. Oke (1982) suggests values

for cg of 0.05-0.25 for rural areas and 0.25-0.30 for urban areas. The larger values for urban areas

reflect the greater thennal conductivity and heat capacity of building materials. Holtslag and van

Ulden (1983) use a value of 0.1 for a grass covered surface.

The anthropogenic heat flux, Qf' is a function of the population density and per capita

energy usage. Oke (1978) summarizes annual and seasonally- averaged Qf values for several

urban areas. Although the Qf tenn has been retained for generality, it is usually small compared

to the other terms.

The net radiation, Q., is the residual of incoming (short-wave plus long-wave) radiation and

outgoing (long-wave) radiation. Q. can be expressed (Holtslag and van Ulden, 1983; Landsberg,

1981) as:

Q . • Q".. (l - A) + Qlw-<l - Qlw-II (4.14)

57

where

Qsw is the incoming short-wave radiation (W/m2), consisting of a direct solar

radiation term (Qsw-s) plus a diffuse radiation term (Qsw-d),

A is the albedo of the surface,

Qlw-d is the incoming long-wave atmospheric radiation (W/m2), and,

QIW-u is the long-wave radiation (W/m2) emitted by the surface.

The method of Holtslag and van Ulden (1983) is used to estimate Q •. The result of their

parameterization of each of the terms in eqn. (4.14) is:

(4.15)

(4.16)

where

T is the measured air temperature (deg. K),

(J is the Stefan-Boltzmann constant (5.67 x 10-8 W/m2/deg. K4),

N is the fraction of the sky covered by clouds, and

<t> is the solar elevation angle (deg.).

Thelast term in eqn. (4.16) accounts for the reduction of incoming solar radiation due to the

presence of clouds. The values for the empirical constants c l, c2, c3, aI' ~, bl, and b2 suggested

by Holtslagand van Ulden (1983) are used (Table 4.1, APPENDIX - 4A). The solar elevation

angle is computed at the midpoint of each hour using equations described by Scire et al. (1984).

The Monin-Obukhov length is defined as:

3 L • -PCp T u.

kg Qh

58

(4.17)

where

T is the temperature CK),

cp is the specific heat of air at constant pressure (996 m2/(s2. OK)},

p is the density of air (kg/m3), and

g is the acceleration due to gravity (m/s2).

Eqn. (4.16) is used to obtain an initial guess for u. assuming neutral conditions (L = 00).

This value of u. is used in eqn. (4.17) to estimate L. A new value for u. is then computed with

eqn. (4.17) and L. The procedure is repeated until convergence is obtained. Holtslag and van

Ulden (1983) suggest that three iterations are usually sufficient.

During stable conditions, Wei I and Brower (1983) compute u. with the following method

based on Venkatram (1980a):

CDN U [ II2J u=--I.C . 2 (4.18)

(C ~ 0) (4.19)

2 YZmg e, u a __

o T (4.20)

where

CON is the neutral drag coefficient [k/ln(zm/zo)]'

y is a constant ('" 4.7), and,

Zm is the measurement height (m) of the wind speed, u.

The temperature scale, e., is computed as the minimum of two estimates:

(4.21)

The estimate of 8. is based on Holtslag and van Ulden (1982):

e.1 • 0.09 (I - 0.5 N 2) (4.22)

and 8.2 is:

59

(4.23)

The heatflux is related to u. and e. by:

(4.24)

and L is computed from eqn. (4.17).

The daytime mixing height is computed using a modified Carson (1973) method based on

Maul (1980). Knowing the hourly variation in the surface heat flux from eqn. (4.24) and the

vertical temperature profile from the twice-daily sounding data, the convective mixing height at

time t+dt can be estimated from its value at time t in a stepwise manner:

f 2 2 Qh (1 + E) dt 2 dBr hr]12 dBr.dr

hr.dr • hr + - + -

"'1 P Cp "'1 "'1 (4.25)

[2 "'1 E Qh dr]12 dB/.d,' --'----

P Cp

(4.26)

where

ljT I is the potential temperature lapse rate in the layer above ~,

de is the temperature jump at the top of the mixed layer (K), and,

E is a constant ("" 0.15).

The potential temperature lapse rate is determined through a layer above the previous hour's

convective mixing height.

The neutral (mechanical) boundary layer height is estimated by Venkatram (1 980b ) as:

Bu h· --'-[! NBjl2

(4.27)

where

f is the Coriolis parameter ('" 1 0-4 S-I)

B is a constant ('" 2 112), and,

Ns is the Brunt-Vaisala frequency in the stable layer aloft.

The daytime mixing height could then be taken as the maximum of the convective and

60

mechanical values predicted by eqns. (4.25) and (4.27), however, such a procedure could cause

the resulting x-y field of mixing heights to have unreasonably large cell-to-cell variations, as each

grid cell's values of hI and h are computed independently.

In the stable boundary layer, mechanical turbulence production determines the vertical

extent of dispersion. Venkatram (1980a) provides the following empirical relationship to

estimate the stable mixing height.

(4.28)

where B2 is a constant ('" 2400).

The stable boundary layer height is estimated by Zilitinkevich (1972) as

(4.29)

CALMET defines the stable overland boundary layer height as the minimum of h) and h2•

In the convective boundary layer, the appropriate velocity scale is W., which can be computed

directly from its definition using the results of eqns. (4.15) and (4.25).

(4.30)

where hI is the convective mixing height.

4.4 Input data required by CALMET

4.4.1 SUlface Meteorological Data: Hourly Observation of wind speed (mls), wind direction

(degree), temperature (K), cloud cover (tenths), ceiling height, (hundreds of fee!), surface

pressure (mb), relative humidity (percent), precipitation type code.

61

4.4.2 Upper Air Data: Twice-daily observed vertical profile of wind speed (mls), wind

direction (degree), temperature (K), pressure (mb), elevation (m).

4.4.3 Geophysical Data: Gridded fields of terrain elevations (USGS 1 km terrain elevation

resolution data set) , land use categories, surface roughness length, albedo, Bowen ratio, Soil

heat, flux constant, anthropogenic heat flux, vegetation leaf area index (fable 4.2, AP P ENDIX-

4B).

4.5 Experiment

The output data of ARPS model forms the input to the CALMET model by way of free

formatted files for surface data and in appropriate CALMET data format for upper air & geo­

physical data. The model was run for II-12th of January, April, August and October for the years

1991 to 1995. Since there was no major disturbance during these months over the years, these . .

days were assumed to represent the Winter, Summer, Monsoon and Post-monsoon seasons

respectively. Missing values of temperature, cloud cover, ceiling height, surface pressure and

relative humidity are internally replaced by values at the nearest station with non-missing data.

Missing upper air wind speed, wind direction, or temperature are interpolated by CALMET. As

the program does not extrapolate upper air data, the top valid level must be at or above the model

domain and the lowest ( surface) level of the sounding must be valid.

The model generated temperature field, wind field, mixing height, stability, Monin-Obukov

length etc. at the center of each grid point for the representative months over the periods '91 "to

'95. Since, the pattern of different fields are more or less the same for corresponding seasons over

the years, the simulated results for '95 only are discussed in this chapter. Out of the 132 grid point

values, two grids (8,8) and (7,2) were chosen (corresponding to warm pocket and cold pools

ofNCT of Delhi) and the diurnal variation of temperature, horizontal wind field, mixing height

and ventilation coefficients were plotted. Also stability classes and visibility range for different

seasons are plotted.

62

4. 6 Results and Discussion

Fig. 4.2 (a) - 4.2 (d) & Fig. 4.3 (a) - 4.3 (d) show the spatial variation of wind speed and

horizontal wind field respectively. The wind field is influenced by topography and temperature

anamoly at the surface level. The winds accelerated from south (cold pool) towards north (warm

pocket) ip. January (winter). Thus whichever grid is observed the wind direct towards warm

pocket. In April (summer) the winds which are relatively weak converged towards the warm

pocket in the north and diverged from the cold pool in the south. In the dense built up area winds

are further weakened (in the west). In the monsoon season, winds are strong and is generally

westerly/easterly depending upon the location of monsoon trough. In the present case the strong

westerly winds turned north-westerly/northerly, probably the coriolis force assisted in deviating

the wind direction. In the post-monsoon season winds are strong south-westerly deviating

towards east. Here too the winds originally blowing towards heat island in the north turned east

most likely due to coriolis effect.

On a rolling terrain with marginal variation, the effects on wind is found to be not

significant. So the plots of horizontal wind vector from CALl\1ET model simulation taking into

account the terrain features of the region is found to be the same as that obtained from the ARPS

simulated results discussed in the previous chapter.

Fig. 4.4 (a) - 4.4 (d) show the diurnal variation of simulated temperature at warm and cold grid

points for the representative months of '95. The simulation indicates an increase of temperature

from 00 GMT reaching its maximum value at 11 GMT both at urban and rural locations, then it

decreases slowly. In all the seasons this trend is more or less the same. In simulating the diurnal

variation, the radiative properties of the pollutants are not taken care of

Fig. 4.5 (a) - 4.5 (d) show the percentage frequency of different stability classes at warm and

cold pockets for the representative months of'95. The percentage frequency of stability classes

suggest, in the post-monsoon and winter months stable classes prevail. In summer more unstable

classes prevail. Due to strong winds and mixing, stability is more or less neutral most of the time

in monsoon.

63

Fig. 4.1

5

4

3

2

(a)

(d)

1 2 3 4 5 6 7 8 9 10 11

1 2 3 4 5 6 7 8 9 10 11

4

3

(b)

(c)

1 2 3 4 5 6 7 8 9 10 11

1 2 3 4 5 6 7 8 9 10 11

Numerical Simulation at 11 UTe of the Spatial variation of wind speed (m) for the four representative months (in clockytise) of '95

4

3

2

· .... . · .... .

.. /./ .. //./././.J .. ..... ' .

//·//Ijll // 1/ I / I If III/III! / ..

"TII'rIII II )'j"j-;-rfJ!!

I I I i : , ... -: ..... /"",i

1 ... { .. J .... ,.

00 1 2 3 4 5 6 7 8 9 10 11

(a)

· .. ' · .....

.... /.//.////// · ....

///////// .... . . . . .

///////// · ...... .

.. ///////// · ... : : :. . 777777777 · ... .. ..... .

"';/7/;';/7/77 /'/////.//-....... " ........ ", ..... ,' . '" ... .

////)..J-..J..._-

/,~««---

00 1 2 3 4 5 6 7 8 9 10 11

(d)

11~>:/

10 -;;':,'i:\: 9 ..... ~ ..... : .. : .... : . , . .

'; i~/I ,\,

7,\';:/111:1" : : ; ; ; ...

8 ·····~\i~iirnr 111 5 ..... : ..

!' ~ i.. ~ .. ~. ~ .: .: .; 3 . , .... ,.: : .. , .. ' ..... . . . . . 2 ..... 1 .. ( j.j.:.J ... ;.' ..... l ... 11.

: : : : : :

1'-'1 '/'Ij+thlj" 00 1 2 3 4 5 8 7 8 9 10 11

(b)

~: .JJ .. J J[\ .. \..I) 1 •• 9 1J .1.\.\\\ II 8 JJJ \\\ lUI 7 .... L.J .. .\,\.\\\··1/. 6 .. .1. :/.1:\.\.\111· 5 .. I·Jl··\···VV··\·I·/·· 4IlH\VVII I 311 i\ :t \ \1 I I 2'1'1'\'\'\,\1"'1 1 ... t···'1····\····\·· '\"'\"\"""1"" 00 1 2 3 4 5 8 7 8 9 10 11

(c)

Fig. 4.3 Numerical Simulation at 11 UTe of the Spatial variation of horizontal wind field for the four representotive months (in clockwise) of '95

285.5 299

285 298.5

284.5 298 g 284 g 297.5 CD ! ... 283.5 :s :s ... ... 297 ~ ~

CD 283 CD Q. Q. 296.5 E 282.5 E .s .s

282 296

281.5 295.5

281 295 0 10 20 0

time (hour)

299 302

301

298 300 g g ! ! 299 :s :s .. 297 .. ~ ~ CD 8. 298 Q. E E .s

296 S 297

296

295 295 0 10 20 0

time (hour)

Fig. 4.4. Diurnal variation of temperature at warm & cold grid points for the four representative months (in clockwise) of '95 . .

10 20

time (hour)

10 20

time (hour)

[-;-- ------j

35 50

>- >- 45 u 30 u

40 c c Q) Q) ~ 25 ~ 35 0" 0" !!! !!! 30 .... 20 .... .... ....

25 0 , 0 Q) 15 Q) Cl Cl 20 2 I 2

15 c 10 c Q) ell U u 10 ... I ... ell 5 ! ell C. c. 5 J

0 I

2 3 4 5 6 I PGT stability classes I

--t-50 I 80 I 45 70 >- >-u 40 u c c 60 ell Q)

~ 35 ~ 0" 0"

50 !!! 30 ~u~;nll

!!! .... .... '0 ....

40 25 0 ell ~~ura~ J ! ell Cl 20 Cl

"' 2 30 .... c 15 c ell Q) U u 20 ... 10 ... ell ell a. a. 10 5

0 0 2 3 4 5 6

PGT stability classes

Fig. 4.5. Percentage frequencies of stability at warm & cold grid points for the four representative months (in clockwise) of '95.

_._----._-,

I !

[;~ban 1 ·_~~!~LJ

2 3 4 5 6

PGT stability classes I

--- ---------' :

18-~~ba~-1

/!I~U!.a..I _1

2 3 4 5 6

PGT stability classes i I ________ ..1

Fig. 4.6 (a) - 4.6 (d) show the diurnal variation of Monin-Obukhov length at warm and cold

pockets for the representative months of 195. The diurnal variation of Monin-Obukhov length

further corroborates by registering more stable conditions from late night to early morning in

almost all the seasons with large duration during winter compared to other seasons.

Fig 4.7 (a) - 4.7 (d) show the diurnal variation of mixing height at warm and cold grid points for

the representative seasonal months of 195. As expected, the mixing height increases from

minimum in the morning to a maximum around 11 GMT and decreases thereafter. This response

is clearly due to diurnal variation in surface temperature. Winter months are characterised by low

values of mixing heights (both maximum and minimum). Summer and post monsoon months

show comparatively high value of maximum mixing heights. Monsoon months show high values

of morning mixing heights and comparatively low values of afternoon mixing heights. There is

a bodily shift of-these curves from urban to rural and vice-versa due to urban effects on the

radiative characteristics.

Table 4.3 show the minimum (3 GMT) and maximum (11 GMT) mixing heights and ventilation

coefficients for the representative seasonal months (mean of 191 to 195). Morning ventilation

coefficients are very low in all the seasons. According to Gross (1970) criteria for high pollution

potential, the morning mixing heights should be :::; 500m and transport wind :::; 4 mls and

afternoon ventilation coefficients should be :::; 6000m2/s and transport wind :::; 4m1s. Applying

these criteria to Delhi it is found that morning periods have high pollution potential in all seasons

and it decreases gradually with time by the afternoon.

4.8 Conclusion

1. The diurnal variation of temperatures at both the warm and cold pockets followed same

trend and attained peak values in the afternoons.

11 . Mixing heights also exhibited similar trends as that of the temperature. Mixing heights

during winter are lowest in all the months. On the otherhand mixing height are highest

in summer and monsoon months. Urban mixing heights are relatively higher than rural

and the time of Occurrence is later at the latter location.

64

580 155

135 480

115 g 380 g

95 .s::. ;; oOJ

CI CI 280 75 c c .!! ,. .!! 0 q 55 , 180 ::E ::E

35 80 15 ---20

0 10 20 10

time (hour) time (~our)

1925 480

1725 430

1525 380

330 1325

g g 1125 280 .s::. .s::. oOJ

oOJ CI 925 CI 230 c c .!! .!! q 725 q 180 ::E ::E 525 130

80 325

30 125

-20 0 10 20 -75 0 10

time (hour) time (hour)

Fig. 4.6. Diurnal variation of Monin-Obukhov length at warm & cold grid points for the four representative months (in clockwise) of '95.

20

20

600 800

500 700

g g 600 400 .... .... 500 .J::. .J::.

C! C! 'iii 300 'CD 400 .J::. .J::. C! C! c: c: 300 'j( 200 'x 'E E 200

100 100

0 0 10 20 o .

time (hour)

1000 800 ·

900 700 800

600 g 700 E .... .... . 600 1: 500 .J::. en en

'CD 500 Gi 400 .J::. .J::. en 400 en c: c 300 'x 300

'j( 'E 'E 200

200 100 100

0 0 0 10 20 0

time (hour)

Fig, 4}. Diurnal variation of mixing height at warm & cold grid points . .. for the four representative months (in clockwise) of '95,

---~~- _ ..... _ -- -

10 20

time (hour)

---

10 20

time (hour)

--- ---- -

Table 4.3

Mean Mixing height (at 3 GMT & 11 GMT) at {(S,S) grid point} NeT of Delhi.

Month/Season

January (winter) April (summer) August ( monsoon) October (post-monsoon)

3 GMT

100 135 185 225

Mixing height 11 GMT

575 785 750 850

Mean ventilation coefficients (at 3 GMT & 11 GMT) at {(S,S) grid point} NeT of Delhi.

Month/Season Ventilation coefficient

January (winter) April (summer) August (monsoon) October (post-monsoon)

3 GMT 11 GMT

500 2100 1700 1200

6,000 6,600 6,300 6,600

111. More stable periods occurred in post-monsoon and winter seasons but more unstable

periods are registered in summer. Monsoon season recorded more neutral stabilities.

IV. This is further supported by Monin-Obukhov length which showed more stable

conditions from late night to early morning - the duration varied with season.

v. Diurnal and seasonal ventilation coefficients suggest high pollution potential during

morning compared to afternoons and in winter compared to summer.

In the next chapter, a brief description about the puff apporoach in studing the diffusion of

pollutants , the Gaussian-puff model to study this effect and the assimilative capacity of the

atmosphere are discussed.

65