consider radar noise level in range correction

[adokter]

Radar noise level is available in ODIM polar volumes through the NEZH and derived quantities. They express the minimum dBZ value detectable at 1 km range.

For NEXRAD files, information on where/how noise level information is stored needs to be investigated. In the following document:
https://www.roc.noaa.gov/public-documents/wsr88d/NEXRAD-Technical-Information.pdf we find:

• Minimum required signal detection, short pulse: -9.5 dBZe at 50 km
• Minimum required signal detection, long pulse: -19.5 dBZe at 50 km

Especially for weak migration events at large ranges, eta_expected in the range correction method may be below the noise level. In those instances values should report NaN instead of zero. In case all sweeps contribute NaN the eta_sum_expected value will be NaN as well, and the whole pixel of the range corrected image should be NaN.

[adokter]

If at range $R_0$ km, the minimum detectable reflectivity (the noise threshold) is $Z_0$ in dBZ, we may write for a general range R:

$Z(R) = Z_0 \left(\frac{R}{R_0}\right)^4$

In terms of dBZ:
$10\log_{10}(Z(R))$ = $10 \log_{10}(Z_0) + 10\log_{10}\left(\frac{R}{R_0}\right)^4$

$\Rightarrow \text{dBZ}(R) = \text{dBZ}(R_0) + 40 \log_{10}\left( \frac{R}{R_0} \right)$

For NEXRAD at 100 km this gives us
dBZ(100) = $-9.5 + 40 \log_{10} (\frac{100}{50})^4)$ = -9.5+48 =39.5 dBZ for short pulse
dBZ(100) = $-19.5 + 40 \log_{10} (\frac{100}{50})^4)$ = -19.5+48 = 29.5 dBZ for long pulse