Computation of Showalter Index by an Iterative Method

In order to improve computational accuracy of Showalter Index, a bisection iterative method (BIM) is introduced to the calculating scheme in two parts: One part is the computation of atmospheric properties of lifted condensation level (LCL), which are requisite to potential pseudo-equivalent temperature (PET) calculation. The other is computation of 500 hPa temperature of the parcel lifted pseudo-adiabatically from LCL keeping PET conservation. Comparing BIM with schemes of Zhang shows that Showalter Index computed by BIM reaches an acceptable accuracy level. Furthermore, the BIM is evaluated by contrasting it to table interpolating method (TIM) of Shou through their 500 hPa parcel temperature difference analysis. Result shows that BIM temperatures are less than those of TIM uniformly with the maximal absolute error of 1.36 ℃. Statistically, the average (-0.68 ℃) and average absolute errors (0.69 ℃) are quite close in magnitude, which shows that the differences are systematic ones. The possible cause is that to the BIM, pseudo-adiabatic parcel ascent is considered, in which all condensed water is instantly removed from the parcel. While the 500 hPa parcel temperature of TIM might be obtained by adiabatic process with entrainment of all condensed water, which can be regarded as the inner heat source of the parcel system consisting of saturated air parcel and condensed water of the adiabatic ascent. The physics difference means that the nearer to saturate the air parcel at initial position of 850 hPa is, the larger negative difference in magnitude between BIM and TIM parcel temperature on 500 hPa there is. In the lower section between -5 and 10 ℃ of 850 hPa air parcel temperature, the 500 hPa parcel temperature difference distribution is consistent with the above mechanism. While in the left interval from 11 to 30 ℃ upper section, the magnitude of 500 hPa temperature difference decreases following an increasing process with 850 hPa dew point depression increasing, which can be only partly interpreted through the mechanism. Computational algorithm and adopted experiential formula difference might be the other cause of 500 hPa parcel temperature difference distribution. The BIM is introduced to compute the parcel temperature at given pressure level lifted adiabatically from initial level with known atmospheric properties, which is essential for stability analysis through parcel method. As a result BIM can also be used in the computation of many stability indexes such as modified Showalter Index, lift index, CAPE (convective available potential energy) and CIN (convective inhibition energy). The great computational efficiency and application convenience makes BIM useful for weather diagnostics.