## Hydrostatic Integral Constraint

A conceptual innovation we have come to realize is that measurements of absorption lineshape can provide the boundary condition for the hydrostatic integral at very high altitudes. Kursinski et al. (2002) showed that temperature accuracies of 1 K can be achieved up to 40 km altitude using just the ATOMMS observations themselves and no external information for the hydrostatic constraint. This is achieved by combining the refractivity profile, hydrostatic equilibrium, and the pressure and temperature constraints imbedded in the profile of the 183 GHz line shape. We have come to realize that sub-Kelvin performance can be extended to much higher altitudes with accurate measurements of the Doppler broadened line shape at higher altitudes that yield a direct estimate of temperature. This temperature constraint in combination with density (derived from bending angle) yields pressure and therefore constrains the hydrostatic integral. The approximate altitudes at which the Doppler linewidth is 10 times that of the collisional linewidth are 80 km, 77 km, and 70 km for 118 GHz (O2), 183 GHz (H2O), and 557 GHz (H2O), respectively.

The strength of the 183 GHz line combined with ppm middle atmospheric water vapor mixing ratios is not sufficient for the 183 GHz observations to accurately determine the 183 GHz linewidth at 77 km altitude. The 50-60 GHz and 118 GHz O2 lines can provide this hydrostatic constraint. Wu et al. (2003) have demonstrated that temperatures can be derived from emission in the 50-60 GHz O2 band with accuracies of approximately 8 K and 15 K at 80 km and 90 km altitude, respectively. From a climate perspective, the complication is the O2 lines result from magnetic dipoles and are therefore sensitive to the Earth's magnetic field and Zeeman splitting complicating and likely limiting the ultimate accuracy of the retrieval.

The best approach may be to probe the very strong 557 GHz water line and profile water vapor to much higher altitudes than is possible with the 183 GHz line. Furthermore, observations between 500 GHz and 600 GHz can accurately profile water isotopes in the middle atmosphere as well as provide information to cross-compare with the 183 GHz water results. Sensitivity to the ionosphere at 557 GHz is an order of magnitude smaller than that at 183 GHz. Occultation SNRs can be higher at 557 GHz because of higher antenna gain. The wind induced Doppler shift of the 557 GHz line is also 3 times larger (although the pressure induced line shift is 4 times larger, the uncertainties of which may limit the accuracy of wind estimates). The Doppler linewidth is 3 times larger so the Doppler linewidth dominates the collisional width at lower altitudes. Figure 1 shows the approximate accuracy of temperature versus altitude derived from including occultation measurements of the

Fig. 1 The temperature error versus altitude in the upper middle atmosphere and lower thermosphere, representative of a typical ATOMMS profile. Temperature has been derived combining density from occultation-derived profiles of refractivity and the Doppler width of the 557 GHz water line in combination with the hydrostatic integral

557 GHz linewidth. We note that since the accuracy will depend on the accuracy of the spectroscopy, ATOMMS should sample the line with at least one more tone than that the number required for the temperature and wind retrievals in order to provide information needed to assess and refine the spectroscopy.

3 Assessing the Impact of Turbulence on ATOMMS Observations and Retrievals

The potential importance of turbulence to ATOMMS was identified in a talk at OPAC-1 (Feng et al. 2002). Propagation of electromagnetic signals through a turbulent refractive medium creates interference through diffraction that produces phase and amplitude scintillations. From the standpoint of measuring the absorption signatures of atmospheric water vapor and ozone, turbulent amplitude scintillations are a noise source. For those interested in turbulence, ATOMMS is a planetary-scale microwave scintillometer that will provide an unprecedented global turbulence monitor.

We summarize our findings concerning the impact of amplitude scintillations due to turbulence on the ATOMMS measurements. The differential opacity measurement approach used by ATOMMS and described by Kursinski et al. (2002) is key to controlling the impact of turbulence.

3.1 Simulation Results for Variations in the Refractive Index

To evaluate the effects of 3-D turbulent variations in the refractive index, we have used a method suggested by R. Frehlich at NCAR and set up a numerical occultation signal propagation simulator using a simple Cartesian geometry with a plane wave source on one side of a box filled with turbulence. Microwave signals are propagated through the box, and then through an additional 3000 km of vacuum to approximate the signal propagation measured by a satellite in an Earth occultation geometry. We have specified the turbulent spectrum as 3-D, homogeneous von Karman turbulence with an inner scale of 10 cm and an outer scale of 500 m, and a magnitude of the turbulence defined by the refractive index structure parameter, C^. Besides testing the effectiveness of amplitude ratioing on the directly measured signal amplitudes, we have also considered how 1-D back-propagation (the simplest form of diffraction correction) together with vertical smoothing can reduce amplitude scintillations.

Figure 2 shows two examples of scintillation simulations results. The left hand figure is representative of wet turbulence contributions in the mid-troposphere near the 22 GHz water line. The turbulent magnitude was specified by setting the real refractive index structure parameter, C^, equal to 10-16 (Jursa 1985). The right hand panel is representative of dry turbulence contributions in the upper troposphere near the 183 GHz water line, where a typical value for the dry-real refractive index structure parameter of C^ = 10-17 has been used (Jursa 1985). The amplitude variations are caused by diffraction, since no absorption is included in the simulations, i.e., the imaginary part of the refractive index is zero. The standard deviations of the single frequency raw amplitude variations (before applying a 1-D back propagation and smoothing) are roughly 7-8% for both the 22 GHz and 183 GHz simulations. The combination of 1-D back propagation and smoothing reduces the raw single

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Fig. 2 Simulation of the impact of turbulent variations in the refractive index on occultation amplitudes. (a) Tropospheric conditions (C^ = 10-16) at frequencies near the 22 GHz water line after applying 1-D back propagation and 200 m smoothing. (b) Upper tropospheric jet stream conditions C = 10-17) at frequencies near the 183 GHz water line after applying 1-D back propagation and 50 m smoothing. Relative means that an amplitude of unity would be measured in the absence of turbulence. In both cases, the amplitude standard deviation for individual frequencies is ~7-8%, and the standard deviation of the amplitude ratio is ~1-2%

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Fig. 2 Simulation of the impact of turbulent variations in the refractive index on occultation amplitudes. (a) Tropospheric conditions (C^ = 10-16) at frequencies near the 22 GHz water line after applying 1-D back propagation and 200 m smoothing. (b) Upper tropospheric jet stream conditions C = 10-17) at frequencies near the 183 GHz water line after applying 1-D back propagation and 50 m smoothing. Relative means that an amplitude of unity would be measured in the absence of turbulence. In both cases, the amplitude standard deviation for individual frequencies is ~7-8%, and the standard deviation of the amplitude ratio is ~1-2%

channel standard deviations by roughly a factor of 2. Note that for both the 22 GHz and 183 GHz regions, the smoothing is over a scale similar to the diameter of the first Fresnel zone. Therefore, there is little loss in resolution or information content associated with this smoothing.

The results indicate how the ratioing approach will reduce the impact of turbulence at frequencies near the 22 GHz and 183 GHz water absorption lines. Although the raw amplitude scintillations are comparable in the two panels (since shorter wavelengths are more affected by turbulence), the closer fractional separation of the calibrations tones near 183 GHz yields better cancellation of the turbulence effects after ratioing.

To understand the optimal separation between signal frequencies, we did many simulations with different frequency separations and turbulence realizations to reveal the statistical behavior shown in Fig. 3. Figure 3 shows that the amplitude errors can be reduced significantly by a combination of amplitude ratioing, vertical smoothing, and 1-D back propagation. For the simulated conditions, the single frequency 22 GHz amplitude variations without vertical smoothing are about 13% and about 8% after applying 200 m vertical smoothing. Thus amplitude ratioing can effectively reduce the retrieval errors caused by turbulence. Based on these results, two trade-offs in the ATOMMS system are apparent. First, the amplitude diffraction error decreases as the frequency separation between signal pairs decreases. However, as the frequency separation decreases, the differential absorption signature, due to the difference between the water vapor absorption at the two frequencies, also decreases. Secondly, the standard trade-off exists between the retrieved vertical resolution and the level of vertical smoothing required to satisfactorily reduce measurement fluctuations.

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Fig. 3 Standard deviation of the error in measuring amplitude ratios due to turbulence for the atmospheric conditions specified in Fig. 2. The base frequency is 22 GHz and frequency ratio refers to base frequency divided by the second frequency. Three pairs of curves are shown, upper curves drawn with dashed lines indicating no 1-D back propagation applied and lower curves drawn with solid lines indicating 1-D back propagation applied. The three pairs of curves correspond to no vertical smoothing applied to the amplitude ratio, 200 m vertical smoothing applied, and 500 m vertical smoothing applied

Fig. 3 Standard deviation of the error in measuring amplitude ratios due to turbulence for the atmospheric conditions specified in Fig. 2. The base frequency is 22 GHz and frequency ratio refers to base frequency divided by the second frequency. Three pairs of curves are shown, upper curves drawn with dashed lines indicating no 1-D back propagation applied and lower curves drawn with solid lines indicating 1-D back propagation applied. The three pairs of curves correspond to no vertical smoothing applied to the amplitude ratio, 200 m vertical smoothing applied, and 500 m vertical smoothing applied

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