From d54fe7c1f704a63824c5bfa0ece65245572e9b27 Mon Sep 17 00:00:00 2001 From: Joseph Hunkeler Date: Wed, 4 Mar 2015 21:21:30 -0500 Subject: Initial commit --- src/slalib/sun67.htx/node166.html | 428 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 428 insertions(+) create mode 100644 src/slalib/sun67.htx/node166.html (limited to 'src/slalib/sun67.htx/node166.html') diff --git a/src/slalib/sun67.htx/node166.html b/src/slalib/sun67.htx/node166.html new file mode 100644 index 0000000..4dd74d2 --- /dev/null +++ b/src/slalib/sun67.htx/node166.html @@ -0,0 +1,428 @@ + + + + +SLA_REFCOQ - Refraction Constants (fast) + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_REFRO - Refraction +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_REFCO - Refraction Constants +

+

+

SLA_REFCOQ - Refraction Constants (fast) +   +

+
+
ACTION: +
Determine the constants a and b in the +atmospheric refraction model + $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$, where $\zeta$ is the observed zenith distance + (i.e. affected by refraction) and $\Delta \zeta$ is + what to add to $\zeta$ to give the topocentric + (i.e. in vacuo) zenith distance. (This is a fast + alternative to the sla_REFCO routine - see notes.) +

CALL: +
CALL sla_REFCOQ (TDK, PMB, RH, WL, REFA, REFB) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + +
TDKDambient temperature at the observer (degrees K)
PMBDpressure at the observer (mB)
RHDrelative humidity at the observer (range 0-1)
WLDeffective wavelength of the source ($\mu{\rm m}$)
+

+
RETURNED: +
+
+ + + + + + + + + +
REFAD$\tan \zeta$ coefficient (radians)
REFBD$\tan^{3} \zeta$ coefficient (radians)
+

+
NOTES: +
+
1. +
The radio refraction is chosen by specifying WL >100 $\mu{\rm m}$.
2. +
The model is an approximation, for moderate zenith distances, +to the predictions of the sla_REFRO routine. The approximation + is maintained across a range of conditions, and applies to + both optical/IR and radio. +
3. +
The algorithm is a fast alternative to the sla_REFCO routine. + The latter calls the sla_REFRO routine itself: this involves + integrations through a model atmosphere, and is costly in + processor time. However, the model which is produced is precisely + correct for two zenith distances ($45^\circ$ and $\sim\!76^\circ$) and at other zenith distances is limited in accuracy only by the + $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$ formulation + itself. The present routine is not as accurate, though it + satisfies most practical requirements. +
4. +
The model omits the effects of (i) height above sea level (apart + from the reduced pressure itself), (ii) latitude (i.e. the + flattening of the Earth) and (iii) variations in tropospheric + lapse rate. +
5. +
The model has been tested using the following range of conditions: +
+
$\cdot$
lapse rates 0.0055, 0.0065, 0.0075 degrees K per metre +
$\cdot$
latitudes $0^{\circ}$, $25^\circ$, $50^\circ$, $75^\circ$
$\cdot$
heights 0, 2500, 5000 metres above sea level +
$\cdot$
pressures mean for height -10% to +5% in steps of 5% +
$\cdot$
temperatures $-10^\circ$ to $+20^\circ$ with respect to + $280^\circ$K at sea level +
$\cdot$
relative humidity 0, 0.5, 1 +
$\cdot$
wavelength 0.4, 0.6, ... $2\mu{\rm m}$, + radio +
$\cdot$
zenith distances $15^\circ$, $45^\circ$, $75^\circ$
+ For the above conditions, the comparison with sla_REFRO + was as follows: +


+
+
+

           + + + + + + + + + + + + + + + + + +
 worstRMS
optical/IR628
radio31949
 masmas
+


+
+
+
+

+For this particular set of conditions: +

+
$\cdot$
lapse rate $6.5^\circ K km^{-1}$
$\cdot$
latitude $50^\circ$
$\cdot$
sea level +
$\cdot$
pressure 1005mB +
$\cdot$
temperature $7^\circ$C +
$\cdot$
humidity 80% +
$\cdot$
wavelength 5740A +
+ the results were as follows: +


+
+
+

           + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
$\zeta$sla_REFROsla_REFCOQSaastamoinen
1010.2710.2710.27
2021.1921.2021.19
3033.6133.6133.60
4048.8248.8348.81
4558.1658.1858.16
5069.2869.3069.27
5582.9782.9982.95
60100.51100.54100.50
65124.23124.26124.20
70158.63158.68158.61
72177.32177.37177.31
74200.35200.38200.32
76229.45229.43229.42
78267.44267.29267.41
80319.13318.55319.10
degarcsecarcsecarcsec
+


+
+
+
+

+The values for Saastamoinen's formula (which includes terms + up to $\tan^5$) are taken from Hohenkerk and Sinclair (1985). +

+The results from the much slower but more accurate sla_REFCO + routine have not been included in the tabulation as they are + identical to those in the sla_REFRO column to the + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.01$

+resolution used. +

6. +
Outlandish input parameters are silently limited + to mathematically safe values. Zero pressure is permissible, + and causes zeroes to be returned. +
7. +
The algorithm draws on several sources, as follows: +
    +
  • The formula for the saturation vapour pressure of water as + a function of temperature and temperature is taken from + expressions A4.5-A4.7 of Gill (1982). +
  • The formula for the water vapour pressure, given the + saturation pressure and the relative humidity is from + Crane (1976), expression 2.5.5. +
  • The refractivity of air is a function of temperature, + total pressure, water-vapour pressure and, in the case + of optical/IR but not radio, wavelength. The formulae + for the two cases are developed from the Essen and Froome + expressions adopted in Resolution 1 of the 12th International + Geodesy Association General Assembly (1963). +
+ The above three items are as used in the sla_REFRO routine. +
    +
  • The formula for $\beta~(=H_0/r_0)$ is + an adaption of expression 9 from Stone (1996). The + adaptations, arrived at empirically, consist of (i) a + small adjustment to the coefficient and (ii) a humidity + term for the radio case only. +
  • The formulae for the refraction constants as a function of + n-1 and $\beta$ are from Green (1987), expression 4.31. +
+

+
REFERENCES: +
+
1. +
Crane, R.K., Meeks, M.L. (ed), ``Refraction Effects in +the Neutral Atmosphere'', +Methods of Experimental Physics: Astrophysics 12B, + Academic Press, 1976. +
2. +
Gill, Adrian E., Atmosphere-Ocean Dynamics, + Academic Press, 1982. +
3. +
Hohenkerk, C.Y., & Sinclair, A.T., NAO Technical Note + No. 63, 1985. +
4. +
International Geodesy Association General Assembly, Bulletin + Géodésique 70 p390, 1963. +
5. +
Stone, Ronald C., P.A.S.P. 108 1051-1058, 1996. +
6. +
Green, R.M., Spherical Astronomy, Cambridge + University Press, 1987. +
+
+ +next + +up + +previous +
+ Next: SLA_REFRO - Refraction +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_REFCO - Refraction Constants +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + -- cgit