STABILITY PARAMETERS AND THEIR SKILL TO FORECAST THUNDERSTORM

Transcription

1 International Journal of Physics, Vol. 4, No. 1, January-June 2011 pp STABILITY PARAMETERS AND THEIR SKILL TO FORECAST THUNDERSTORM R. Bhattacharya * and A. Bhattacharya Department of Environmental Science, University of Kalyani, Kalyani , West Bengal, India. Abstract: Atmospheric instabilities of pre monsoon months March to May are studied using RS/RW data of Kolkata, West Bengal. Occurrences of thunderstorm days are differentiated from non thunderstorm days from the report of any one among the five observatories Dum Dum, Bankura, Ulberia, Bagati and Digha. The object of the paper is to investigate the role of Lifted index(li), Cross Total (CT), Vertical Total (VT), Total Total (TT), Windex (WI), Deep Convective Index (DCI), Severe Weather Threat Index (SWEAT), Convective Available Potential Energy (CAPE), Convective Inhibition Energy (CIN) and Bulk Richardson Number (BRN) to forecast thunderstorm day and to compute threshold value of these indices by an iteration process starting from their average value on thundery days for the period 2000 to 2007 till the best possible forecast skill scores POD (Probability of detection), CSI (Critical success index), EI (Efficiency index), FAR (False alarm rate) are achieved. The result is then verified for the independent year Linear regression equations among different indices are computed. The degree of forecasts using TT>40.2, DCI>30.1 and WI>75.5 are found significant among all the ten instability indices. The estimated POD scores of the above three indices are 87%, 79% and 55% respectively. FAR is found good (0.22) for the index WI. However 100% POD cannot be achieved from a single index alone. Keywords: Atmospheric stability, Instability indices, Skill scores, Equivalent success rate. 1. INTRODUCTION Thunderstorms are common in the tropics particularly during pre monsoon months (March to May). Pre monsoon storms in West Bengal known as Nor westers are characterized by thunder squall, torrential rainfall and low level wind causing extensive loss in life, property and agriculture. It also exhibits intra cloud (IC), cloud to cloud (CC) and cloud to ground (CG) lightning discharges. The lightning and down burst from a thunderstorm results severe aviation hazards. The highest number of hazards reported due to thunder storms alone [1]. Instability, lifting and presence of moisture are the three major factors required to produce deep moist convection [2]. The generation of thunderstorms is mainly governed by the thermodynamic conditions of atmosphere. A number of studies have been conducted to get * Corresponding author: rinaenv@yahoo.com

2 22 International Journal of Physics information of pre and post features associated with thunderstorm [3 8]. Forecasting of thunderstorms is one of the harder problems because of its complex nature. The microphysical and electrical properties of thunder cells govern the severity of the storms.the analysis of atmospheric data has introduced different parameters which give information regarding the stability of the atmosphere. Many researchers all over the globe have used stability parameters to relate them with thunderstorms [9 13]. But the threshold values of the indices are yet to be standardized so that best skill in forecasting deep convective days can be made. 2. STABILITY OF THE ATMOSPHERE The stability of the atmosphere depends on the environmental lapse rate and adiabatic lapse rate. When ELR (environmental lapse rate) < PLR (parcel lapse rate), the air parcel is cooler than its surrounding medium and the atmosphere is said to be stable. When ELR and PLR are exactly same, the atmosphere is neutrally stable. But if ELR > PLR, the air parcel is warmer than the environmental atmosphere and rises up till ELR = PLR. Conditional instability exists when ELR is between DALR (Dry adiabatic lapse rat e) and WALR (Wet adiabatic lapse rate). The atmosphere is unstable with respect to WALR. Convective instability exists when equivalent potential temperature dθe/dz < 0 and the air parcel lifted from the BL (boundary layer) to LFC (level of free convection). Figure 1 shows the skew T plot of a calm day and a storm day as reported by the observatory Dum Dum. Lifted index (LI) is designed to measure difference of temperature between lifted parcel and the surrounding at 500 hpa level in order to account average moisture and temperature within PBL (Planetary boundary layer) [14]. Total Total index (TT) consists of two parts: (i) Vertical Total (VT) which represents lapse rate between 850 hpa and 500 hpa and (ii) Cross Total (CT) takes into account the dew point at 850 hpa [5,15]. The parameter SWEAT Figure 1: Skew T Plot of a Calm Day (Left) and a Deep Convective Day (Right)

3 Stability Parameters and their Skill to Forecast Thunderstorm 23 incorporates kinematics and thermodynamic information to assess potential of storm [16]. CAPE represents the amount of buoyant energy available to lifting parcel until its temperature becomes equal to the temperature of the environment [17 19]. It is the positive area between the moist adiabat and the environmental temperature curve from LFC (level of free convection) to EL (equilibrium level). CIN defines the work required to bring parcel to the LFC. Bulk Richardson Number (BRN) combines buoyant energy (CAPE) and vertical shear of the horizontal wind [20, 21]. Deep convective Index combines the properties of equivalent potential temperature at 850 hpa with instability [22]. The absorption of latent heat during melting cools air parcels and they become negatively buoyant. Hence environmental lapse rate must be considered from surface to melting point. The parameter Windex (WI) includes the melting level and is based on the studies of observed and theoretical models of microbursts [23, 24]. Atmospheric convection depends on stability of the atmosphere. The thunderstorms are probable in regions where the stability indices are above the critical values as shown in Table 1. BRN > 50 often results multicell development which produce severe weather. SWEAT > 300 represents potential for thunderstorm and SWEAT > 400 have potential for tornadoes [25]. Tornadoes may occur below 400 if thunderstorms and or boundary interactions increase the shear. DCI is a new index and have no critical values. But DCI > 30 indicate development of Cb cells. WINDX is used for microbursts. Thunderstorms are dissipated by several ways one of which is downing the mid tropospheric wind towards the ground known as down bursts and hence we apply this index to study thunderstorms. The stability indices LI, TT, CT, VT, SWEAT, CAPE, CIN, BRN, DCI and WI are studied for forecasting atmospheric stability and potential for thunderstorms in and around Kolkata, West Bengal. Table 1 Critical Values of the Stability Parameters Parameters Critical Value Parameters Critical Value Lifted Index (LI) -3 SWEAT 300 CT 18 CAPE 1000 VT 26 BRN 50 Total Total Index (TT) DATA ANALYSIS Occurrences of thunderstorm/high convective days are differentiated by non thunderstorm days from the report of the Observatories Dum Dum (22.65 N, E), Bankura (24.15 N, E), Ulberia (22.5 N, E), Bagati (22.59 N, E) and Digha (21.41 N, E). If any of the above station has reported occurrence of thunderstorm then that day is taken as thunderstorm day. Daily Radiosonde data of DumDum (42809) at 0Z and 12Z for the pre monsoon months March, April and May during are used in our study. At first a (2 x 2) contingency table is prepared on the basis of observations (Table 2).The threshold or best value of each index is achieved by an iteration process starting from the mean value for the period 2000 to 2007 till the best possible forecast skill scores POD

4 24 International Journal of Physics (probability of detection), CSI (Critical success index), EI (Efficiency index), FAR (False alarm rate) as given in Table 3 are achieved. For good prediction the scores of CSI, FI, and POD should be close to unity and FAR must be close to zero. The efficiency of the best value of the stability parameters thus obtained is verified for the independent year Table 2 Contingency Table Prediction Event observed Event not observed Event predicted N 1 (correct) N 2 (false) Event not predicted N 3 (false) N 4 (correct) Table 3 Description of Different Skill Scores POD = N 1 /( N 1 + N 3 ) EI = (N 1 + N 4 )/ N 1 + N 2 + N 3 + N 4 ) CSI = N 1 /( N 1 + N 2 + N 3 ) FAR = N 2 /( N 1 + N 2 ) 4. RESULTS AND DISCUSSION Interrelation among different indices: Different stability indices are computed on thunderstorms/high convective days and analyzed to find out simple linear regression equations. Figure 2 represents the scattered diagrams of different indices (LI, TT, VT, CT, CAPE, CIN, BRN and DCI) vs WI. The correlation coefficients are all found significant at LS = 0.05 except CIN and BRN. The simple regression equations of WI with other stability parameters are given: WI = *LI (1) WI = 0.91 *CT (2) WI = 1.48 *VT (3) WI = 0.73 *TT (4) WI = 0.78 * DCI (5) WI =0.04*SWEAT (6) WI = 0.003*CAPE (7) WI = 0.01* BRN (8) WI = 0.05*CIN (9) Figure 3 represents scattered graph of different indices (LI, TT, VT, CT, CAPE, CIN, BRN and WI) vs DCI. The correlation coefficients are all found highly significant at LS = 0.05 except LI, CAPE, BRN and CIN. The simple regression equations of DCI with other parameters are given: DCI =-1.21* LI (10)

5 Stability Parameters and their Skill to Forecast Thunderstorm 25 DCI = 0.49 * CT (11) DCI = 0.98 * VT (12) DCI = 1.01 * TT (13) DCI = 0.42 * WI (14) DCI = 0.04 *SWEAT (15) Figure 2: Scattered Plot of the Stability Indices vs WI

6 26 International Journal of Physics DCI = * CAPE (16) DCI = * BRN (17) DCI = * CIN (18) Threshold Value of the indices: Descriptive statistics of the stability indices are presented in Table 4. The marginal value of the indices above which the possibility of thunderstorms is taken to be the mean value over the period 2000 to 2007 and then the critical values are Figure 3: Scattered Plot of the Stability Indices vs DCI

7 Stability Parameters and their Skill to Forecast Thunderstorm 27 achieved by iteration processes using the skill scores. The best values and the corresponding skill scores are given in Table 5. Table 4 Descriptive Statistics of the Stability Indices Parameters Mean SD Skewness Parameters Mean SD Skewness LI WI CT SWEAT VT CAPE TT BRN DCI CIN Table 5 Critical Values of the Stability Indices and Associated Skill Scores Parameters Best Value CSI EI POD FAR LI CT VT TT DCI WI SWEAT CAPE BRN CIN Skill of forecast: Best value of the stability parameters are used to test the degree of forecast for the year The different skill scores are illustrated in Table 6. Table 6 Different Skill Scores for Verifying Year 2008 Parameters Best Value CSI EI POD FAR LI CT VT TT DCI WI SWEAT CAPE BRN CIN

8 28 International Journal of Physics Using the optimum value for stability parameters as depicted in Table 5 statistical analysis (Chi-square test) are done to verify the significance of forecasts of thundery days during pre-monsoon months for the year The critical value of χ 2 = 3.84 at df = 1 and LS = If the calculated value of χ 2 at df = 1 and LS = 0.05 exceeds the critical value the result will be significant (S) and if it is less than the critical value the result will be insignificant (NS). From the Table 7 it is noted that forecast with respect to WI is just significant. Validity of success of yes or no forecasts is also done by Equivalent Percentage of Success (EPS) method and the computation shows that the success rate using the indices TT, WI and DCI are 66.45%, 66.87% and 67.3% respectively. Table 7 Computed 2 Value for Different Indices Indices χ 2 (Calculated) Remark Indices χ 2 (Calculated) Remarks LI 0.09 NS WI 3.98 S CT 8.30 S SWEAT 0.58 NS VT 4.72 S CAPE NS TT 4.01 S BRN NS DCI 5.66 S CIN 0.13 NS Deviation of the critical values for tornadoes: The stability parameters are analyzed for 17 tornado events over West Bengal, Bangladesh and NE India. It is noted that the average values of the stability parameters are much higher than the estimated threshold values of the parameters as obtained by iteration processes. Table 8 shows the average values of the stability indices for the cases of thunderstorm and tornado. Table 8 Comparison Between Thunderstorm and Tornado Events Mean value on Events Mean value on Events Indices Thunderstorm Tornado Indices Thunderstorm Tornado LI WI CT SWEAT VT CAPE TT BRN DCI CIN CONCLUSIONS The probabilities of detection with indices TT and DCI are respectively 87 % and 79%. But the False Alarm rate is found minimum for the index WI. However the skill score POD of WI is found quite good (87%) for the verifying year Therefore among the stability indices TT, DCI and WI can be used as predictor of convective days. Moreover average values of the indices are found high than the estimated threshold values in case of severe

9 Stability Parameters and their Skill to Forecast Thunderstorm 29 tornadoes. Sharma et al [26] have used radio occulation data for better atmospheric stability estimation. Practically it is impossible to forecast thunderstorm days by a single index. A combined estimation of TT, DCI and WI may give better result. Acknowledgements The authors are thankful to India Meteorological Department for providing some of the relevant information. Data obtained from Wyoming University archives is also thankfully acknowledged. References [1] Tyagi, A., Thunderstorm Climatology Over Indian Region Mausam, 58, 189, (2007). [2] Doswell, CA, The Distinction Between Large-scale and Mesoscale Contribution to Severe Convection: A Case Study Example, Wea. Forecast., 2, 3, (1987). [3] Johns, RH and Doswell, CA, Severe Local Storms Forecasting, Wea. Forecast., 7, 588, (1991). [4] Khole, M. and Biswas, HR., Role of Total-totals Stability Index in Forecasting of Thunderstorm/ Non-thunderstorm Days Over Kolkata during Pre-monsoon Season, Mausam, 58, 369, (2007). [5] Litta, AJ and Mohanty, UC, Simulation of a Severe Thunderstorm Event during the Field Experiment of Storm Programme 2006 using WRF-NMM model, Curr. Sci., 95, 204, (2008). [6] Manohar, GK and Kesarkar, AP., Climatology of Thunderstorm Activity Over the Indian Region a Study of East West Contrast, Mausam, 54, 819, (2003). [7] Seshadri, N and Jain, PS., Study of Role of Stability Index in Forecasting of Thunderstorms, Mausam, 41, 102, (1990). [8] Bhattacharya, R, Bhattacharya, A, Guha, R, and Pal, S, WINDEX A Tool for Forecasting Thunderstorm Potential, Proc. National Conf. MDCCT, IETE, Burdwan, 2, 46-47, (2010). [9] Doswell, CA and Schultz, D M, On the Use of Indices and Parameters in Forecasting Severe Storms, Electronic J. Severe Storms Meteor., 1, 1, (2006). [10] Haklander, A J and Van Delden, A., Thunderstorm Predictors and their Forecast Skill for the Netherlands, Atmospheric Research, 67-68, 273, (2003). [11] Huntrieser, H, Schiesser, HH, Schmid, W and Waldvogel, A, Comparison of Traditional and Newly Developed Thunderstorm Indices for Switzerland, Wea. Forecasting, 12, 108, (1997). [12] Karmakar, S and Alam, M., Interrelation Among Different Instability Indices of the Troposphere Over Dhaka Associated with Thunderstorms/nor westers over Bangladesh during the Pre-monsoon Season, Mausam, 57, 629, (2007). [13] Roy, SS and Bhowmik, SKR, Evaluation of Thermodynamics of the Atmosphere in Relation to Premonsoon Convective Activity Over North India, Mausam, 54, 397, (2003). [14] Galway, JG, The Lifted Index as a Predictor of Latent Instability, Bull. Amer. Meteor. Soc., 43, 528, (1956). [15] Jacovides CP and Yonetani T., An Evaluation of Stability Indices for Thunderstorm Prediction in Greater Cyprus, Wea. Forecast., 5, 559, (1990). [16] Miller, RC., Notes on Analysis and Severe Storm Forecasting Procedures of the Air Force Global Weather Central. Tech. Report 200(R), Headquarters, Air Weather Service, Scott Air Force Base, IL 62225, 190, (1972).

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