Quadratic growth hypothesis for reaction time prediction and ‘rate of growth’ based classification of cumulus

Abstract

Research is motivated by unsatisfactory results in hail mitigation operations, anywhere in the world. In this paper, a new concept of quadratic growth hypothesis (QGH) has been proposed and examined in the prediction of hailstorm. Another new concept of reaction time (RT) has been presented which is useful for efficient seeding in hail mitigation campaigns. Given complex nature of cumulus growth, rate of growth of cumulus cloud (r) has been broadly categorized as slow $$\text{(}r \le 0.2\,{\text{dBZ/min}})$$ , moderate $$(0.2 < r < 0.8\, {\text{dBZ/min}})$$ and fast $$(r \ge 0.8\,{\text{dBZ/min}} )$$ . Often cumulus shows reverse growth too. It is found that QGH-based predictions are 100% correct for slow-growing cumulus and 62.5% accurate for moderate. However, QGH predictions are incorrect when the cumulus growth reverses or when it is fast. Empirically a ‘QGH-Rectangle’ has been identified wherein QGH is precisely valid. Prediction skill scores [= (correct prediction/total predictions made)] of 0.79, 0.79 and 0.75 are obtained from scan intervals (time interval between the beginnings of any two adjacent volume scans) of 10-, 12- and 19-min radar data, respectively. Amongst the three data sets, 10-min scan interval is operationally safer for RT computation during hail mitigation campaigns. In most of the cases, RT may range from 17.3 to 29.6 min. Maximum RT of 43 min is also noted for slow-growing cumulus. Linear extrapolation (LE) has been used to predict the cumulus cloud motion speed which has been observed from 5 m/s to as high as 19.3 m/s. It is noted that larger scan interval of Doppler weather radar data would exhibit more consistent and reliable speed prediction by LE method.