Weather recursive · not sovereign

Thunderstorm and Hail

An updraft that feeds itself on warm, moist air, grows hail in the part strong enough to hold it, and lives only as long as its own outflow does not cut it off.

A thunderstorm is a loop. Warm, moist air rises; its water vapor condenses and releases heat; the heat makes the air more buoyant, and the stronger updraft draws in more warm, moist air. Hail grows inside that loop: small ice particles are carried up through supercooled cloud water, collect it, and fall once they are too heavy for the updraft to hold. The same hail can end the storm. Falling hail and rain chill the air beneath it into a pool of cold outflow that spreads under the inflow and cuts off the supply. Wind shear is what lets a storm survive its own hail: it leans the updraft so the hail falls beside it rather than into it.

A Slice Through the Storm

30 km across, 15 km tall · the updraft leans downshear, to the right

updraft, brighter is faster hail under 1 cm 1 to 2.5 cm 2.54 cm (1 inch) and larger dashed lines: 0 °C, −40 °C, tropopause

updraft strength (m/s)—

storm age (min)—

largest stone aloft (cm)—

updraft needed to hold it at 6 km (m/s)—

largest stone at the ground (cm)—

stones at the ground, 2.54 cm or larger—

building

A teaching model, not a cloud model. The updraft has a prescribed shape. Its strength follows a simple rule: instability sets the supply, and hail in the updraft core and the cold pool at the ground choke it, with shear keeping them apart. Hail fall speeds and growth use standard formulas for a smooth ice sphere; melting is simplified. Storm lifetimes come out of that rule and are the right order, not a forecast. A slice cannot rotate, so with strong shear the model adds up to 30% more lift, standing in for the pressure forces a rotating updraft gets. Time is the solver’s clock, 150 model seconds for each real second.

Why It Reads as Recursive, Not Sovereign

an authored reading, not a measurement

The loop is real. Rising air releases heat that makes more air rise, and the storm runs at a real cost, spending the instability of the air it draws in. Press Cut the warm inflow and the loop stops. That places it with the flame on the Sovereignty page, not with the attractlets. Like the flame, its edge is a gradient of cloud and clear air, not a boundary it builds and defends. Recursive, but not sovereign.

This panel is not the storm. The program that runs it is an attractlet model under § 7.4, as on the Lorenz page. The reading above is of the real storm.

The Shape of the Basin

what the storm comes back from

The basin is the set of unstable columns of air that organize into a self-sustaining updraft. Press Send an outflow pulse to push a surge of cold air under the storm. With strong shear the updraft dips and keeps going. With weak shear the same pulse finishes it, and even without one, a weak-shear storm chokes on its own hail in about half an hour. Shear widens what the storm can come back from.

Hail and the Updraft That Holds It

fall speed of a smooth ice sphere

A stone stays aloft only where the updraft is at least as fast as the stone falls. For a smooth ice sphere (density 900 kg/m³, drag coefficient 0.6) in air of 1.0 kg/m³, roughly 2 km up:

Size	Diameter	Fall speed
Pea	0.6 cm	11 m/s · 25 mph
Penny	1.9 cm	19 m/s · 43 mph
Quarter	2.5 cm	22 m/s · 50 mph
Golf ball	4.4 cm	30 m/s · 66 mph
Baseball	7.0 cm	37 m/s · 83 mph
Softball	10.2 cm	45 m/s · 100 mph

Real hailstones are rough, lobed and sometimes spongy, and fall at speeds that differ from these. The readout’s “updraft needed” uses the same formula at 6 km, where thinner air lets a stone fall faster. Gold stones are 2.54 cm (1 inch) or larger, the U.S. National Weather Service threshold for severe hail.

In this model the largest stones stay near golf-ball size. Growing bigger takes updrafts stronger than its simple supply rule allows.

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