# Climate-Quality Calibration for Low Earth-Orbit Microwave Radiometry +
## 3 Co-Located Radio-Occultation Reference
Consequently, these comparisons would be useful for channels in an O\({}_{2}\)-band but less so for water or window channels. Oxygen-band weighting functions that peak in the troposphere for a near-nadir view angle will move into the stratosphere at limb-viewing angles. Hence a full channel set can be compared at the limb with RO measurements, whereas comparisons of tropospheric channels near nadir would require ancillary knowledge of humidity. Surface emissivity also ceases to be a significant factor at the limb. Due to its dependence on both microwave transmittance model and refractivity retrieval, it is unlikely that the RO reference would improve on the absolute accuracy of on-board calibration with the target and cold space (at least at launch), but if the computer algorithms are applied in a uniform way to a time series of measurements [23], then RO provides a stable reference to determine whether the on-board target's calibration is also stable. Although no physical mechanism causing changes in target components has been identified, their long-term stability in the space environment cannot be verified  
Figure 2: Basic geometry of co-located GNSS-RO microwave radiometer calibration [11]. without reference to an independent standard. Ideally, GNSS-RO comparisons would verify that the on-board calibration is stable over many years; and indeed, over a 14-year time span, stratospheric AMSU channels on the Aqua satellite closely tracked RO temperature retrievals [24]. (The stratospheric channels of AMSU have a phase-locked local oscillator.) But if such comparisons diverge over an instrument's lifetime, the trend derived from the radiometer could be adjusted accordingly. The \"long-term stability\" in Table 1 is derived from the variance of uncertainty in determination of the trend \(m\) in a time series over an interval \(\Delta t\)[25]. \[\langle(\delta m)^{2}\rangle=12(\Delta t)^{-3}\sum_{i}{\sigma_{i}}^{2}\tau_{i}, \tag{2}\]  
in which the summation is over independent sources of error with variances \({\sigma_{i}}^{2}\) and autocorrelation time constants \(\tau_{i}\). Here we consider only the contribution of the variance associated with the radiometer-to-RO comparison. In other words, any bias due to the transmittance and refraction models does not affect the precision of the comparison. Also, we do not distinguish here between a trend due to climate change and a trend due to shorter-term atmospheric variability over the interval \(\Delta t\). Replacing \(\delta m\) with \(\delta T_{A}/\Delta t\), where \(\delta T_{A}\) is the uncertainty in the calibration adjustment from the RO comparisons, gives  
\[\langle(\delta T_{A})^{2}\rangle\Delta t=12\sigma^{2}\tau. \tag{3}\]  
Simulations of radiometer calibration in the 50-60 GHz band with RO [11] show rms uncertainty of 0.1 to 0.25 K, depending on how well antenna pointing is known. Considering random errors to be uncorrelated between occultations, \(\tau\) will be the average time between occultations. We assume 4000 occultations per year to be selected from \(>\)60,000 potential occultations for one receiving satellite (this degree of selectivity might not require any azimuthal steering of the radiometer beam). Then setting \(\sigma=0.2\) K yields \((\delta T_{A})_{rms}=0.01\) K in one year, or 0.003 K in a decade. For a constant rate of occultations, \((\delta T_{A})_{rms}\) decreases with the square root of the time interval, in analogy with the behavior of integrated radiometer noise. Because of the traceability of their measurements to frequency standards, changes of GNSS-RO instruments do not introduce offsets in a long-term record [20]. Thus, for the purpose of creating a multi-decadal climate record during which replacement of reference-radiometer satellites is necessary, inter-radiometer calibration offsets would be removed by double-differencing with the RO reference. Overlap of reference microwave radiometers' lifetimes would be less important and probably not even necessary.