Some excerpts taken from the book:
Pressure Instruments

CHAPTER 9
THE VERTICAL SPEED INDICATOR
A Vertical Speed Indicator (VSI) is the DR reference for the rate of climb and descend (Fig. 1.3 and 9.1). A rate of climb or descend is the kind of motion which takes place only in the vertical plane, just like a balloon. In meteorological forecasting, this kind of motion does not play a significant role unless a circulation mechanism (like the equation of continuity) is coupled to it; or if it is vertically integrated (as in the Altimeter equations 8.1 and 8.3). Likewise, the VSI is not used as a principal DR reference for the Triangle of Velocities (Drg. 1.1); and potential weather instability does not affect it.
The navigational properties of the VSI are generally described by the vertical component of the aircraft speed (equation 8.4). The following sections give in detail the contribution of each of the terms in this equation.
9.1. Barometric Error.
The word ‘barometer’ always signifies the ‘air- pressure’ . Therefore, according to the VSI equation (8.5) the barometric error is represented by . Its speed relationship is:

Equation (9.1) implies that when a pilot over- flies a region
of low pressure the VSI displays a climb and vice versa. Pilots are advised; therefore, to carry SIG. weather charts on board so that they can identify the positions of high and low pressure en- route.
9.2. Wind- Shear.
Significant en- route features are known to be the surface pressure , and the terrain . The VSI error associated with is the barometric error (section 9.1). The VSI error associated with is called the wind- shear. According to the VSI equation (8.5) the wind- shear is represented by . Its height relationship is:
………..………….. (9.2)
The expression states that when a pilot flies over a high mountain, the VSI over- reads. In meteorology, the expression states that when an air- mass crosses a mountain barrier it rises and becomes unstable. Normally, wind- shear results in obstacle- clearance problems. Many aircrafts crash on mountains because of the wind- shear in the VSI. A special type of the VSI, known as the Energy VSI [8] is now available. It alerts pilots about any wind- shear error in the VSI.
Equation (9.1) implies that when a pilot over- flies a region
of low pressure the VSI displays a climb and vice versa. Pilots are advised; therefore, to carry SIG. weather charts on board so that they can identify the positions of high and low pressure en- route.
9.2. Wind- Shear.
Significant en- route features are known to be the surface pressure , and the terrain . The VSI error associated with is the barometric error (section 9.1). The VSI error associated with is called the wind- shear. According to the VSI equation (8.5) the wind- shear is represented by . Its height relationship is:
………..………….. (9.2)
The expression states that when a pilot flies over a high mountain, the VSI over- reads. In meteorology, the expression states that when an air- mass crosses a mountain barrier it rises and becomes unstable. Normally, wind- shear results in obstacle- clearance problems. Many aircrafts crash on mountains because of the wind- shear in the VSI. A special type of the VSI, known as the Energy VSI [8] is now available. It alerts pilots about any wind- shear error in the VSI.