# Climate-Quality Calibration for Low Earth-Orbit Microwave Radiometry +
## 3 Co-Located Radio-Occultation Reference  
The radiometer would be accompanied by a GNSS-RO receiver and antenna, to enable referencing of limb measurements to microwave brightness temperatures inferred from simultaneous radio-occultation measurements of refractivity at the same elevation and azimuth angles [11]. This achieves similar horizontal averaging along the path through the atmosphere, as illustrated by Figure 2. (Elevation is equivalent to scan angle, and azimuthal alignment of the radiometer beam with the GNSS signal could be achieved either by adjustment of spacecraft yaw, or with a gimbal mount for the radiometer, see for example [17]). Occultations that occur close to the plane of the orbit are the most desirable, because a satellite in a low earth orbit moves faster than a GNSS satellite. These comparisons will track long-term stability of the target's emissivity and temperature sensors, and also provide another way to monitor possible scene-dependent error over time, because limb brightness temperature varies with angle over a wide range. \begin{table}
\begin{tabular}{l c l} \hline \hline
**Parameter** & **Value** & **Comments** \\ \hline (noise-equivalent \(\Delta T\)) \(\cdot\tau_{r}^{1/2}\) & \(\leq\)0.05 K s\({}^{1/2}\) & for dual-polarization average \\ absolute accuracy of calibration at launch & \(\pm\)0.1 K & for antenna temperature \\ (long-term calibration stability \(\delta T_{A}\)) \(\cdot(\Delta t)^{1/2}\) & \(\pm\)0.01 K yr\({}^{1/2}\) & Equation (3), with GNSS-RO reference \\ lifetime frequency stability & \(\pm\)1 MHz & with phase-locked LO \\ antenna 3 dB beamwidth & 5\({}^{\circ}\) & from [11] \\ antenna stray factor (1 – beam-efficiency) & \(\leq\)1\% & \textgreater{}15\({}^{\circ}\) from beam center \\ antenna off-earth stray factor & \(\leq\)0.03\% & for nadir view \\ non-linearity max. deviation (before correction) & \(\leq\)0.1 K & for 3 \(\leq T_{A}\leq\) 300 K \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of a calibration-reference radiometer for 50–60 GHz. Figure 1: Radiometer/antenna/target scanning configuration. The underlying observable in RO is the additional Doppler shift of the GNSS signal relative to that which would be observed in the absence of an atmosphere [18]. That Doppler shift is the time-derivative of phase delay due to refractive index along the atmospheric path, and it can be accurately measured [19; 20]. Thus, the RO atmospheric refractivity profile is ultimately traceable to a frequency standard. Radiometer comparisons with occulted GNSS signals would depend on the microwave transmittance model used to calculate brightness temperature and on the atmospheric refractivity retrieval. Uncertainties in microwave spectroscopic parameters have been reviewed, and their influence on calculated brightness temperature quantified, in [21]. The refractive index \(n\) of the clear atmosphere can be modeled as  
\[n-1=k_{1}\rho_{f}+(k_{2}+k_{3}/T)\rho_{w}+k_{4}\rho_{c}, \tag{1}\]  
where \(\rho_{f},\rho_{w}\) and \(\rho_{c}\) are the number densities of fixed-abundance gases, water vapor, and carbon dioxide respectively, and \(T\) is Kelvin temperature. A recent review of published measurements of the coefficients \(k_{1},k_{2},k_{3}\) and \(k_{4}\) is given in [22]. There is some dispersion within the oxygen band, but the microwave value of \((n-1)\) would be within a few percent of its value for the lower frequencies of the GNSS signals. Hence a microwave ray through the limb atmosphere would closely approximate the GNSS signal path. The main difference is that the radiometer measures brightness temperature integrated over the antenna's directivity pattern. In the stratosphere, where the atmosphere is very dry, the hydrostatic equation can be used to unambiguously relate refractivity to the profiles of temperature and pressure vs. height [18], which determine the limb brightness temperature by means of the transmittance model. The lower troposphere generally contains more moisture, which varies independently of temperature.