[mmaimcal] height matters

[Simon Radford]

Steve,

For submm/THz observations, height matters, with or without an inversion
layer. 

Signals are exponentially attenuated by the atmosphere,
  Signal ~ exp(-tau). 
The system noise has (dominant) contributions from the receiver and from
the atmosphere, 
  Noise ~ Trec + Tatm(1 - exp(-tau)). 
In the happy circumstance where the receiver noise, Trec, is
insignificant, the signal to noise ratio 
  SNR ~ 1/[ exp(tau) (1 - exp(-tau)) ]. 
Integration time to a fixed SNR is, of course, proportional to the
inverse square of the SNR,
  time ~ 1/ SNR^2.

For submm observations at Chajnantor, a typical optical depth, tau, is 1
and for THz observations, the typical optical depth might be 3
(Matsushita et al. 1999 PASJ 51, 603). The optical depth is proportional
to the water vapor column, which is also distributed exponentially so
  tau ~ tau0 exp(-z/h).
A typical water vapor scale height is 1400 m (Butler's analysis of
radiosondes).

Then a 200 m increase in elevation when tau = 1 would increase the SNR
by 25%, which means 35% less integration time. The improvement is even
more dramatic for tau = 3 or larger increase in elevation (Table below).

Simon

h      1400 m   water vapor scale height
tau0            optical depth at lower altitude
z               elevation increase

Integration time needed for fixed SNR
z [m]        1          3  <-  tau0     
200        0.64       0.42
400        0.42       0.20
600        0.28       0.10