Comparison with measured opacity

Since water vapor is one of the primary contributors to the opacity at radio wavelengths, the opacity is expected to correlate very well with the amount of precipitable water. However, there is some disagreement about whether surface measurements can yield any reasonable estimate of the precipitable water (e.g. Reber & Swope 1972). In order to test whether the precipitable water derived via the technique outlined above has a good correlation with true opacity, I took the results of reliable TIP data taken at K-band (frequencies between about 21 and 25 GHz) over the last 3 years (177 TIP scans in total), and plotted the measured opacity (via the technique outlined in Butler 1996) against the estimated precipitable water (via the technique outlined above - the temperature and dew point are provided with each set of TIP data). The result is shown in Figure 6. A good correlation is seen, and a fit with a second order polynomial is also shown in Figure 6. This fit is of the type:

$$\tau = a_0 + a_1 \, h + a_2 \, h^2 \quad ,$$

where the three coefficients are: $a_0 = 3.8\%$, $a_1 = 0.23\%$, $a_2 = 0.065\%$. While individual data points can be significantly different from the fit, for the purposes of statistical analysis it seems quite valid to use the surface measurements to predict precipitable water (and hence opacity).

Figure 6: Measured opacity at K-band at the VLA (via TIP scans) compared with estimated precipitable water over the past 3 years.

Is this correlation unique to K-band, the VLA band where the opacity effects of atmospheric water are greatest? In order to test this, I took TIP data at Q-band (I used data only from frequencies between 42 and 44 GHz) from the same 3 year period (164 TIP scans in total), and plotted the same quantities (measured opacity against estimated precipitable water). The result is shown in Figure 7. Again, a good correlation is seen. The fit coefficients are: $a_0 = 5.5\%, a_1 = 0.19\%$, and $a_2 = 0.0026\%$.

Figure 7: Measured opacity at Q-band at the VLA (via TIP scans) compared with estimated precipitable water over the past 3 years.