I am studying microwave radiometry and confused over this apparent contradiction: Microwaves emitted at 2.45 GHz (~15 cm) are absorbed by water molecules, causing the molecules to rotate under the influence of the electric field component so producing kinetic (thermal) energy that cooks food. Going out to 3 GHz, (~10 cm), we see that weather radar pulses are scattered by water molecules in rain drops (and other airborne particulates), which is the source of the "echo" used to create radar maps. Both types of microwaves are in the S-band, so what explains the difference in absorption by water molecules at 2.45 GHz vs. scattering (reflection) at 3 GHz? Are microwave echoes detected via weather radar actually "scattered" or are they being absorbed and re-emitted according to Kirchoff's radiation law?
There is no essential difference between 2.45 GHz and 3 GHz microwaves regarding absorption and reflection from regions in the atmosphere or food containing water. Microwave ovens use 2.45 GHz because the frequency is in an industrial band, and magnetrons producing the necessary power in that range are relatively inexpensive.
In a radar system much of the incident radiation reflects or scatters off of the higher effective dielectric permitivity of the air mass containing water vapor and droplets. There is some absorption, but the reflected energy is easily detected, providing information about positon and velocity of the clouds. Since power in the transmitted beam falls off as $1/r^2$, and the radar is usually pulsed, energy density is low compared to that in a microwave oven.
In a microwave oven, water in the food absorbs energy from continuous microwave irradiation. The cavity is designed to heat food uniformly, by reflecting microwave energy randomly around the oven (avoiding cavity resonances and standing waves which degrade uniformity), sometimes using a mixing fan at the waveguide output. Microwave energy scatters off the food in addition to some being absorbed. Even though only a small amount of energy is absorbed from any direction at a given time, power density remains high, and re-reflected microwave energy continully passes back and forth through food in the oven.