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How do the atmospheric conditions that produce sleet differ from those that produce hail?

Sleet forms when there is a layer of above freezing temperatures below cloud base but the temperatures at the surface are below freezing. A snowflake falling out of the cloud will melt in the above freezing layer producing a rain drop. The below freezing surface layer must be thick and cold enough to refreeze the raindrop before reaching the ground.
Hail is produced inside a cumulonimbus cloud by accretion of super-cooled liquid water onto a large frozen embryo caught in a strong updraft. Continuous cycles through areas of super-cooled liquid water will cause the hailstone to increase in size until it can overcome the upward vertical velocity and eventually fall to the earth’s surface.

What is the difference between freezing rain and sleet?

Freezing rain is liquid (super-cooled) that will freeze on contact with objects that are below freezing on the surface. The determining factor between sleet and freezing rain as a precipitation type, is the depth and coldness of the subfreezing layer near the surface.
Sleet is usually a transparent or translucent ice ball around .2 inches or less in diameter. When it hits the ground it can bounce. The formation of sleet was discussed in the previous question.

Describe how hail might form in a cumulonimbus cloud?

Hail is formed when clouds, specifically cumulonimbus clouds, have both high altitudes and powerful updrafts within the condensation layer of the cloud. As rain droplets form, they are frozen and then carried aloft again, where their temperature condenses additional water on the exterior, which then also freezes. After an extended period of gaining an increasing number of ice layers, the hailstones at some point are too heavy for the updrafts to lift, and they fall to the ground, sometimes losing layers to melting in

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