- Review: Exp(tau*AirMass) atmospheric correction and associated uncertainties
- Air Mass estimations -- proposed model
- Tatm estimations used by Tippings -- necessary accuracy and proposed model
- For 1% accuracy in calibration, requires knowing tau to 0.01 and air mass to 0.1.
- Tau*AirMass <~ 1 will be our working, ballpark, guideline for 'useful' observing condition.
- The full equation for estimating air mass is given in: Rohlfs ("Tools of Radio Astronomy", 1986, 7.110). One needs the index of refraction and densities as a function of height above the observatory.
- The inaccuracy of A = 1/sin(el) exceeds our 0.1 error budget when El < 12 deg.
- The inaccuracy of the Bemporad/Schoenberg power-law model exceeds our 0.1 error budget when El < 5 deg.
- Using the archived vertical weather data we've been archiving as representative of the weather over Green Bank, one can derive the index of refraction and densities needed for the equation in Rohlfs.
- Used over 1400 archived vertical weather profiles scattered over 1 year, to derive a better model for air mass:
if {elev < 39} {
A = -0.0234374 + 1.01396 / [ sin(elev + 5.17743 / (elev + 3.35434)) ]
} else {
A = 1./sin( elev)
}
- Under average weather conditions, this model provides an estimated air mass that doesn't exceed our error budget to an elevation of 0.2 deg under 'average' weather conditions.
- At 5 deg elevation, the daily deviations of the weather from the 'average' will introduce an air mass error of 0.1. At 0 deg elevation, the daily deviations of the weather introduce an air mass error of 8. This implies that, if an accuracy of better than 1% is required, or if observing will be below 5 deg., then one needs to use the details of vertical weather over Green Bank to estimate air mass.
- One of the attached figures show the 1400 air masses from the vertical profiles overlayed by the various models discussed. A second figure shows a time series of air mass derived from vertical profiles for an elevation of 5 deg. The latter figures provides an estimate of how much differences in the daily weather affect air mass estimates.
Conclusion: The above, new model has the required accuracy for all intended observing frequencies
- Used in two of the simpler tipping models.
- The accuracy of the derived opacity is related to the inaccuracy of the value of Tatm by:
delta_tau / Tau ~ delta_Tatm / Tatm
- Note that the higher the Tau, the more accurate one needs to know Tatm. Example: If Tau = 0.3, one needs to know Tatm to 9 K to achieve a 0.01 accuracy in tau, which is needed to acheive a 1% calibration accuracy.
- The definition of Tatm is:
Tatm = Integral ( kappa(h) * T(h) * del_h) / Integral( kappa(h) * del_h)
- kappa is frequency dependent, a function of height above the observatory, and equals kappa_o2Line + kappa_o2Cont + kappa_H2oLine + kappa_Hydrosols + .... T(h) is the physical temperature of the atmosphere as a function of height.
- Used over 1400 archived vertical weather profiles scattered over 1 year as representative of the weather over Green Bank. Derived Kappa for each layer for each vertical profile for frequencies between 6 and 115 GHz. Then could derive Tatm for each date/time, and frequency.
- The 3rd attached plot show the derived Tatm at 6 and 95 GHz plotted against ground-level air temperature. The 9 K full scatter in the plot suggests that one can predict Tatm to an rms of ~ 3 K from a combination of the observing frequency and ground air temperature.
- A temperature-frequency-Tatm look-up table should provide Tatm with a 3 K accuracy, more than enough for all but those observing under the highest opacities. The 4th figure is a contour plot of a preliminary version of such a table.
- The group decided that the number of data points at low temperatures is too few and that I should increase the number of vertical profiles that will be used in creating the look-up table.
- The group is interested in seeing a scatter plot of the residuals from applying a look-up table to the individual Tatm from vertical profiles.
- For observing under high opacities, or for those wanted to do better than 1% calibration accuracy, one will need to derive Tatm from the detailed vertical profiles for the instance of the observation.
Conclusion: We will go with a temperature-frequency-Tatm look-up table that is derived from a greater number of vertical profiles than that used in the data presented at the meeting.
- Regenerated the plot for air mass at a 5 deg elevation for a full year, instead of the 4 months presented at the meeting. The conclusions remain the same. The rms is 0.016 and peak-to-peak is typically 0.05. The mean is 0.01 from that predicted by the model, well below our error budget. Only 5 times, out of 1741 estimates, did the air mass differ from the model by more than our budget of 0.1.
-- RonMaddalena - 14 Mar 2006
AirMass.gif 
