Comparison with Turbulence Estimates of Gorbunov and Kirchengast 2007

Gorbunov and Kirchengast (2007) (GK07) performed 2-D occultation simulations to assess the effects of turbulence near 22 GHz. Our Cartesian turbulence simulations are less realistic in that the turbulence effects are not imbedded in a full occultation retrieval simulation. This is adequate if the process is linear. On the other hand, our simulations are more realistic than GK07 in that they include the turbulence effects of all 3 dimensions. This is important because a limitation of occultation diffraction correction schemes is that they are 2-D, designed for cylindrical atmospheres with no variation in the dimension orthogonal to the occultation plane. Clearly there are turbulent variations in that dimension that must be considered. Our approach has the advantage of being much faster computationally, allowing us to simulate a large number of cases to yield the smooth statistical behavior evident in Fig. 3 in order to parameterize the turbulent errors for inclusion in our error covari-ance studies.

We can compare GK07 and our estimates of turbulence errors. In GK07 Fig. 6, the differential transmission error using frequencies of 9.7 GHz and 17.25 GHz in the 5-8 km altitude interval at low latitudes is ~0.05 dB or 1% for anisotropy coefficients of > 4. Our turbulence parameterization estimates indicate that for typical mid-latitude summer conditions, the fractional amplitude error at 22 GHz measured at 6.5 km altitude is approximately 6% (see Fig. 4b). From Fig. 2 (where the fractional amplitude error at 22 GHz is 13%), the fractional error in the amplitude ratio for a frequency ratio of 1.8 is 5%. So, based on our findings regarding how turbulence errors scale, the fractional error in the ratio of the 9.7 GHz and 17.25 GHz amplitudes under low latitude conditions near 6.5 km altitude will be 2% = 6% (5/13)(17.25/22)0'35. This is equivalent to the "differential transmission error" as defined by GK07. So our estimate of the differential transmission error for low latitude, mid-tropospheric conditions is approximately twice that of GK07. Interestingly our approach, which is simpler, actually predicts larger errors.

The similarity of these two error estimates is promising as it suggests that despite the very different approaches used to simulate the effects of turbulence, the levels of turbulent noise behavior being approximated are somewhat realistic. A better understanding and reconciliation of the differences between the two error estimate approaches clearly warrants more attention. Our understanding will improve and uncertainties will decrease dramatically with the aircraft to aircraft occultations which will directly measure the real impact of turbulence on ATOMMS occultation measurements and retrievals.

4 Simulated Retrieval Errors (Clear Sky)

Figure 5 shows the computed errors in the retrieved temperature and water vapor pressure for six Lowtran atmospheres under clear-sky conditions. The simulations include the following sources of uncertainty: uncertainty in the near vertical profile of refractivity is set based on refractivity errors estimated for GPS/MET by Kursinski et al. (1995, 1997), instrumental measurement errors in difference optical depths for frequency pairs are based on Kursinski et al. (2002), and uncertainty in determining the difference optical depths due to amplitude scintillations resulting from turbulent variations in the real part of the atmospheric index of refraction. The latter source of uncertainty accounts for both the dry (non-water vapor) as well as the wet (water vapor) contribution to turbulent variations in the refractivity. Extending upward in altitude, the standard deviation of the temperature error remains below

Fig. 5 Computed standard deviation of the error in the retrievals of temperature (left panel), expressed in Kelvin and water vapor partial pressure (rightpanel), expressed in percent, using simulated ATOMMS observations for the six labeled Lowtran atmospheres (Trop = tropical; MLS = mid-latitude summer; MLW = mid-latitude winter; ArS = Arctic summer; ArW = Arctic winter; USS = U.S. Standard)

Fig. 5 Computed standard deviation of the error in the retrievals of temperature (left panel), expressed in Kelvin and water vapor partial pressure (rightpanel), expressed in percent, using simulated ATOMMS observations for the six labeled Lowtran atmospheres (Trop = tropical; MLS = mid-latitude summer; MLW = mid-latitude winter; ArS = Arctic summer; ArW = Arctic winter; USS = U.S. Standard)

1 K and the standard deviation of the water vapor error remains below 2% up to at least 60 km (not shown).

It is only at the lowest altitudes, below about 5 km, where we begin to see the retrieval errors increase significantly. There are several related reasons for this that are associated with the increase in air pressure and water vapor content as the ground surface is approached. As the water vapor content increases, the absorption optical depth becomes large which necessitates using occultation tone frequencies farther below the 22 GHz line center. Because of collisional line broadening, the difference in the optical depths at our closely spaced frequency pairs becomes smaller (the absorption line shape broadens), which reduces the information content of the measurements. At the same time, the orthogonality between the refractivity information and the absorption information for separating water vapor from temperature decreases as the amount of water vapor increases (Kursinski et al. 2002). On top of these, turbulent fluctuations in refractivity generally increase as the surface is approached which increase the error in the measured amplitudes and derived optical depths. Thus, the ability to produce accurate retrievals at low altitudes is limited by effects related to the mean amount of water vapor. For example, for the dry arctic winter case, temperature errors of less than 1 K are estimated to extend essentially right down to the surface, whereas for the tropical atmosphere, temperature errors become larger than 1 K below about 5 km in altitude. Errors in water vapor retrievals are approximately 2-3% above 3 km altitude and increase to 6-30% at the surface for arctic winter and tropical conditions, respectively.

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