4.3 Methodology of stability analyses .1 Analysis of unmodified stability indices
4.3.2 Modified stability indices
Some of the stability indices have been modified by taking into account of the mean low level moisture and temperature. The reason is that the low level moisture plays an important role in convective activity. Moreover, the standard isobaric surfaces were designated before as 1000,
73
850, 700 hPa and so on, but recently 925 hPa has been included as an standard isobaric surface and as such data at 925 hPa have been considered instead of 850 hPa to modify the stability indices. It has been found that 850 hPa level has less moisture at 0000 UTC in most of the dates of occurrence of nor'westers in Bangladesh and the stability indices do not show sufficient instability of the troposphere favourable for the occurrence of nor'westers. But in the afternoon/evening, nor'westers occur in Bangladesh. So, the existing instability indices are not
V enough to show the instability of the troposphere with which a forecaster cannot issue forecast for nor'westers and therefore, it has become imperative to modify the instability indices. The moisture conditions in terms of dew point temperature at 925 hPa and 850 hPa are shown in Fig.
4.2.
A
35 30
25
>-.
U 20 U
15 L.
10
5
0
.
3I Frcquency of Td850
\
--- Frequency ofTd925
21 1'
\
20II
p
• I 8/
12
4
C? li, t r1=1c "r 1000 rl .0 s000
0299 99222 00000000
- -. 00 '0 • 00 r'l . '0 00 ('1
'0 -rf- r1 - • r' r1
Ran of Td (C)
Fig. 4.2: Comparison of dew point temperatures (TdTd in °C) at 850 hPa and 925 hPa over Dhaka at 0000 UTC on the dates of occurrence of nor'westers in Bangladesh
It is seen that the dew-point temperature at 850 hPa level is :!~ 14 °C in most of the cases (in 77 out 108 i.e. 71.30% nor'westers) on the dates of occurrence and it is below 0°C to -16°C in 6 cases (5.56%). This indicates highly dry condition at 850 hPa. Whereas at 925 hPa level, the dew-point temperature is ~: 14°C in 86 nor'westers (i.e. 79.63%) and is above 4°C. It is interesting to note that the two curves meet near 14°C and that is why 14°C may be taken as the threshold value above which the lower level may be considered as the moist level and below which the lower level may be considered as the dry level on the dates of occurrence of nor'westers. This is why 925 hPa has been considered instead of 850 hPa in the study.
In this study, 925 hPa has been considered as the low level, which is also the mean of 1000 and 850 hPa. The formulations of modified stability indices are given below:
74
4.3.2.1 Modified Cross Total Index (MCT)
Considering the 'dew-point temperature of 925 hPa instead of 850 hPa, the C I has modified. It is given by
MCI' = Id925 T500
Where Td925 = 925-hPa dew-point temperature in °C.
4.3.2.2 Modified Vertical Total Index (MVT)
Considering the temperature of 925 hPa instead of 850 hPa, the VT has been modified as given below:
MVT=1925 -1500 (12)
Where T925 = 925-hPa temperature in °C.
4.3.2.3 Modified Total Totals Index (MTT)
Considering the temperature and dew-point temperature of 925 hPa instead of 850 hPa, the TI has been modified. It is given by
MTT=MVT+ MCT
= (1925 + Td925) - 2 T500 (13)
Where T925 = 925-hPa temperature in °C
= 925-hPa dew-point temperature in °C.
4.3.2.4 Modified Severe Weather Threat Index (MSWI)
Considering the temperature and dew point temperature of 925 hPa instead of 850 hPa, the SWI been has modified. 'Ihe MSWI Index is defined by:
MSWI =12Td925 + 20(MTT-49) +2f 9+f 5 + 125(S + 0.2) (14) Where 1d925 = 925 hPa dew-point temperature in °C
MTT = Modified Total Totals Index = (T925 + Td925) - 2T500 75
= 500—hPa temperature in °C f9 = 925—hPa wind speed in knots.
15 = 500—hPa wind speed in knots.
S = Sin (as - (X9)
= 500 hPa wind direction measured from the true north.
= 850 hPa wind direction measured from the true north.
None of the terms may be negative. 1-lence if Td925 <0, the first term is set to zero; if MTT <49, the second term is set to zero; and the last term is set to zero if any of the following conditions are not met:.a9 between 130° and 2500, a5 between 2100 and 3 10°, a5 - a9 >0, and both f9, J ~ IS knots.
4.3.2.5 Modified Energy Index (MEl)
The modified El has been calculated by considering moist static energy of 925-hPa level instead of moist energy of 850-hPa level. It is given by:
ME! = MSE500 — MSE925 (15)
Where
MSE925 = Moist Static Energy at 925 hPa in Joule/gm, and
•MSE500 = = Moist Static Energy at 850 hPa in Joule/gm.
MSE = CT + gZ + Lq.
Cp = Sensible heat content of the atmosphere T = Temperature in °K
g = Acceleration due to gravity in ms ',
Z = Geopotential height in geopotential meter, and V = wind speed,
76
L = Latent heat of condensation and q = Specific humidity.
4.3.2.6 Modified K-Index (MKI)
Considering the temperature and dew point temperature of 925 hPa instead of 850 hPa, the K! has been modified. The MKI can be computed by
MKI = (T925+ Td925) - (Td700 + T500) (16) Where T925 = Temperature at 925 hPa in °C.
Td925 =Dew-point temperature at 925 hPa in °C.
Td700 = Dew-point temperature at 700 hPa in °C.
1'500= Temperature at 500 hPa in °C.
Linear correlations between the unmodified instability indices such as SI, LI, DPI, DII, CT, VT, TT, KI, El and the modified instability indices such as MCT, MVT, MTT, MKI, MEL computed on the days of occurrence of 108 nor'westers have been studied and the corresponding correlation co-efficients are computed. The regression equations and the co-efficient of determination (R2) have been obtained through scatter diagrams by taking two indices at a time.
-s