Assessing the contribution from different parts of Canary islands to the hemispheric spectral sky radiance levels over European Northern Observatories

A technical report prepared for Instituto de Astrofisica de Canarias

May 2010

Martin Aubé (1) (2) (3) (4)

Jean-Denis Giguère (2)

(3) Centre de recherche en astrophysique du Québec, Canada
(4) Instituto de Astrofisica de Canarias, Spain

Abstract

We suggest to use a sky radiance model which account for heterogeneous distribution of light fixtures, their photometry, the ground reflectance and topography to infer the point to point contribution of Canary islands to the artificial sky radiance at Observatorio del Teide (Tenerife) and Observatorio Roque de los Muchachos (La Palma). In-situ hyperspectral sky radiance measurements have been used to calibrate the model and to evaluate its inherent error. The project aim to identify and characterize zones at which any lighting level increase or decrease may have a larger impact on light pollution at both European Northern Observatory sites, and then help to control and/or reduce their light pollution levels.

1.  Introduction

A measurement campaign was made across Tenerife and La Palma islands but mainly over Observatorio del Teide (OT, 28° 18.0295' N 16° 30.7381' W 2379m) and Observatorio del Roque de los Muchachos (ORM, 28.76224° N 17.891895° W 2180m). We aimed to get a relatively good angular sampling of the spectral sky brightness levels at those sites. Measurements were made all over the sky at 20o, 45o, and 90o above horizon. That dataset was used as tie down points to calibrate and evaluate errors of the light pollution model. The instrument, which was used to accomplish observations, is the third version of the Spectrometer for Aerosol Night Detection (SAND-3). SAND-3 have been designed by CélesTech, a non profit research society. The instrument and relevant software are published under GNU Public Licence (GPL) in order to ensure maximum accessibility to the scientific community. The spectrometer is robotized so that it may operate by its own without human intervention. SAND have been used successfully for about 4 years to characterize light pollution on many astronomical sites across North America (e.g. Palomar, Kitt Peak National Observatory (KPNO), Fred Lawrence Whipple Observatory (FLWO), US Naval Observatory (USNO), Lowell and Mégantic). The field campaign presented here took place over 3 months around new moon of Feburary, March and April 2010.

The second step of the project was to acquire input database required to run our model called ILLUMINA (Aubé et al. 2005, Aubé 2007). ILLUMINA and some other recent models (e.g. Kocifaj 2007, Luginbuhl et al. 2009) may be described as a third generation light pollution model. First generation models (e.g. Walker 1977) mainly address the sky brightness to distance relationship following an empirical approach. Second generation models (e.g. Garstang 1986, Cinzano 2000) implements mulitangular dependence and atmospheric properties but relies on some basic assumptions about the geometry of light distribution on the ground (circular cities) and ground homogeneity. They also used empirical parametrization of atmospheric radiative transfer process and light output angular pattern. 2nd generation models can only caracterize sky brightness in the principal plane defined by the city center, the observer and zenith. Improvements of 3rd generation models resides in their capability to simulate any heterogeneous distribution of a variety of light fixtures with their own intensities, spectral characteristics and angular light output patterns (LOP). Each model have its own specificities. As an example, our model account for shadowing effects associated with topography, for gridded variation in ground reflectance and blocking by subgrid obstacles (trees, buildings, etc.). Some of these processes are not considered in other models. Luginbuhl for instance account for subgrid obstacles while Kocifaj do not. ILLUMINA compute explicit 1st and 2nd order scattering, extinction from aerosols and molecules, and the vertical profile of atmospheric constituants is taken into account. ILLUMINA also compute optical impact of size distribution and composition of aerosol content which may be quite useful during pollution events like important biomass burning or saharian sand storms. To perform a modeling experiment, we have to feed the model with gridded dataset of 1-light intensities per spectra and LOPs, 2- lamp pole height, 3- digital elevation model (DEM), and 4- ground spectral reflectance. The model also requires typical mean light free path toward the ground and typical obstacles height, ground atmospheric pressure, aerosol optical depth (AOD) and phase function. Light intensities per spectra were obtained from a combination of local inventories, Defense Meteorological Satellite Program Operational Linescan System (DMSP-OLS) 2008 data (ngdc.noaa 2010) and in-situ sampling. The inventory was simplified according to some basic assumptions which were validated by a local expert having the best possible knowledge of the site reality. Ground spectral reflectance was obtained from remotely sensed data of the MODerate-resolution Imaging Spectroradiometer (MODIS) (Vermote and Vermeulen 1999). Aerosol optical properties have been taken from active NASA-AERONET sunphotometers (Holben et al. 2001) located on Tenerife island and from a portable sun photometer (Microtops-II) for La Palma.

Finally we performed 3280 model runs (5 wavelenght, 41 viewing angles, 2 period of the day (before and after midnight), 4 AOD and 2 observatories). For each observation we searched the most similar case in our model generated lookup database in order to calibrate model results and to map typical model errors. The goal of that experiment was to determine the contribution of each ground point to the sky radiance at each observing site so that one should be able to infer the impact of local change in lighting device inventory. That kind of results will be extremely useful to identify critical zones and then orient any future intervention/abatement. It may be used as a high level decision tool by local decision makers and authorities (IAC or others).

2.  Observations

Observations were made with the Spectrometer for Aerosol Night Detection version 3 (SAND-3). SAND-3 is a CCD based long slit - grating spectrometer. The spectrometer is sensitive to the visible from 400nm to 730nm with a spectral resolution of 2 nm. The spectrometer have a field of view (FOV) of 2.374ox0.082o.

The SAND-3 spectrometer have been photometrically intercalibrated with the CIMEL AERONET sunphotometer of Izana (next to Observatorio del Teide) which is a calibration reference for the NASA's AERONET network. We used the principal plane radiances product and made simultaneous radiances measurements at zenith during daytime. A 2nd order polynomial have been fitted on the SAND-3 vs AERONET data and that polynomial was applied to all spectrums to convert numerical counts into radiances (W/m2/str/nm). Prior to that, the instrument was spectrally calibrated using a linear fit of 16 spectral lines from 400 to 760 nm identified from a fluocompact light bulb spectrum. For each night, we re-validated the offset of the spectral relationship using the 557.7 nm OI line to be shure that no calibration shift had occured.

Data were acquired at 17 viewing angles for the two observatories (see table 1). We repeated the first measurement at the end of the night to get some information on the before/after midnight sky radiance change. This was made for azimuth 180o at both sites for every elevation angle sampled.

Table 1: Viewing angles for OT and ORM

 Elevation(deg.) Azimuth ->(deg.) 20 0 45 90 135 180 225 270 315 45 0 45 90 135 180 225 270 315 90 - - - - - - - -

3.  Modeling experiment

Computations have been done on the supercomputer Mammouth-serial-II (MS-II) (Sherbrooke, Canada). This facility is a part of the Réseau québécois de calcul de haute performance (RQCHP) which is affiliated to Compute Canada, a consortium of canadian computing facilities. MS-II is made of 308 computing nodes (SGI XE320) with 2 processors Intel Xeon E5462 quad-core, 2.8 GHz. So there are 2464 computing units. As of now, MS-II is the #1 ranking computer in Canada. Our experiment required around 120 000 CPU-hours.

Table 2: Modeling angles for OT and ORM

 Elevation(deg.) Azimuth ->(deg.) 20 0 22 45 67 90 112 135 157 20 180 202 225 257 270 292 315 337 30 0 45 90 135 180 225 270 315 45 0 45 90 135 180 225 270 315 70 0 45 90 135 180 225 270 315 90 - - - - - - - -

3.1  Modeling domain

The modeling domain include the main light sources which may have a significant effect on ORM and OT sites. At the beginning, we roughly estimated that considering Gran Canaria island was required at least for the modeling of the OT site. That island is somewhat far but have an important lighting infrastructure.

When using ILLUMINA we have to choose the resolution low enough to ensure that a grid cell may contain many light fixtures so that the combination of their installation orientation could be considered randomly distributed. This is required since up to now, ILLUMINA can not account for azimuthal anisothropy of LOP. In fact when defining the LOP of a given light fixture, we average horizontally the bidirectionnal radiometry data from IESNA radiometic file. Generally the spatial resolution should be larger than ~200 m. In that study we set the resolution to 1 km. This resolution have been choosen to correspond to the worst gridded dataset to be used, namely the DMSP-OLS nighttime satellite radiances. The model boundaries have been choosen to ensure a buffer region of at least 120 km between any observatory and its nearest domaine limit. Giving that the model height is 30 km, this means that we can model zenith angles up to ~75o. In fact our lowest angle measurement for validation have been done at 70o from zenith (elevation of 20o).

Table 3: Summary of modeling domain properties

 W-E domain size 400 km S-N domain size 300 km Model height 30 km Domain center coordinate Latitude : 28.530724 ; Longitude : -17.196738 Horizontal grid resolution 1 km SW pixel coordinate Latitude : 27.136585 ; Longitude : -19.180081 SE pixel coordinate Latitude : 27.198827 ; Longitude : -15.156082 NE pixel coordinate Latitude : 29.897704 ; Longitude : -15.160113 NW pixel coordinate Latitude : 29.828107 ; Longitude : -19.287647

3.2  Getting input data

Finding relevant input data for ILLUMINA is not a simple task. As stated before we need many gridded information which represents a large amount of in-situ data. One efficient way to determine gridded terrestrial information over large spatial domains is to use remotely sensed satellite data. In our case we used satellite data to estimate the light installed luminosity data, the ground reflectance and the topography.

LOP function have been estimated by regions and was determined by a linear combination of 4 generic lamp fixtures corresponding to 4 different type of application. The coefficients of that combination were estimated with the help of a local expert who had a good knowledge of the in-situ light fixture inventory. For that study we have been helped by Francesco Javier Diaz Castro, which is the head of the Oficina Tecnica para la proteccion de la Calidad del Cielo (OTPCC) in Instituto de Astrofisica de Canarias, Spain. The pole height of the light fixtures was set to a constant value of 7 m.

AOD was obtained either from NASA-GSFC AERONET sun photometer network or from a handhelp Microtops-II sunphotometer when there was no nearby AERONET site (e.g. La Palma).

Sea level pressure was taken to be 101.3 KPa.

The mean free path of light toward the ground and mean subgrid obstacle height were respectively set to 15m and 10m which are typical of street width and building height in Canary island cities.

3.3  Key wavelength

We choose a set of five spectral lines for that study. This choice was made in a way that the lines are:

1. easy to distinguish from the stellar background pseudo continium,
2. not contaminated by atmospheric natural lines or major Fraunhofer lines,
3. weakly affected by atmospheric absorption and
4. suffisently narrow so that their shape is independant on lamp manufacturers and lamp age.

The resultant choice is given in table 4. We excluded the NAD 589 nm line because it is embeded in the peak of the large High Pressure Sodium (HPS) feature spanning from ~540 to ~700 nm. That line is also nearby an atmospheric water vapor absorption band as shown in figure 1. Figure 1 have been computed with MODTRAN model (Berk et al. 1999) for a typical mid-latitude summer atmosphere with rural aerosol (visibility of 23 km and AOD(550nm)=0.325). Finally, NAD 589 nm line is coming in part from atmospheric natural excitation and then it is difficult to distinguish natural from human emitted.

 (a) (b)

Figure 1: (a) Atmospheric H2O visible transmittance according to MODTRAN simulation. (b) typical zenith sky radiance at OT. This spectrum was taken at 22h52 (7200 s integration time). We identified the main spectral lines and circled our experiment key wavelenghts.

3.4  Ground reflectance

The ground reflectance was taken from the NASA's Moderate Resolution Imaging Spectroradiometer (MODIS) Surface-Reflectance Product (MOD09A1, Vermote and Vermeulen 1999). For the visible part of the spectrum, we retained the MODIS Level 3 land bands 1, 3, and 4 (centered at 648 nm, 470 nm, 555 nm respectively). Each of the key wavelength have been associated to the nearest MODIS reflectance band (see table 4). The spatial resolution of the reflectance product for those 3 bands is 500 m. Reflectance data is a combination of the 8 days L3 composite from 2009-02-26 to 2009-03-05. The composite contain the best possible observation during a 8-day period as selected on the basis of high observation coverage, low view angle, the absence of clouds or cloud shadow, and low aerosol loading.

 (a) (b) (c)

Figure 2: MODIS reflectance for (a) band 1, (b) band 3, and (c) band 4.

Table 4: Key wavelength used in the modeling

 Element Wavelenght+-0.3 Nearest reflectance MODIS band Hg 435.5 nm band 3: 470 nm Na 498.0 nm band 3: 470 nm Hg 546.0 nm band 4: 555 nm Na 569.0 nm band 4: 555 nm Na 615.5 nm band 1: 648 nm

3.5  Ground luminosity data

We used DMSP-OLS satellite night upward relative radiance measurements (Version 4, Elvidge 2008) to estimate the ground luminosity data. DMSP-OLS dataset is maintained by the Earth Observation Group of the National Geophysical Data Center (NGDC) which is a part of the US National Oceanic and Atmospheric Administration (NOAA). OLS data are coded from 0 to 63 on a linear but relative sensitivity scale. Some pixels may be saturated and in that case are set as numerical value 63. An image showing possibly saturated pixels for Canary islands is presented in figure A1 of appendix A. There are only a few possibly saturated pixels in Santa-Cruz de Tenerife and Los Cristianos, most of them are located on Gran Canaria. DMSP-OLS data shows some overspill out of cities limits. This rely in part on the large original resolution of ~2.7km which have been resampled to ~1 km. Cinzano and Elvidge 2004, used Lucy-Richardson spatial deconvolution filter to reduce that problem but for our study, we decided to keep the dataset at its simplest state and thus we did not applied any filters to the original data. OLS is using a photomultiplier sensor during nighttime measurements. The dataset is a composite wich is an average of a filtered set of measurements over a year. The OLS stable light product and data coverage are shown in figure 3. Data have been acquired between 19h30 and 21h30 local time so they are representative of light emitted before midnight. In fact La Palma and western part of Tenerife are included in the Canary Sky Law which prescribe a lighting reduction after midnight (McNally 1994). But other zones/islands also have modest but significant light intensity reduction after midnight. These reductions are prensented in the last column of table 6. DMSP are in sun-synchronous polar orbits. Data with cloud contamination, moon light, glare and auroras have been removed from the calculation of the final composite. Moreover, data have been filtered over time to remove non permanent sources like forest fires or fishing boats (stable light product). The dataset is released at a resolution of 30 arc second on a lat-lon scale. This give a typical resolution of the order of 1 km for our modeling domain.

OPTCC have a complete and up-to-date light fixture inventory for the island of La Palma but not for other islands. According that La Palma inventory is anyway too detailed for its expected impact with respect to model acuracy, we decided to use a satellite derived lighting model. This model was based on the use of the OLS upward radiance and rely on the simplistic assumption that this radiance come from direct upward flux and reflected upward flux. In fact variation in atmospheric extinction should have been corrected but we neglected it because most of light installation are about the same range of altitude (near the coast). These assumptions may be summarize by equation 1.

L_{OLS} \propto \Phi(\frac{1}{\pi} (1-F_{up})\rho cos(z)+ LOP(z)) (1)

Where
L_{OLS} is the relative OLS radiance,
\Phi is the radiant flux or luminosity of light fixtures,
\rho is the underlying reflectance.
LOP(z) is the angular light output pattern giving the emission per unit of solid angle at a given zenith angle z, and
F_{up} is the uplight fraction. This value is obtained from the integration of LOP(z) from z=0 to z=\pi/2

 (a) (b)

Figure 3: DMSP-OLS V4 (a) relative radiance and (b) corresponding number of data used in the composite.

Equation 1 may be inverted in order to give a relative estimate of the light fixture luminosity or radiant flux. We assumed a zenith angle of z=0.

\Phi = \frac{R_{\lambda} L_{OLS}}{(\frac{1}{\pi} (1-F_{up})\rho + LOP(0))} (2)

where R_{\lambda} is the calibration constant for the key wavelength \lambda .

3.6  Lighting inventory

With the help of our local expert Francisco Javier Diaz-Castro we tried to simplify the lighting inventory by characterizing it from a combination of 4 generic LOP with respective Uplight percentage of 0%, 1%, 6% and 50% (see table A1 in appendix A) and 3 lamp spectrums (high pressure sodium (HPS), low pressure sodium (LPS) and mercury/metal halide (HG)). The 50% uplight case stand basically for commercial advertizing. The lamp spectra to use is given by the origin of the spectral line studied. In that study, sodium lines are attributed to HPS and mercury lines to HG. As said in section 3.3, we did not used LPS 589 nm line for that study. We distinguished 2 distinct combination corresponding to 2 distinct periods (before and after midnight). Three different geographical zones have been also used (La Palma, Tenerife west and all other places). The parameters used to characterize the simplified inventory are summarize in tables 5 and 6.

Table 5: Contribution to total flux before midnight

 Zone ResultantUplight HPS LPS HG Commercial (50%UP) Street 1(1%UP) Street 6 (6%UP) Street 0 (0%UP) Total of Satellite La Palma 3.0% 20% 80% 0% 5% 15% 5% 75% 100% Tenerife W 3.3% 95% 0% 5% 5% 15% 10% 70% 100% Tenerife E & other islands 6.2% 70% 0% 30% 10% 15% 15% 60% 100%

Table 6: Contribution to total flux after midnight

 Zone ResultantUplight HPS LPS HG Commercial (50%UP) Street 1 (1%UP) Street 6 (6%UP) Street 0 (0%UP) Total of satellite La Palma 0.4% 10% 90% 0% 0% 8% 2% 40% 50% Tenerife W 3.5% 95% 0% 5% 3% 10% 8% 40% 61% Tenerife E & other islands 6.7% 70% 0% 30% 9% 10% 10% 50% 79%

The OLS before midnight total relative luminosity derived from equation 2, have been multiplied by the spectra fraction and Total of satellite fraction to generate the relative luminosity at each spectral line for each zone and each period. So, lets give some examples of how we determined the inventory.

1. If we want to derive the HPS 569 nm luminosity map after midnight for La Palma island, we only have to multiply the map generated from equation 2 by 10% (Table 6->line 2->column 3) and by 50% (Table 6->line 2->column 10).
2. To determine the HG 546 nm line luminosity before midnight in Tenerife west we are multiplying equation 2 by 5% (Table 5->line 3->column 5) and by 100% (Table 5->line 3->column 10)

At this step, there is a remaining factor which is not known; namely the ground level strenth of a given spectral line. This strength is relative to the typical mixed spectrum of lamp bulbs and we do not know this parameter. So we decided to infer that strenght factor from a model-measurement intercalibration but this step will be discussed later in section 3.8.

The second element of the inventory was to determine a typical LOP for each geographical modeling zones and period. To determine those 6 different LOP (3 zones for 2 periods), we took the weighted average of generic lamps LOP where the weights were given by the fraction of each lamp in that zone (column 6-9 of table 5 or table 6). The resultant LOP are shown in figure 4. Globally all these LOP may almost look similar but there are some important differences in their upward emission functions. Comparison of figure 4 (b) and 4 (d) for zenith angles smaller than 90o (in that figure the zenith is upward) indicate that the upward flux is clearly reduced after midnight for the La Palma zone. This is the opposite for "other islands" zone but to a smaller magnitude and there is almost no upward change for Tenerife west zone. The initial LOP of each generic lamps and equivalent lamp fixture photograph are presented in table A1 of appendix A.

 (a) (b) (c) (d)

Figure 4: (a) Before midnight LOPs used in the modeling experiment and (b) zoom on the upper hemisphere part of before midnight LOPs. (c) After midnight LOPs (d) zoom on the upper hemisphere part of the after midnight LOPs.

3.7  Digital elevation model

The digital elevation model (DEM) was obtained mostly from the 3 arc second resolution product of the Shuttle Radar Topography Mission (SRTM V2) (Farr et al. 2007). SRTM vertical resolution is 16 m in absolute values and 10m in relative values. Data points lacking from SRTM product were taken from the WPS service of Cartográfica de Canarias (GRAFCAN) (grafcan 2010). The resultant DEM is shown in figure 5.

 (a) (b)

Figure 5: Digital elevation model. (a) SRTM and grafcan elevation data and (b) holes (white) in the SRTM dataset which have been replaced by grafcan data.

3.8  Model calibration

Since we do not have any information on lamp flux into each spectral lines, we decided to proceed to a post modeling calibration with measured sky radiances in those spectral lines. The idea is to find a ratio (R_{\lambda}) between the modeled radiances and corresponding measurements for each key spectral line. We used the 20o elevation after midnight data for the most stable clear night at OT. We choose after midnight data because we noticed that low altitude clouds were generally vanishing in the 2nd half of the night. We also retain 20o elevation data to be more sensitive to the light fixture inventory and to benefit of a better signal to noise ratio.

Knowing R_{\lambda}, we can then convert modeled data into real radiances. Unfortunately the model - measurement comparizon is subject to many error. We identify the following sources of errors for the modeled data:

• errors in lamp inventory;
• This error is quite difficult to estimate, we did not find a relevant way to evaluate it.
• use of the nearest MODIS band to estimate ground reflectance at a given key wavelenght;
• Examination of MODIS reflectance show approximate reflectance variations of 0.02 for typical differences in wavelength from our key modeled wavelength and the nominal MODIS wavelength. This reflectance error imply a relative lamp flux error of 10%. Since lamp flux is proportionnal to sky radiance, this give 10% error on radiances.
• limited set of modeled AOD which leed to nearest AOD comparison
• For a typical error of 0.05 on AOD (from the real AOD to the modeled AOD set), a relative radiance error of 4% is expected.
• AOD changes during the night;
• According to our simulations, typical variations of 0.05 to 0.1 on AOD during a 12h period give a radiance relative error of 8%. Note that the typical variations of AOD have been taken from the daytime measurements on observation for preceeding and following days. It is difficult to confirm that similar variations are undergoing during the night.
• possible impact of low altitude clouds on MODIS reflectances products;
• This error was not evaluated in the present work.
• intrinsec model errors
• It is very difficult to evaluate this error but we are currently doing model evaluation/validation experiments in that scope.

So the known modeled radiance error is given by \Delta L_{mod} \geq 0.2 L_{mod} (0.1+0.04+0.08~0.2)

Observational errors may be associated to change of some environmental parameters during the night. The instrumental error may be associated to:

• thermal noise and cosmics rays
• presence of low altitude clouds which partly masked the underlying city light and which were highly variables during the night;
• Of coarse this experimental error is specific to the Canary islands context.
• shutdown of some light fixture during the night

We determined the R_{\lambda} for each key spectral lines and the results are show in table 7. Ratios from table 7, give us the complete information to generate spectral line based flux inventories when using the methodology proposed above with equation 2. We used ratio variation during the night to estimate the error. This error is more or less 40%. This large error is the net combination of modeling and observational errors. Are these ratios transferables for other modeling sites? This is not obvious but maybe yes to a certain extent. Answering to that question may require some more case studies validation. In principle ratios should rely on mean characteristics of lamp spectrum installed in the domain. So the transferability question could be answered by the following question: Are HPS, HG and Metal Halides (MH) spectrums in the Canary islands similar to everywhere in the world? If yes, then the table 7 ratios could be transferables anywhere.

Table 7: Model calibration constants for each key spectral line.

 Line wavelength (nm) SAND/ILLUMINA ratio+/- 40% 435 0.043 498 0.014 546 0.031 569 0.033 615 0.008

We used these ratios to convert uncalibrated model output to calibrated model results.

4.  Results and discussion

This section aim to present some samples of the modeling experiment results. These results will be presented into 3 subsections. In the first one we will discuss of the differences between before and after midnight results. Then we will present the relative contribution to zenith 546 nm and 569 nm sky radiance in OT and ORM and finally we will show some of our all sky plots for the same lines and sites. Other plots may be obtained on the following URL http://cegepsherbrooke.qc.ca/~aubema/index.php/Prof/Tenerife2010report

4.1  Comparison of OT and ORM zenith spectrum with KPNO

As a first step we wanted to compare OT and ORM zenith spectrums with previous measurement taken in Kitt Peak National Observatory (KPNO) in 2005. In 2005 we were using the version 1 of SAND (SAND-1) which had a lower signal to noise ratio and a lower spectral resolution (5 nm compared to 2 nm for SAND-3). The FOV of SAND-1 was about 10o which is many times larger than SAND-3. A larger FOV is not a big problem since sky radiance is a very smooth function of the viewing angle around zenith. The KPNO spectrum have been taken from the Sky spectral luminance database (SSLD 2010) which is a collection of low resolution spectrums of the night sky acquired on some sites mainly over astronomical observatories of North America. In figure 6, the plots of OT and KPNO have been shifted up by 1x10-8 and 2x10-8 to facilitate comparison. The first thing that is noticeable on these spectrums is that HPS and HG spectral lines are stronger in OT compared to KPNO. The integrated flux found of OT zenith HPS 498 line is 4.6x10-9 +/- 3x10-10 W/m2/str compared to KPNO 3.0x10-9 +/- 9x10-10 W/m2/str. The OT/KPNO ratio is then 1.5x with an uncertainty of 30%. ORM is clearly lower in term of its contribution at 498 nm HPS line. Our line integration give 8x10-10 +/- 4x10-10 W/m2/str. This huge relative error is explained by the fact that artificial spectral line fluxes are very low in ORM (except for the NAD 589 nm LPS line) and then the signal is almost comparable to termal noise. But the errors given here are many times lower than the one defined in the model calibration section. This is because of the method used to do the line integration. In the calibration process we used an automated method and integrated the line over a larger spectral window which imply more probability of cosmic rays contamination. Moreover in the present error estimation, we visually removed all pixels contaminated with cosmic rays. So that errors given here are basically only coming from thermal noise. In fact we evaluated the error on the basis of the pixel to pixel fluctuations in the pseudo continium region of the spectrum. OT/ORM ratio is about 6x but the relative error on that value is 50%. The OT measurement was taken ~1h before midnight for an integration time of 2h so that the value is underestimated compare to the ORM before midnight measurement. A before/after 498 nm zenith radiance ratio of 1.4x is expected according to our modeling (AOD=0.1). The corrected value for before midnight should be 1.2x largeur as half the integration time was done before midnight. According to that, OT/KPNO and OT/ORM before midnight should be respectively 1.8x and 7. Of coarse, a change of spectral line should modify all the ratios and fluxes given above. A qualitative comparison of the spectrums show for example that in the HG 436 nm line the OT flux is many times larger than KPNO. This probably indicate that there is a largeur proportion of HG or MH lamps in the vincinity of OT compared to KPNO.

Figure 6: Comparison of OT and ORM spectrums with previously acquired Kitt Peak National Observatory (KPNO) spectrum. On this plot, we draw vertical magenta lines at our key wavelenght and a yellow line at the NAD 589 nm LPS.

4.2  Comparison of before and after midnight spectrum

The measurement comparison before and after midnight for an elevation angle of 20o and an azimuth of 180o is given in figure 7 for both observatories. Those plots gave us a surprising result because the after midnight reduction was expected to be larger. In fact for the OT observatory, no significant difference have been noticed. For that site and that viewing angle, our simulation indicate that we are mainly influenced by the southern part of Tenerife Island (Arico, Granadilla de Abona, Aeropuerto Sur etc (as shown on figure 8 (a) and (b))). Figure 8 represents the model derived relative contribution to the azimut 180o and elevation 20o at 546 nm HG line and 569 HPS line. In that figure, each pixel correspond to a 1 square km foot print and its color give the percentage contribution to the total 546 nm or 569 nm line radiance. The southern part of Tenerife is not under effect of the Canary Sky Law so that the reduction is expected to be smaller (according to our estimated light fixture inventory, we were expecting a ratio after/before of the order of 80% in that zone). It is possible that these municipalities do not have a lot of lamps shutting down after midnight or have a proportion far below the east Tenerife average.

For ORM, one can see a ratio after/before of 75% for the NAD 589nm line when a 50% ratio was expected according to our inventory. One possible explanation is that we often noticed the presence of low altitude clouds over the nearby cities at the beginning of the night wich evaporates during the night and vanished completely at the end of the night. So the before midnight sky radiance is then underestimated compared to the one at the end of the night. Maybe it can explain at least a part of that observation. Benn and Ellison, 1998 reported that according to many authors, the natural sky glow may randomly vary by a few 10s of % during the night. Their experiment during 1995 western Canary islands blackout reported that natural sky glow contribute to 30% of the total NAD 589 nm line flux (30 Rayleigh over a total of 100 Rayleigh before and after the blackout). According to Allen 1973, there is a strong seasonal variations of the natural sky glow which is about 30 Rayleigh in summer and ~ 180 in winter. Pedani 2004 reported that the natural NAD 589 nm flux was between 90 and 100 Rayleigh in september and he noticed an increase of artificial NAD 589 nm line by a factor of 1.5-2 compared to 1998 results. Pedani 2004 also reported the frequent presence of what he called «sea of cloud» below the thermal inversion layer during winter months while they are more dispersed in summer. So basically if we assume that the light pollution level did not change since 2004, the artificial contribution in the NAD 589 nm line should be between 105 and 140 Rayleigh compared to a natural contribution ranging from 30 to 180 Rayleigh. According that observations have been made in march, we can roughly assume by taking the averaged values that the natural contribution to the NAD 589 nm line was ~ 50% (120R/(120R+105R)) then \frac{L_{artif}}{L_{nat}} \approx 1 . That level of natural contribution explain the observed reduction after midnight if we assume that the natural contribution was constant during the night. In fact, we obtain

 \frac {L_{after}}{L_{before}} = \frac {L_{nat}+L_{artif} \times 0.5}{L_{nat}+L_{artif}} = \frac {1.5 L_{nat}}{2 L_{nat}} = 0.75 .


As we can notice, spectrums from OT and ORM are quite different. Basically the only easily detectable line with our instrument in ORM was the NAD 589nm line. Figure 8 (c) show the model derived relative contribution to the azimut 180o and elevation 20o HG 546 nm line. This figure show that a large part of the 546 nm radiance originate from El Hierro even if this island is quite small and far from ORM (~ 105 km). In fact no mercury/metal halide lamps was included in the La Palma inventory. It is interesting to look at the equivalent figure for the HPS 569 nm line (figure 8 (d)) where for the same site and same viewing angle, the main contribution is originating from Los Llanos de Aridane (~ 12km S-SW direction from ORM). The 546 nm and 569 nm reduction after midnight is evident for ORM on figure 7 b) but the very low intensity of those lines after midnight render it difficult to evaluate with confidence the relative reduction.

HPS and HG lines are easily visible on the OT spectrum. LPS lamps are the most common spectra type on La Palma island (at least 80% of the total lumens).

 (a) (b)

Figure 7: Comparison of observed spectral radiances before (red line) and after midnight (green line) for (a) Observatorio del Teide and (b) Roque de los Muchachos.

 (a) (b) (c) (d)

Figure 8: Radiance contribution map (%) to the sky radiance observed at elevation 20o and azimuth 180o per square km for a sea level AOD of 0.1. (a) from OT at a wavelength of 546 nm (HG) and (b) at a wavelenght of 569 nm (HPS), (c) from ORM at 546 nm and (d) 569 nm.

4.3  Relative contribution results

In order to provide to the astronomical community a powerfull diagnostic tool to infer the geographical origin of the radiance at a given wavelenght, at a given viewing angle from a given observing site, we computed two maps as a standard output of the model. The first one is giving the contribution (in percent) of each squared kilometer sea level footprint of the domain to the sky radiance (hereafter called Radiance Contribution Map (RCM)) while the second one give the contribution (in percent) of each squared kilometer sea level footprint of the domain to the sky radiance per lumen installed (hereafter called Radiance per lumen Sensivity Map (RSM)). RCM allow the identification of the origin of the radiance while the RSM give a map of the most sensitive zones in term of possible increase or decrease of the radiance with any change in the light fixture inventory.

Figure 9 show RCM for zenith viewing angle and for both observatories at HG 546 nm and HPS 569 nm. As a first observation, it is interesting to note that, for both observatories, the contribution of Gran Canaria island is clearly neglectable even if this island have an important lighting infrastructure.

For ORM, we can explain this by the fact that Gran Canaria is far (~ 235km) and also by the fact that it is masked by the Tenerife island. For the case of OT, this is simply the fact that Tenerife have a lot of lighting devices so that they have larger impact giving their proximity compared to Gran Canaria.

Surprisingly La Gomera and El Hierro could not be neglected for their contribution to ORM HG 546 nm light pollution. In fact we can see on figure 9 (b) that a large part of the zenith radiance at this wavelenght originate from La Gomera. The most contributing region is La Calera in the western side of the island. Northern part of La Gomera also contributed significantly but less than La Calera and surroundings. But we have to keep in mind that HG lines are weak in ORM sky, so overall those sources are not polluting too much in absolute values.

In the HPS 569 nm line, the most contributing site to ORM zenith radiance is located at Los Llanos de Aridane (figure 9 (d)).

For OT in the HG 546 nm line, Guimar and Arafo are responsible for a large part of the zenith radiance. It is interesting to note that the Puerto de la Cruz surroundings have a low impact in that spectral line. This is a nice consequence of the Canary Sky Law.

In the HPS 569 nm line the pattern is different. Guimar and Arafo remain two important sources but they are just a little bit more contibuting than the combination of La Orotava and Puerto de la Cruz.

 (a) (b) (c) (d)

Figure 9: Radiance contribution (RCM) in percent per km2 to the zenith light pollution levels before midnight at OT (a and c) and ORM (b and d) at HG 546 nm line (a and b) and HPS 569 nm line (c and d) (sea level AOD=0.1).

In a very simple case with no obstacles, no topography, no reflection, no atmospheric absorption/scattering and for point like sources, RSM should be essentially proportionnal to 1/r2 (r is the distance to the observer), but when accounting for heterogeneity of the environment RSM will be more complex.

It is very important to realize that no RSM values could not be computed for regions with no lamp luminosity in the lamp inventory of OLS radiance map. Let us now discuss of the RSM maps shown in figure 10. In these maps, we can identify the most sensitive places to any change in the lighting installations in term of their impact on the zenith radiance.

ORM zenith sky radiance in HG 546 nm line (figure 10 (b)) is sensitive to many places located on La Gomera island. Amongs them lets mention in decreasing sensitivity order:

1. the junction of TF-711 and TF-713 roads beteen Epina and Acardece:
2. a place between Arguamul and Valle de Abojo;
3. another spot between Tazo and Arguamul;
4. Ambrosio;
5. and Benchijugua.

In the HPS 569 nm line (figure 10 (d)) the most sensitive spots are located along a circle with a radius of ~8 km centered 2 km SE from Roque de los Muchachos look-out. This circle shaped distribution is an artefact originating from a light luminosity hole around the Caldera de Taburiente as shown in figure 3 (a). So basically this means that other sensitive zone exists inside the caldera but fortunately this is a national park and so we do not expect any instrusive light installation there. Most of the highest sensitivity sites are located on the south-western half of that circle. The most contributing sites are in order of decreasing importance:

1. a place between Los Barros and Amagar;
2. between El Pueblo and Bellido;
3. 3 km north of El Paso;
4. 1.5 km eastward from Puntagorda;
5. and 1.5 km E-SE from San Antonio.

OT zenith sky radiance in HG 546 nm line (figure 10 (a)) is mostly sensitive to a place located 4.5 km NW of OT on the TF-21 road 8.5 km before entering Aguamansa but there is no lighting installation up there now.

The HPS 569 nm sensitivity at OT (figure 10 (c)) is more complex since it is more or less equally distributed along two croissant shape of ~ 4 to 6 km of radius from OT. Again this shape is an artefact of the absence of lamp luminosity in the center of the island. The northern croissant if more important in term of sensitivity.

 (a) (b) (c) (d)

Figure 10: Radiance sensitivity (RSM) per lumen in percent per km2 to the zenith light pollution levels before midnight at OT (a and c) and ORM (b and d) at HG 546 nm line (a and b) and HPS 569 nm line (c and d) (sea level AOD=0.1).

4.4  All sky results

We generated all sky radiance plots by using all the model viewing angles calculations for a given wavelength, AOD, site and period. The modeled data have been fitted with a 2D 5 order polynomial. A part of those plots are presented in figure 11. We decided to show the before midnight radiances for the two observatories at HG 546 nm and HPS 569 nm. These two lines are representative of the two main typical lighting spectra (when ignoring LPS of coarse). We choose to present the plots for an AOD of 0.1 which seems to be a frequent value for Canary islands. First of all, lets say some words on radiances levels at zenith. We found a HG 546 nm zenith radiance of 7.5x10-10 W/m2/str for OT and 2.4x10-13 W/m2/str for ORM. This basically means that HG zenith light pollution level at ORM is 3000 times lower than OT (8.7 magnitude). For the 569 nm HPS line, the OT zenith radiance is 2.9x10-09 W/m2/str while it is 2.2x10-10 W/m2/str at ORM. The HPS zenith light pollution at ORM is then 12 times lower than in OT (2.9 magnitude). The ratio for HPS is lower than for HG because there is no HG lamps in La Palma and the most contributing HG lamps are located in the remote La Gomera island. This is of coarse not the case for OT where we can find HG lamps right on the Tenerife island.

 (a) (b) (c) (d)

Figure 11: All sky radiance maps before midnight for OT (a and c) and ORM (b and d) at HG 546 nm (a and b) and HPS 569 nm (c and d) lines (AOD=0.1).

The sky of ORM in the HG 546 nm line reach a radiance maximum in the E-SE direction while the minimal value may be found in the W-NW direction. In the HPS 569 nm line, the maximum is reached toward south while the minimum is located in the NE direction at a zenith angle of ~30o. For OT, the HG 546 nm line reach a radiance maximum in the E-NE direction but there is a second maximum toward south which is almost as high as the E-NE. The minimum is toward SE at a zenith angle of ~40o. In the HPS 569 line, the maximum is reached toward north and the minimum is also in the SE direction at a zenith angle of ~40o.

5.  Conclusion

5.1  Summary

We tried to use a sky radiance heterogeneous model to infer the point to point contribution of Canary islands to the artificial sky radiance at Observatorio del Teide (Tenerife) and Observatorio Roque de los Muchachos (La Palma). Since we did not know the exact lamp flux in each spectral lines, we conduct an in-situ hyperspectral sky radiance measurements experiment to calibrate the model and to evaluate its inherent error. The determination of the point to point contribution and sensitivity is a new result that we hope will be used as an intelligent decision tool to improve night sky quality and offer a better protection to the few remaining dark site on the earth. Based on this analysis, we identified the sites that should be protected from new lighting installation for both observatories. One striking result is that if one want to protect the ORM La Palma observatory, a special attention should be brought to avoid installation of HG or MH lamps in Valle Gran Rey, Alojera and Lomo del Gato which are remote and mostly uninhabited places on La Gomera island. This work also showed that for the sodium lines, one should concentrate the protection works along a circle or 7 km of radius centered near the Roque de los Muchachos. Up to now, most of these sites are uninhabited but these things can change.

This study had also provided, all sky radiance plots and a very extensive all sky spectral measurement database for the two observatories. The large amount of data produced for that study have not been presented here but they may be obtained from http://cegepsherbrooke.qc.ca/~aubema/index.php/Prof/Tenerife2010report in the add-on section. Point to point contribution and sensitivity data have been formated as kml google earth overlays and may then be easily georeferenced for unexpert use from the same URL.

5.2  Ongoing works

Interesting works remains to be done and amongs them, we should try in the future the use of Lucy-Richardson filter to reduce the overspill of DMSP-OLS data. We should also find a way to filter out data that have been contaminated by low level clouds (city light masking effect). One interesting experiment should be to repeat the validation and sampling process during summer time where other authors reported that low level clouds are more dispersed. In fact this phenomenon is largely responsible for errors in the model calibration process and then in model absolute results. Model evaluation/validation work have also to be pursued to get a systematic evaluation of intrinsec model errors. It should be very interesting to extend the modelling process to all known contributing wavelengths in order to integrate sky radiance in the UBV photometric system. More specifically in the B and V filters. Another interesting experiment should be to integrate modeled spectrums multiplied by the CIE 1951 scotopic luminosity function in order to generate human eye perception of the all sky light pollution. It may be done simply by cutting the visible spectrum in equal spectral bands and then run the model over center wavelenght of these bands (for example 33 bands of 10 nm width). Of coarse each of these bands should be calibrated with sky spectral observation separately. Even if the implied computation time is quite huge, we already have the required observation to calibrate them.

6.  Acknowledgments

Funding for this research was provided by the fond québécois pour la recherche sur la nature et les technologie (FQRNT), by Éducation, loisirs et sports Québec, and by the Instituto de Astrofisica de Canarias (IAC). A special thanks go to Casiana Munoz-Tunon, which is the head of IAC's sky quality group. We want to thanks Francisco Javier Castro Diaz for his help in validating our simplified lighting inventory and for his help in logistics during my stay in Tenerife. We want to thanks Alex Oscoz and Juan Carlos Perez Arencibia respectively site managers of Teide and Roque de los Muchachos observatories for their help in organising the observing runs. Computation time have been provided by the Reseau Quebecois de Calcul Haute Performance (RQCHP) a member of Compute Canada. We thanks Francisco Javier Expósito González and Philippe Goloub for theirs effort in establishing and maintaining La Laguna and Izana AERONET sites. We thanks MODIS land product team. MODIS reflectance data are distributed by the Land Processes Distributed Active Archive Center (LP DAAC), located at the U.S. Geological Survey (USGS) Earth Resources Observation and Science (EROS) Center (lpdaac.usgs.gov). We thanks NOAA's National Geophysical Data Center for DMSP-OLS image and data processing and more specifically Dr. Chris Elvidge for his support. DMSP data are collected by US Air Force Weather Agency.

7.  References

• Allen C.W. (1973) Astrophysical Quantities, 3rd edition (Athlone Press), p. 134
• Aubé, M. (2007) Light pollution modeling and detection in a heterogeneous environment, Proceedings of Starlight a common heritage, pp. 351-358.
• Aubé, M.; Franchomme-Fosse, L.; Robert-Staehler, P.; Houle, V. (2005) Light pollution modelling and detection in a heterogeneous environment: toward a night-time aerosol optical depth retreival method, Atmospheric and Environmental Remote Sensing Data Processing and Utilization: Numerical Atmospheric Prediction and Environmental Monitoring. Edited by Huang, Hung-Lung A.; Bloom, Hal J.; Xu, Xiaofeng; Dittberner, Gerald J. Proceedings of the SPIE, Volume 5890, pp. 248-256
• Benn, C.R.; Ellison S.L. (1998) La Palma technical note 115.
• Berk, A.; Anderson, G.P.; Bernstein, L.S.; Acharya, P.K.; Dothe, H.; Matthew, M.W.; Adler-Golden, S.M.; Chetwynd, J.H.; Richtsmeier, S.C.; Pukall, B.; Allred, C.L.; Jeong, L.S.; Hoke, M.L. (1999) MODTRAN4 radiative transfer modeling for atmospheric correction, Proc. SPIE Vol. 3756, p. 348-353, Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research III, Allen M. Larar
• Cinzano, P. (2000) The propagation of light pollution in diffusely urbanised areas, Memorie della Societa Astronomia Italiana, Vol. 71, p.93
• Cinzano, P.; Elvidge, C.D. (2004) Night sky brightness at sites from DMSP-OLS satellite measurements, Monthly Notices of the Royal Astronomical Society, Volume 353, Issue 6, pp. 1107-1116.
• Farr, T.G; Rosen, P.A.; Caro, E.; Crippen, R.; Duren, R.; Hensley, S.; Kobrick, M.; Paller, M.; Rodriguez, E.; Roth, L.; Seal, D.; Shaffer, S.; Shimada, J.; Umland, J.; Werner, M.; Oskin, M.; Burbank, D.; Alsdorf, D. (2007) The Shuttle Radar Topography Mission, Reviews of geophysics, vol. 45, 33 pp.
• Garstang, R. H. (1986) Model for Artificial Night-Sky Illumination, ASTRON. SOC. PACIFIC. PUB. V. 98, NO.601/MAR, P. 364.
• grafcan (2010) http://idecan5.grafcan.es/ServicioWPS/mdt?service=wps&version=1.0.0&request=DescribeProcess
• Holben, B. N.; Tanré, D.; Smirnov, A.; Eck, T. F.; Slutsker, I.; Abuhassan, N.; Newcomb, W. W.; Schafer, J. S.; Chatenet, B.; Lavenu, F.; Kaufman, Y. J.; Castle, J. Vande; Setzer, A.; Markham, B.; Clark, D.; Frouin, R.; Halthore, R.; Karneli, A.; O'Neill, N. T.; Pietras, C.; Pinker, R. T.; Voss, K.; Zibordi, G. (2001) An emerging ground-based aerosol climatology: Aerosol optical depth from AERONET, Journal of Geophysical Research, Volume 106, Issue D11, p. 12067-12098.
• Kocifaj, M. (2007) Light-pollution model for cloudy and cloudless night skies with ground-based light sources, Applied Optics IP, vol. 46, Issue 15, pp.3013-3022
• Luginbuhl, C.B.; Duriscoe, D.M.; Moore, C.W.; Richman, A.; Lockwood, G.W.; Davis, D.R. (2009) From the Ground Up II: Sky Glow and Near-Ground Artificial Light Propagation in Flagstaff, Arizona, Publications of the Astronomical Society of the Pacific, Volume 121, issue 876, pp.204-212.
• McNally, D. (1994) The vanishing universe: adverse environmental impacts on astronomy, The vanishing universe: adverse environmental impacts on astronomy, Proceedings of the conference held at Unesco, Paris, June 30-July 2, 1992, Cambridge; New York: Cambridge University Press.
• Pedani, M. (2004) Light pollution at the Roque de los Muchachos Observatory, New Astronomy, Volume 9, Issue 8, p. 641-650.
• SSLD (2010) Sky spectral luminance database, http://www.cegepsherbrooke.qc.ca/~graphycs/aubema/recherches/data_usage.html, Cégep de Sherbrooke, Canada.
• Vermote, E. F.; and Vermeulen, A. (1999). Atmospheric correction algorithm: Spectral reflectances (MOD09), ATBD version 4.0., NASA contract NAS5-96062, http://modis-sr.ltdri.org/MAIN_PUBLICATIONS/Papers/atbd_mod09.pdf
• Walker, M. F. (1977) The effects of urban lighting on the brightness of the night sky, Astronomical Society of the Pacific, Publications, vol. 89, June-July 1977, p. 405-409.

8.  Appendix A

Figure A1: Potentially saturated pixels in red from the DMSP-OLS version 4 data base.

Table A1: Generic lamps used in our simplified inventory

 Generic name Model UpLight IESNA file ILLUMINA file Image Commercial - 50% - iso_fctem_01.dat Street 1 Indalux Villa 1.1% 3008554CANARIAS.ies Indalux-Villa_fctem_01.dat Street 6 COOPER cobrahead 6.3% RY15H3AL.ies cobrahead_fctem_01.dat Street 0 GE Euro-2 0.2% 9V148_70WHPS-curvedglass-EURO2.IES euro2_fctem_01.dat

9.  Add-on and full data access

9.1  Some google earth kml overlays

Maps showing which part of the islands contributed to the measured radiance.

• Zenith HG 546 nm at AOD=0.1 for OT
• Zenith HPS 569 nm at AOD=0.1 for OT
• Zenith HG 546 nm at AOD=0.1 for ORM
• Zenith HPS 569 nm at AOD=0.1 for ORM

Showing the most important part of the islands to protect in order to constrains light pollution.

• Zenith HG 546 nm at AOD=0.1 for OT
• Zenith HPS 569 nm at AOD=0.1 for OT
• Zenith HG 546 nm at AOD=0.1 for ORM
• Zenith HPS 569 nm at AOD=0.1 for ORM

Note: To visualize RCM and RSM maps as google earth overlays please save .kml files on your computer and double click on them. You need Google Earth version 5 or later installed. For some unknown reasons there is a problem with linux version of Google Earth and the overlays superpositions, we hope that it will be fixed in a future version of that application.

Model output plots using guide

Content summary:

1. Relative contribution maps (RCM)
• Give the origin in percent per km^2 to a given sky radiance (direction, aerosol optical depth, site, wavelength)
2. Relative sensitivity maps (RSM)
• Give the sensitivity of the sky radiance in percent per km^2 to any change in the lighting infrastructure (direction, aerosol optical depth, site, wavelength). It give a good idea of how much radiance change with an addition of 1 lumen at a given grid cell of 1 km^2 in comparison to the same addition anywhere else.
3. AllSky
• Give a plot of the sky above for each radiance computed (W/str/m^2/nm) and for mag V for each site, direction, aerosol optical depth, and wavelength. This is a model result but the model have been calibrated with our sky radiance measurement so that it is very representative of the reality (in accordance with model and measurement errors).

The model outputs have been placed in the following directory structure:

1. ORM ->(Observatorio Roque de los Muchachos)
1. AllSky ->(all sky plots)
1. AOD0.025 ->(sea level aerosol optical depth of 0.025)

Naming convention: ex.: ORM-after_00-rd4000-ta0.025-wl435.png

• ORM=Observatory
• after_00=after_midnight
• rd4000=2nd order scattering radius = 4 km, rd0=no 2nd order of scatering
• ta0.025=sea level aerosol optical depth of 0.025r
• wl435=wavelenght of 435nm (Vmag stands for V magnitude)
1. AOD0.050 ->(sea level aerosol optical depth of 0.050)
2. AOD0.100 ->(sea level aerosol optical depth of 0.100)
3. AOD0.200 ->(sea level aerosol optical depth of 0.200)
1. RCM ->(Relative contribution maps: i.e. from where come the light pollution)
1. AOD0.025 ->(sea level aerosol optical depth of 0.025)
1. 435nm ->(HG 435nm line)

Naming convention: ex.: ORM-RCM-after_00-rd4000-ta0.025-wl435-el20-az0.kml

• ORM=Observatory
• RCM=relative contribution map
• after_00=after midnight
• rd4000=2nd order scattering radius = 4 km
• ta0.025=sea level aerosol optical depth of 0.025
• wl435=wavelenght of 435nm
• el20=elevation angle of 20 deg. (i.e. zenith angle of 70 deg.)
• az0=azimuth angle of 0 deg. (0=North, 90=East and so on)
• .klm= layer file to open with google earth (first save the file and then open it with google earth); there is also a .png file which is the plot displayed by the .kml file.
1. 498nm ->(HPS 498nm line)
2. 546nm ->(HG 546nm line)
3. 569nm ->(HPS 569nm line)
4. 615nm ->(HPS 615nm line)
1. AOD0.050 ->(sea level aerosol optical depth of 0.050)
2. AOD0.100 ->(sea level aerosol optical depth of 0.100)
3. AOD0.200 ->(sea level aerosol optical depth of 0.200)
1. RSM ->(Relative sensitivity maps: i.e. the most sensitive places to any change in the lighting installation)
1. AOD0.025 ->(sea level aerosol optical depth of 0.025)
1. 435nm ->(HG 435nm line)

Naming convention: ex.: ORM-RSM-after_00-ta0.025-wl435-el20-az0.kml

• ORM=Observatory
• RSM=relative sensivity map
• after_00=after midnight
• rd4000=2nd order scattering radius = 4 km
• ta0.025=sea level aerosol optical depth of 0.025
• wl435=wavelenght of 435nm
• el20=elevation angle of 20 deg. (i.e. zenith angle of 70 deg.)
• az0=azimuth angle of 0 deg. (0=North, 90=East and so on)
• .klm= layer file to open with google earth (first save the file and then open it with google earth); there is also a .png file which is the plot displayed by the .kml file.
1. 498nm ->(HPS 498nm line)
2. 546nm ->(HG 546nm line)
3. 569nm ->(HPS 569nm line)
4. 615nm ->(HPS 615nm line)
1. AOD0.050 ->(sea level aerosol optical depth of 0.050)
2. AOD0.100 ->(sea level aerosol optical depth of 0.100)
3. AOD0.200 ->(sea level aerosol optical depth of 0.200)
1. OT ->(Observatorio del Teide)

9.4  Conversion from model all sky plots to V brightness (mag arcsec-2)

We used the ORM and OT V sky brightness measurements from Francisco Javier Diaz Castro to convert our modeled radiance data into V sky brightness data. According to Diaz Castro measurements, the zenith V sky brightness after midnight is 21.68 mag arcsec-2 in ORM and 21.4 mag arcsec-2 for OT. If we assume a natural sky brightness of V = 21.9 mag arcsec-2 taken from Table 2 of Benn and Ellison, 1998, we can then estimate the V sky brightness from our artificial sky radiance. The natural sky brightness level is relative to solar-minimum sky brightnesses at ecliptic latitude > 40o and ecliptic longitude > 120o from that of the sun (change in zodiacal-light contribution affect the value by < 0.1 mag).

The modeled all sky plots correspond to artificial sky radiances in each key wavelenght so it should be closely related to the V sky brightness given above. Epecially if we retain key wavelenght near the V band center wavelenght (551 nm). For OT, we suggest to use a ponderation of the HG 546nm and HPS 569nm line radiance to estimate a relative V band radiance and then convert it to absolute values with the zenith Castro Diaz measurements. Assuming a gaussian B band spectral response centered on 551 nm with FWHM of 88 nm, the V band radiance at zenith should be proportionnal to:

L_{r}(90)_V = 0.99 L_{r}(90)_{546} + 0.89 L_{r}(90)_{569} (1)

L_{r}(90)_V stands for relative V band radiance toward zenith

and at any elevation angle

L_{r}(el)_V = 0.99 L_{r}(el)_{546} + 0.89 L_{r}(el)_{569} (2)

The coefficients 0.99 and 0.89 are respectively the transmittance of the V filter at 546 nm and 569 nm.

Of coarse those relative radiance may be converted to real radiance with a relevant but unknown constant (C).

L(90)_V = C L_{r}(90)_V (3)

and

L(el)_V = C L_{r}(el)_V (4)

But the radiance above is only accounting for artificial radiance so that to compare with real sky measurements, we have to add the natural radiance. The natural magnitude is estimated to 21.9. We can write the natural V magnitude at zenith as:

m_N(90)_V = - 2.5 log \left(\frac{L_N(90)_V}{L_{0}} \right) = 21.9 (5)

Also, the zenith V magnitude recorded at OT is 21.40 according to Castro Diaz measurements. The V magnitude may be written as:

L(90)_V=L_N(90)_V+C L_{r}(90)_V (6a)

m(90)_V = - 2.5 log \left(\frac{L(90)_V}{L_{0}} \right) = 21.40 (6)

For simplicity we fitted a 2nd order polynomial on the elevation angle vs natural sky natural magnitude variation which gave:

m_N(el)_V =m_N(90)_V - 1.37029 + 0.0344429 el - 0.000221429 el^2 (7)

m_N(el)_V =21.9 - 1.37029 + 0.0344429 el - 0.000221429 el^2 (7b)

So that

21.9 - 1.37029 + 0.0344429 el - 0.000221429 el^2 = - 2.5 log \left(\frac{L_{N}(el)_V}{L_{0}} \right) (8)

The V magnitude for any zenith angle is then:

m(el)_V = - 2.5 log \left(\frac{L_{N}(el)_V+C L_{r}(el)_V}{L_{0}} \right) (9)

All these relations may be combined to find the V magnitude as a function of known zenith magnitudes and the relative artificial radiance ratio between any zenithal angle and zenith.

From equation 8, we can write:

L_N(el)_V = L_0 10^{\frac{-21.9 + 1.37029 - 0.0344429 el + 0.000221429 el^2}{2.5}} (10)

From equation 3, we can write

C = \frac{ L(90)_V}{L_r(90)_V} (11)

And from equation 6, we can write

L(90)_V = L_0 10^{\frac{-21.40}{2.5}} (12)

If we put equation 12 into equation 11, we obtain

C = \frac{ L_0 10^{\frac{-21.40}{2.5}}}{L_r(90)_V} (13)

Finally, if we put equation 13 and 10 into equation 9,

We have

m(el)_V = - 2.5 log \left(\frac{ L_0 10^{\frac{-21.9 + 1.37029 - 0.0344429 el + 0.000221429 el^2}{2.5}} + \frac{ L_0 10^{\frac{-21.40}{2.5}}}{L_r(90)_V} L_r(el)_V}{L_0} \right) (14)

L_0 vanish so that

m(el)_V = - 2.5 log \left( 10^{\frac{-21.9 + 1.37029 - 0.0344429 el + 0.000221429 el^2}{2.5}} + \frac{L_r(el)_V}{ L_r(90)_V }{ 10^{\frac{-21.40}{2.5}}} \right) (15)

m(el)_V = - 2.5 log \left(\frac{L_{r}(el)_V}{L_{r}(90)_V}\left(10^{\frac{-m(90)_V}{2.5}}-10^{\frac{-m_N(90)_V}{2.5}}\right)+10^{\frac{-m_N(el)_V}{2.5}}\right) (10)

A similar method have been used for ORM, except that we used the HPS 569 and 615 nm lines to estimate the NAD artificial LPS flux. This later is the most contributing artiticial flux so that other lines may be considered neglectable, especially HG lines. We did not use the NAD line directly simply because it is largely contaminated by natural emission. Anyway Pedani 2004 reported that the LPS to HPS line ratio may be considered as constant in La Palma and then HPS line radiances are directly proportionnal to LPS 589 nm artificial radiance.

L_{r}(90) = 0.23 L(90)_{615} + 0.89 L(90)_{569}

and

L_{r}(el) = 0.23 L(el)_{615} + 0.89 L(el)_{569}

The zenith radiance at ORM is estimated to 21.68 according to Castro Diaz measurements.

According to Pedani 2004, NAD intensity to sky brighness have increase of 1.5-2x from 1998 to 2004 at airmass > 1.3. Since Diaz-Castro measurements have been done prior to 1998, we can assume that zenith sky brightness used above are very conservative.