Reflectivity

The corrected reflectivity Z is output using a log scale based on the following equation:

d B Z = 10 \log [\frac{T_{0} - N}{N}] + {d B Z}_{0} + 20 \log r + a r + C C O R

This equation is a dB version of the familiar radar equation for distributed targets. The relationship between the measured autocorrelation function, the received signal and the noise can be expressed as:

T_{0} = g^{t} g^{r} S + N

where g^t and g^r represent the transmitter and receiver gains, S is the average back scattered power from the targets and N is the measured average noise power. Neglecting attenuation and the contribution of ground clutter (for the moment), the radar equation can be written as.

Z = C S r^{2} = [\frac{C r_{0}^{2} N}{g^{r} g^{t}}] [\frac{r^{2}}{r_{0}^{2}}] [\frac{T_{0} - N}{N}]

where C is the radar constant and ro is a reference range which we later set to 1 km. This is identical to the first three terms of the dB version of the equation with the definition that:

Z_{0} = \frac{C r_{0}^{2} N}{g^{r} g^{t}} = C r_{0}^{2} I_{0} w h e r e I_{0} = \frac{N}{g^{r} g^{t}}

where:

Z₀: Calibration reflectivity factor. It is the equivalent radar reflectivity factor at the reference range when the return signal power is equal to the noise power (SNR=0 dB). It is sometimes called the minimum detectable dBZ at 1 km, though it is more correct to call it the 0dB SNR detection level.
I_o: Measured noise power at IF with appropriate calibration for the system gain.

The measurement of I_o is based on the measurement of the system noise at the time of calibration. However, if the receiver gain changes after calibration, the use of periodic noise sampling properly corrects for this. For example, if the receiver gain were to change by a factor k, then we would measure a noise value of kN and an autocorrelation value of kT_o, that is:

Z = C S r^{2} = [\frac{C r_{0}^{2} N}{g^{r} g^{t}}] [\frac{r^{2}}{r_{0}^{2}}] [\frac{{k T}_{0} - k N}{k N}]

Thus the k's cancel to give us the same result for Z. This makes the approach robust to system gain fluctuations. As long as the system sensitivity (noise figure) does not change, then the system does not require re-calibration.

Calibrating RVP10 involves defining the radar constant C and measuring the value of I_o. See Reflectivity Calibration.

The following table shows the individual terms in the dB form of the equation.

Terms in the dB equation format
Term	Term name	Description
1^st Term	$10 \log [\frac{T_{0} - N}{N}] S i g n a l t o N o i s e R a t i o$	The effect of this term is to subtract the measured noise and then divide by that noise. The result is a Signal-to-Noise ratio.
2^nd Term	`dBZ_o`: Calibration Reflectivity (see discussion above)	`dBZ_o` is the minimum detectable dBZ at a reference range `r_o=1 km`
3^rd Term	`20 log r` : Range Normalization	This term is the range normalization expressed in dB form. ${[\frac{r}{r_{0}}]}^{2}$
4^th Term	`ar`: Gaseous Attenuation Correction	This term accounts for gaseous attenuation. The constant `a` is set in the RVP10 EEPROM since it is a function of wavelength. For a C-band system the default value is 0.016 dB per km (for two-way path attenuation).
5^th Term	CCOR: Clutter Correction	This term corrects for the measured ground clutter. See Clutter correction (CCOR threshold).