New observations often bring surprises, which challenge old beliefs but also stimulate the search for improved understanding. The Tropical Rainfall Measuring Mission (TRMM) database is reducing the uncertainty of climatological rainfall estimation. This is good. However, this same database has accelerated a quiet revolution in our capabilities to use remote sensing to infer the properties of convective systems. For example, we can distinguish rainfall from mesoscale convective systems (MCSs) from that from more isolated convection, and learn that the fraction of rain from MCSs can range from 20 to 80 percent in different regimes.

Convective vertical velocity can be inferred from vertical profiles of radar reflectivity, passive microwave radiometry, and lightning frequency. Using a massive TRMM database, we can ask "where are the 'hot towers'"? They are found only rarely over tropical oceans, but favor continents. They favor Africa rather than Indonesia, and are so rare over the Amazon that it has been called the meteorological 'green ocean'. The intense convection that penetrates several kilometers into the stratosphere are generally found in higher latitudes. Studies of stratosphere-troposphere exchange using IR data alone are probably giving the wrong answers.
Modelers have a challenge to construct cloud-resolving models (CRMs) that can distinguish between ordinary and intense convection. There is a major dichotomy in the microphysics of precipitation between updraft speeds of 5 and 10 m/s. There is arguably another major dichotomy in the radiative properties of cirrus anvils between ordinary and intense convection, still poorly explored. The mass flux at cloud base is probably poorly related to mass flux at the tropopause.

Theoretical challenges may not be as daunting. The relationship between convective vertical velocity and convective available potential energy (CAPE) is weak, but the talk closes with an attempt to rationalize the observations in terms of simple parcel theory.

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