Correspondence with Pat Wallace re refraction
Correspondence with Pat Wallace re refraction
From: MX%"ptw@star.rl.ac.uk" 1-JUN-1995 00:56:26.09
Iain:
I plan to improve the SLALIB refraction routine to give greater accuracy
in the radio regime. In the present formulation, the humidity part of the
atmosphere model is adequate for the optical case but not quite good
enough for the radio. According to Chris Mayer you did a lot of work
on this for the JCMT. Have you got any formulae or test examples I
can use for testing the new sla_REFRO?
Patrick Wallace
____________________________________________________________________________
Starlink Project Manager Internet: ptw@star.rl.ac.uk
Rutherford Appleton Laboratory Tel: +44-1235-445372
Chilton, Didcot, Oxon OX11 0QX, UK Fax: +44-1235-445848
____________________________________________________________________________
From: JACH::IMC "Iain Coulson" 2-JUN-1995 15:13:13.66
To: PTW@STAR.RL.AC.UK
CC: IMC
Subj: refraction at JCMT
Hello Patrick -
Yo ! a long time ago that was. I append my report of 1987.
It was converted by the software group into code the TEL task
presumably understands, and has worked well enough since.
Following improvements to other aspects of telescope pointing it
was expected that the model may undergo empirical changes, and
indeed data taken in March and April of 1994 suggested that the
principal term be reduced to 35.6 (arcseconds per 'airmass')
(Made me wonder how meaningful the other smaller terms were . . . )
Since *then* the new model has also performed quite satisfactorily -
ie it is not now the limiting factor to good pointing.
Hope this helps.
regards
Iain
Refraction document of 24 Sept 1987
From: MX%"ptw@star.rl.ac.uk" 19-JUN-1995 00:15:54.70
Iain:
Your refraction paper was very useful.
1) Could you send me a paper version, or some form that contains the
various tables?
2) What reference pressure do you use? (In other words, at what local
pressure does p equal zero in your formulae?)
3) In which direction does your A*tan(z)+B*tan(z)**3 law work? Is z
the observed ZD (i.e. as affected by refraction) or the topocentric
ZD (i.e. in vacuo)?
4) Assuming that p=0 corresponds to 612.7mB (what my standard model
atmosphere gives for 4100 metres), and that the A*tan(z)+B*tan(z)**3
formula starts with observed ZD, the comparison between the SLALIB
routine sla_REFRO and the expressions in your paper is as follows:
Pressure (mB) = 610.0
Height (asl) = 4100.00
Tempr (degK) = 283.15
RH = 50%
Lat (deg) = 20
--optical-- ----radio---
Z S J-S S J-S
0 0.0 +0.00 0.0 +0.00
5 3.1 -0.01 3.5 -0.02
10 6.2 -0.02 7.1 -0.05
15 9.4 -0.02 10.8 -0.08
20 12.7 -0.03 14.6 -0.10
25 16.3 -0.04 18.7 -0.13
30 20.2 -0.05 23.2 -0.16
35 24.5 -0.06 28.1 -0.20
40 29.4 -0.07 33.7 -0.23
45 35.0 -0.09 40.2 -0.28
50 41.7 -0.10 47.9 -0.32
55 49.9 -0.11 57.3 -0.38
60 60.4 -0.12 69.4 -0.45
65 74.7 -0.13 85.8 -0.53
70 95.3 -0.12 109.6 -0.63
75 128.6 -0.05 147.9 -0.72
80 191.5 +0.15 220.9 -0.81
Z is the ZD in degrees. All the other numbers are arcsec. J is the
JCMT refraction and S is sla_REFRO.
The agreement is reassuring. Incidentally, the numbers don't support
your proposed change of the first A term in the radio from 36.8 arcsec
to 35.6 arcsec. Is it possible you're seeing non-Hooke's-law dish
flexure? Most telescopes I have looked at have had significant tanZ-ish
flexure, which I suspect arises from things changing from compression to
tension as the ZD increases.
The above comparisons are with the current good-enough-for-optical-but-
not-for-radio humidity calculations. When I use the new, improved, humidity
formulae recommended by the Green Bank people the agreement worsens by
0.1-0.2 arcsec. However, this is for Mauna Kea conditions - albeit
comparatively wet and warm ones - and says little or nothing about the
40 degC + 100% RH + 1100mB regime which the GBT people need to reach.
Patrick Wallace
____________________________________________________________________________
Starlink Project Manager Internet: ptw@star.rl.ac.uk
Rutherford Appleton Laboratory Tel: +44-1235-445372
Chilton, Didcot, Oxon OX11 0QX, UK Fax: +44-1235-445848
____________________________________________________________________________
Missing here is my reply - which was to answer his questions where I could :
1. I sent him a paper copy of the same work - I can do similar for you
if you think it would help.
2. The local weather boys here use 624mb at that altitude and I've adopted
that as the standard.
3. My algorithm (also) starts with the observed ZD.
____________________________________________________________________________
From: MX%"ptw@star.rl.ac.uk" 26-JUN-1995 22:10:35.69
Iain:
I got your paper yesterday - thanks for sending it.
I've compared the formulae in the paper with the results of the latest
sla_REFRO, using a lapse rate of 0.00667 degC per metre (obtained
from your Hawaiian atmosphere, which has a 40 deg temperature drop
from 4 to 10 km) and a standard pressure of 624 mB. Also, we are
evidently both starting from observed ZD, so that's OK.
The optical agreement is very good - typically 0.1 arcsec at 70 deg ZD.
The agreement in the radio almost as good for standard conditions, but
not quite so convincing for higher temperatures and humidities, and for
pressure changes.
This all looks pretty reassuring, and I'm now fairly confident that
sla_REFRO is calculating the radio refraction properly, at least
with the improved water vapour pressure expressions. Of course, both
our formulations share some common ancestors (Allen, and the use of
numerical integration of a ray through a model atmosphere), and so
might share the same failings. However, I wouldn't mind betting
that your ad hoc adjustments to the main term in A are more to do with
flexure than with anomalous refraction. If it were my telescope (and
I speak as one never averse to fixing things that aren't bust), I'd
switch to using SLALIB routines (which will do the refraction calculation
starting from topocentric ZD if that's what the control system requires)
and then probe the ZD residuals with TPOINT.
The actual numbers from my tests are given below. S is the new
sla_REFRO, and J is your formulation.
Thanks again for your help.
Patrick Wallace
-----------------------------------------------------------------------
T = +5.0degC P = 624mB +.0% H = 20.0%
optical radio
Z S J-S J S-J
0 .0 +.00 .0 +.00
5 3.2 -.01 3.3 -.01
10 6.4 -.02 6.6 -.01
15 9.8 -.02 10.1 -.02
20 13.3 -.02 13.7 -.04
25 17.0 -.02 17.6 -.05
30 21.1 -.02 21.8 -.07
35 25.5 -.02 26.4 -.09
40 30.6 -.02 31.6 -.11
45 36.5 -.01 37.7 -.14
50 43.4 -.02 44.9 -.16
55 52.0 -.02 53.8 -.19
60 63.0 -.04 65.1 -.21
65 77.9 -.08 80.5 -.24
70 99.4 -.14 102.7 -.26
75 134.1 -.25 138.5 -.31
80 199.8 -.34 206.7 -.54
T = -20.0degC P = 624mB +.0% H = 20.0%
optical radio
Z S J-S J S-J
0 .0 +.00 .0 +.00
5 3.5 -.01 3.5 +.01
10 7.1 -.02 7.0 +.01
15 10.8 -.03 10.6 +.02
20 14.6 -.03 14.4 +.02
25 18.7 -.03 18.5 +.02
30 23.2 -.04 22.9 +.02
35 28.1 -.04 27.8 +.02
40 33.6 -.04 33.3 +.02
45 40.1 -.04 39.7 +.02
50 47.8 -.04 47.2 +.02
55 57.2 -.06 56.6 +.03
60 69.3 -.08 68.5 +.06
65 85.6 -.13 84.7 +.10
70 109.4 -.22 108.1 +.18
75 147.6 -.36 145.8 +.30
80 220.4 -.51 217.8 +.43
T = +20.0degC P = 624mB +.0% H = 20.0%
optical radio
Z S J-S J S-J
0 .0 +.00 .0 +.00
5 3.0 -.01 3.4 -.02
10 6.1 -.01 6.8 -.04
15 9.3 -.02 10.3 -.06
20 12.6 -.02 14.0 -.08
25 16.1 -.02 18.0 -.11
30 20.0 -.01 22.3 -.15
35 24.2 -.01 27.0 -.18
40 29.0 +.00 32.3 -.22
45 34.6 +.00 38.5 -.27
50 41.2 +.00 45.9 -.32
55 49.3 +.00 54.9 -.38
60 59.7 -.01 66.6 -.44
65 73.8 -.04 82.2 -.53
70 94.2 -.09 105.0 -.64
75 127.0 -.18 141.6 -.84
80 189.1 -.23 211.3 -1.43
T = +5.0degC P = 624mB+3.0% H = 20.0%
optical radio
Z S J-S J S-J
0 .0 +.00 .0 +.00
5 3.3 -.01 3.4 -.01
10 6.6 -.02 6.8 -.02
15 10.1 -.02 10.4 -.03
20 13.7 -.02 14.1 -.05
25 17.5 -.02 18.1 -.07
30 21.7 -.02 22.4 -.09
35 26.3 -.02 27.2 -.12
40 31.5 -.02 32.6 -.14
45 37.6 -.02 38.8 -.17
50 44.7 -.02 46.2 -.21
55 53.6 -.02 55.4 -.24
60 64.9 -.04 67.1 -.28
65 80.2 -.07 82.9 -.33
70 102.4 -.13 105.8 -.39
75 138.1 -.20 142.7 -.51
80 205.8 -.15 213.0 -.95
T = +5.0degC P = 624mB +.0% H = 90.0%
optical radio
Z S J-S J S-J
0 .0 +.00 .0 +.00
5 3.2 -.01 3.9 -.06
10 6.4 -.01 7.8 -.11
15 9.8 -.02 11.9 -.18
20 13.3 -.02 16.1 -.24
25 17.0 -.02 20.6 -.32
30 21.0 -.02 25.6 -.40
35 25.5 -.01 31.0 -.49
40 30.6 -.01 37.2 -.59
45 36.4 -.01 44.3 -.70
50 43.4 +.00 52.7 -.84
55 51.9 -.01 63.2 -1.00
60 62.9 -.02 76.5 -1.20
65 77.8 -.06 94.6 -1.46
70 99.3 -.12 120.8 -1.84
75 133.9 -.22 163.0 -2.49
80 199.5 -.28 243.9 -4.00
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