What is Process Noise? What are its sources

In theory we often read about the impact of high freq noise affecting derivative control of a PID Controller...!!

Assuming a simple Level or Temperature Control Loop of a static process vessel, what would Process Noise be like...!! What would be the sources of Process Noise which can affect the derivative control...??

Similarly in any rotary equipment, what would be Process Noise and how would it be introduced OR what sources would introduce one, in any simple closed loop...!!

Process noise in level applications can come from
- agitators creating waves with the crests and troughs (top mounted radar/ultrasonic/IR)
- agitator turbulence and flow creates a hydrodynamic force that a hydrostatic head measurement 'sees' but reports it as a presumed hydrostatic force when in fact, it is not, creating an error and process noise.
- filling operations that create waves and/or turbulence or partial blockage/interference of the level sensor (radar/ultrasonic)
- draining operations that create a vortex that varies in intensity which affects hydrostatic head measurement in the vicinity of the vortex
- foam that gets reshaped by agitation or natural formation/collapse (top mounted radar/ultrasonic/IR). Nonhorizontal foam can reflect ultrasonic/radar at non-perpendicular angles.
- changing density in slurries and tanks fill or empty affects hydrostatic head level measurements
- changing vapors or dust density will affect IR level measurements
- the formation of cloud mists of condensing atmospheric water vapor when the tank process temperatures hover around atmospheric dewpoint can affect ultrasonic and some radar level measurements.
- solids level measurement has the inherent process noise of dynamically changing angles of repose
- ultrasonic/radar generally has a 'speed of response' setting that when set too fast reports what looks 'jitter' when examined as a Y-t trend, in part due to the measurements falling at the extremes of the uncertainty band without the 'smoothing/averaging' affect of slower response time reporting.
- deposition of 'process material scale' on nozzles and stilling wells creates false echoes that can become process noise
- the low level signal from an ultrasonic transducer to its electronic 'transmitter' box is subject to EMI interfence which can appear as process noise.