## 4 Preliminary Performance Considerations for IPDALLS  
### First Order Estimation of the Link Budget and Measurement Accuracy  
Here we present a preliminary feasibility study of the IPDALLS concept with respect to our primary mission objective, _i.e._, the profiling of water vapour in the UTLS and above, using a model developed for rough systems trade-offs. In due course, detailed instrument performance end-to-end simulations and corresponding sensitivity studies, noise and error evaluations would be required, as outlined, e.g., in [33, 48, 49, 50, 51, 52] for similarly operating payloads. For a system relying on wavelength pairs with extremely narrow spectral separation, pressure and Doppler broadening of the absorption lines, determining the Voigt line profile, as well as water vapour self-broadening, will become very relevant. Consequently, absorption cross sections will need to be calculated as a function of pressure and temperature, or altitude (as in Figure 5), and corresponding atmospheric profiles assumed, retrieved or modelled as a preliminary step in a retrieval algorithm. Furthermore, the Doppler shifts induced by the diverging spacecraft, different for the forward and the backward paths, will need to be accounted for in the estimation of the absorption cross sections. For these preliminary calculations, we assumed online wavelengths centred on the absorption peaks of motionless molecules at the tangent point and on the forward path, which have thus been previously generated at a slightly higher frequency by the receding transmitter. The Doppler shift induced by the receding retroreflector, and experienced by the same molecules on the backward path, corresponds to an average beat frequency of \(-14.9\) GHz or a red-shift of \(43.6\) pm. In general, this makes the atmosphere more transparent on the backward path, even if the shifted \(\lambda_{\text{on}2}\) now resides in the highly sensitive region of a wing's inflection point, which may introduce a potential source of uncertainty. The equations and  
Figure 5: Water vapour molecular absorption cross sections \(\sigma\) as a function of vacuum wavelength \(\lambda\) using the HITRAN 2008 database [53] for sea level (solid line) and an altitude of \(20\) km (dashed line) according to US Standard Atmosphere conditions. Wavelengths used in this study are indicated by vertical thick lines; the additional thin lines represent the Doppler shifted wavelengths on the backward path. Water vapour absorption of the first and second harmonics generated by the transmitter is negligible. methodology used to estimate the performance of the IPDALLS concept are described in Appendix, and an abbreviated set of baseline instrument parameters is given in Table 1.  
Figure 6(a,b) shows the various transmission profiles in limb sounding geometry for a standard mid-latitude daytime atmospheric profile due to molecular absorption and scattering, respectively. Molecular absorption (in particular due to water vapour) was calculated using the MIPAS Reference Forward Model (RFM, see Appendix) in a standard mid-latitude daytime atmospheric profile, while scattering was calculated with the 1976 US Standard Atmosphere. The differing absorption of the various wavelengths at a given tangent point height is evident, as is the necessity to use several wavelength pairs (with the same reference offline wavelength) to probe different altitudes, since wavelengths with strong absorption coefficients, and hence good sensitivity at heights where water vapour concentrations are low, are completely absorbed in the lower atmospheric layers. Scattering is essentially the same at the on- and offline wavelengths, which is one advantage of this differential absorption technique. A retrieval of atmospheric aerosol, one of the secondary mission objectives, would exploit scattering at