
	SkyCalc - ESO Sky Model Calculator

SkyCalc Web Application

SkyCalc is a web application based on the Cerro Paranal Advanced Sky Model, which was developed in particular to be used in the ESO Exposure Time Calculators, by a team of astronomers at the Institute for Astro- and Particle Physics at the University of Innsbruck, as part of an Austrian in-kind contribution to ESO.

The in-kind contribution also includes two tools to correct observations for atmospheric telluric absorption and emission (Molecfit and Skycorr), which can be found here.

The citations for the Cerro Paranal Sky Model are Noll et al. (2012, A&A 543, A92) and Jones et al. (2013, A&A 560, A91).

A library of telluric transmission spectra with various resolutions and atmospheric conditions has been calculated with the Cerro Paranal Advanced Sky Model. A description of the usage of the spectra can be found in the article Moehler et al. (2014, A&A 568, A9).

ESO SkyCalc Command Line Interface (CLI)

A command-line tool skycalc_cli is available to execute skycalc

Broadband Magnitude Calculations

SkyCalc can compute the broad-band magnitudes per square arc second in the photometric bands UBVRIZYJHKLMNQ. This is done by integrating, across each band pass filter, a low resolution (R=60,000) emission spectrum model, corresponding to the radiance contributions selected in the input form. Note that only the radiance components selected in the input page are included in these magnitude calculations.

The following table provides the photometric zero points (Vega system) and the broad-band filter curves used in the magnitude calculations. These values and filter curves correspond to the ones used in the ESO ETC system.

Band	Filter curve	Photometric zeropoint in ergs/s/cm²/A (flux for zero mag in Vega system)
U	U filter curve	U₀ = 4.18023e-09
B	B filter curve	B₀ = 6.60085e-09
V	V filter curve	V₀ = 3.60994e-09
R	R filter curve	R₀ = 2.28665e-09
I	I filter curve	I₀ = 1.22603e-09
Z	Z filter curve	Z₀ = 7.76068e-10
Y	Y filter curve	Y₀ = 5.973e-10
J	J filter curve	J₀ = 3.12e-10
H	H filter curve	H₀ = 1.14e-10
K	K filter curve	K₀ = 3.94e-11
L	L filter curve	L₀ = 4.83e-12
M	M filter curve	M₀ = 2.04e-12
N	N filter curve	N₀ = 1.23e-13
Q	Q filter curve	Q₀ = 6.8e-15

Temperature and Bolometric Radiance

The bolometric sky temperature corresponds to the bolometric radiance: \[T = \left({\pi R \over \sigma}\right)^{1 \over 4}\] where \(R\) is the bolometric radiance and \(\sigma\) is the Stefan-Boltzmann constant. This is the temperature at which the upper side of a flat, horizontal and perfectly black body on the ground that, exposed to the entire night sky hemisphere, is in thermal radiation balance with the sky.
The ground air temperature corresponds to the sky temperature in wavelength regions where the atmosphere is opaque. It is calculated as the \(T\) parameter in a Planck distribution fit to the thermal (molecular) sky emission envelope.
The bolometric radiance is the integrated radiance of the full sky spectrum.

Sky Model

The Sky Model is configured for the conditions at Cerro Paranal (VLT) as explained in the documentation, except for the observatory altitude above sea level.

Two additional observatory heights 3060m and 5000m were added in version 2.0.0. They correspond to the height of Cerro Armazones (future site of the ELT) and a generic 5000m site. The configuration of the Sky Model for those two sites is the same as for Cerro Paranal except the altitude which affects the pressure parameter.

The output from the SkyCalc includes plots of the transmission and emissivity spectra and optionally the individual components of these. A link to a FITS is also included, the FITS header contains a short summary of the input parameters and legends of the seven data columns:

  COMMENT column lam:     wavelength in micron
  COMMENT column flux:    sky emission radiance flux in ph/s/m2/micron/arcsec2
  COMMENT column dflux1:  sky emission -1sigma flux uncertainty
  COMMENT column dflux2:  sky emission +1sigma flux uncertainty
  COMMENT column dtrans:  sky transmission
  COMMENT column dtrans1: sky transmission -1sigma uncertainty
  COMMENT column dtrans2: sky transmission +1sigma uncertainty

Almanac

Algorithm

Dates and Times

Local Sideral Time is computed following the Astronomical Almanac 1992, B7 and L2. The accuracy is better than 1ms.
Time zones and daylight saving changes are calculated using the standard C library and makes use of timezone information based on the IANA Time Zone Database.

Coordinates

Conversions between coordinate systems (Equatorial, Horizontal, Ecliptic) are implemented with the slalib and Meeus 1998, Chapter 13.
Sun coordinates are calculated using the algorithm of the Astronomical Almanac 1990, C24.
Moon coordinates and topocentric distance are calculated following Meeus 1998, chapter 47. The method is based on the semi-analytic theory ELP 2000-83 of Chapront 1983 and gives an accuracy of 0.01 arcsec on the coordinates.
The topocentric Earth/Moon distance is given in normalised unit relative to the mean distance; it ranges between 0.91 and 1.08.
The Moon Position Angle is calculated following Meeus 1998, Chapter 48. The Moon libration is not included.

Sunrise, Sunset, Moonrise and Moonset, Culmination, Twilights

Sun (Moon) rise and set correspond to times when the whole disk of the Sun (Moon) is just below the horizon. The calculation of the altitude of the Sun (Moon) near the horizon takes into account:
1. the elevation of the observatory above the sea level,
2. the atmospheric refraction of the atmosphere,
3. and the angular diameter of the Sun (Moon).
The angular diameters of the Sun and Moon are calculated as a function of the distance from Earth. A constant atmospheric refraction term of 0.3 deg is applied.
To calculate the Culmination of the Sun (Moon), the inverse of the altitude curve as a function of time is numerically minimized using the GNU Scientific Library Brent Minimizer. The precision is set to 1 sec.
Twilights are calculated in the morning and evening for three altitudes of the center of the Sun below the horizon:
1. Civil Twilight: 6 deg below the horizon,
2. Nautical Twilight: 12 deg below the horizon,
3. Astronomical Twilight: 18 deg below the horizon.

Sun

The historical Monthly Average Solar Flux in the SkyCalc web application is obtained from NRCan (Natural Resources Canada)

Moon

The Illumination fraction of the Moon is computed following the method of Meeus, 1998, Chapter 48. The accuracy is better than 0.0014 on the fraction.

Bibliography

Astronomical Almanac, 1990, United States Naval Observatory and Her Majesty's Nautical Almanac Office.
Astronomical Almanac, 1992, United States Naval Observatory and Her Majesty's Nautical Almanac Office.
Chapront-Touzé & Chapront, 1983, Astronomy & Astrophysics, 124, 50-62.
Meeus, 1998, Willmann-Bell, Astronomical Algorithms, Second Edition.
SLALIB, Positional Astronomy Library.

Version Information

Version 2.0.9 (May 9, 2020)
Added support in skycalc_cli 1.4 for bolometric sky temperature, bolometric radiance and ground air temperature.
Note that the unit of output wavelengths in v.1.4 is nm as opposed to μm in v.1.3.
Version 2.0.8 (Oct 25, 2019)
Bug fix: The instrumental thermal emssion components were not shown in the plots.
Version 2.0.7 (Sept 3, 2019)
Bug fix: The displayed wavelength units were wrong when the resulting spectrum was convolved by a Gaussian or Boxcar LSF.
In the resulting FITS file (skycalc.fits) the scale of the wavelength values in the "LAM" column has been corrected to be consistenly nm as indicated in the FITS header and the documentation.
Version 2.0.6 (February 5, 2019)
Sky Temperature update.
Version 2.0.5 (October 26, 2018)
Added support for lower PWV values.
Version 2.0.4 (August 14, 2018)
Scattered moon light contribution reduced by factor 1/1.2 ≈ 0.83
Sky background library for fixed PWV value now depends on time and season
Added option to calculate the atmosphere temperature and bolometric radiance.
Disabled the observatory height 5000m option.
Version 2.0.3 (June 11, 2018)
Bug fix in the Rayleigh scattering component: It was calculated with Paranal parameters for all observatory heights.
Eliminating "numerical noise" in the very blue part (300nm - 340nm) of the molecular absorption component spectrum.
Version 2.0.2 (February 16, 2018)
Supporting la Silla
Introduced a command line interface (CLI) to skycalc
Version 2.0.1 (October 5, 2017)
Added an option for wavelenghts in vacuum / air
Almanac response optimised
Version 2.0.0 (August 31, 2017)
La silla and two additional observatory heights 3060m and 5000m were added
Almanac backend model extended and improved in terms of accuracy and performance.
Almanac frontend extended to provide additional dynamic visual and textual information, including:
   -illustations of moon and sun coordinates
   -graticule with different coordinate systems and projections
   -visibility chart
   -automatically retrieved historic solar radio flux data.
Dynamic input parameter validation was added to the SkyCalc input form.
Version 1.4.3 (August 30, 2016)
The sky model has been updated with adjusted ozone and CO₂ abundances and minor changes in the moonlight model.
Additional feature: the indvidual components of radiance and transmission spectra can be inspected in separate plots.
Correction in almanac service: The range of the calculated Moon/Sun separation phase angle α is now correctly 0^° ≤ α < 360^° (previously 0^° ≤ α ≤ 180^°)
Version 1.4.2 (June, 2016)
Range of supported Moon/Sun separation phase angle α changed from 0^° ≤ α ≤ 180^° to 0^° ≤ α < 360^°.
The supported range of Moon-Earth distance corrected.
Bug fix in the number format of the plotted ASCII data

Version 1.4.1 (August 31, 2015)
Fixed a mistake in "almanac" mode, the heliocentric ecliptic longitude was not assigned correctly.

Version 1.4.0 (February 26, 2015)
Introduced an "almanac" mode to automatically initialise time/coordinate dependent input parameters to a given time and sky position.

Version 1.3.9 (August 27, 2014)
Corrected a bug: The wavelength unit was wrong (μm instead of nm) when the spectra were convolved by an LSF kernel.

References for the sky model.
Description of the columns.
List of model input parameter values corresponing to the fields in the web application input form.

Version 1.3.8 (June 30, 2014)
Reduced tendency to give a wrong number of spectral bins, when the option "fixed wavelength step" is used.

Version 1.3.7 (April 3, 2014)
Updated documentation and added references and links to the sky correction tools Molecfit and Skycorr.

Version 1.3.6 (February 24, 2014)
Added a validation layer for all input parameters.

Version 1.3.5 (July 1, 2013)
New version of the code. Now supporting the option to calculate broad-band magnitudes per square arcsec, corresponding to the spectrum with selected radiance components.

Send comments and questions via https://support.eso.org/

SkyCalc - ESO Sky Model Calculator