The decibel system is used to compare two power values using the logarithm of their ratio. Basically, it is a matter of mathematical convenience to use the decibel system for power comparison purposes. A decibel, abbreviate “dB” is one tenth of a bel, the fundamental unit. We use Decibels (dB) to compare two power levels in relative sense. The strength of the echo is given by the power returned (in Watts).

The difference in two power values, expressed in decibels, is determined by the relationship:

dB = 10 log₁₀ (P2/P1)

The decibel system is useful for comparing power values which differ greatly. Manual attenuation of weather radars is applied (or removed) in 3 dB increments, each corresponding to halving (or doubling) the equivalent power return. The mathematical proof of this statement is provided below for the case of halving the equivalent power return (adding 3 dB of attenuation).

The dBm (decibel above a milliwatt) system compares a given power value to a milliwatt (one thousandth of a watt). The given power value can be expressed in dBm according to equation #2:

This equation is used in setting the minimum discernible signal (MDS) of weather radars, as it allows measurement of power returned (backscattered) from a meteorological target by comparing it to a known reference value. For purposes of comparison among various radars, it is desirable that MDS is a fixed and known quantity. The dB system of comparison is relative (both power values can change); the dBm system is absolute (only one power value can change).

Conventional radars use the measured average returned power from a target to estimate the equivalent reflectivity, Ze (also referred to as the effective reflectivity factor). Because values of Ze typically span many orders of magnitude, equivalent reflectivity is usually expressed in decibels (dBz) as a matter of mathematical convenience. Equivalent reflectivity will be covered in the, Radar Reflectivity module.

dBm = Absolute Power

dB = Relative Power