Determining dBZo

The calibration reflectivity is determined from the radar equation as follows:

where Io is in mW (corrected for receive losses), the reference range ro is 1 km, and the radar constant C is:

where:

$λ$

Radar wavelength in cm.

$P t$

Transmitted peak power in kW.

$L t$

Transmit loss (for example, 3 dB corresponds to $L t = 2$ )

$τ$

Pulse width in microseconds.

$θ$

Horizontal half-power full beamwidth.

$φ$

Vertical half-power full beamwidth.

$G$

Antenna gain (dimensionless) on beam axis.

The radar constant is determined from the characteristics of your radar (check with the manufacturer if you are unsure of the values). Note that transmit losses are accounted for in the radar constant, while receiver loss is usually included in the calculation of I0.

If the value of I0 calculated above was not based on loss-corrected dBm values, correct I0 as follows:

Example Calculation of dBZo

Use this sample calculation to check your arithmetic. The radar parameters:

Radar Parameters

Parameter	Description	Value
$λ$	Radar wavelength in cm.	5 cm
$P t$	Transmitted power in kW.	500 kW
$L t$	Transmit loss.	2 (3 dB)
$τ$	Pulse width in microseconds.	1 microsecond
$θ$	Horizontal half-power beamwidth in degrees.	1°
$φ$	Vertical half-power beamwidth in degrees.	1°
$G$	Antenna gain (dimensionless) on beam axis.	19,953 (43.0 dB)

The radar constant for this example is,

$C = 2.69 × 10 16 λ 2 P t τ θ ϕ G 2 L t = ( 2.69 × 10 16 ) ( 5 ) 2 ( 500 ) ( 1 ) ( 1 ) ( 19 , 953 ) 2 ( 2.0 ) = 6.76 × 10 6 [ m m 6 m − 3 k m − 2 m W − 1 ]$

Assume that I0 with loss correction is calculated to be -105 dBm (3.16 × 10^-11 mW), then dBZ_o is:

$d B Z 0 = 10 log ⁡ [ C r 0 2 I 0 ] = 10 log ⁡ [ ( 6.76 × 10 6 ) ( 1 ) 2 ( 3.16 × 10 11 ) ] = − 36.7 d B ( m m 6 m − 3 )$

You can download this value to the signal processor using the SOPRM command.