% this is lp_quant.tex in fact, 
% see lp_quant.pdf or lp_quant.html for easy reading;

% the needed non-standard files for typesetting this file are inside
% http://amper.ped.muni.cz/jenik/auxfiles

\input a4_12.ltx
\input mypdfbr.lt
\input myhtml.lt
\pagestyle{plain}

\begin{document}

\author{\JHet\footnote{see also \cite{czechsite}}}
\title{Light pollution quantification}
\date{December 2, 2002}
\maketitle

\thispagestyle{empty}


\begin{htmlonly}
\tableofcontents
\end{htmlonly}

\section{Introduction}

Many non-astronomers ask, which way of artificial outdoor lighting
brings the least light pollution. The answer is very simple: the fully
shielded (FS) one, i.e., allowing no direct light over horizon.\footnote
 {I've seen a HCO short as well, meaning Horizontal Cut Off}
The
same simple criterion reduces glare and most of the light into the
windows, into distant areas etc., simply the light pollution in the
broadest sense.

This secondary virtue is due to the simple fact that when the
light-sending parts of the luminaire 
\newold{become a just a line segment}{have a zero space angle [bef. Dec 5]} when
viewed horizontally (an usual condition to have a fully shielded
luminaire), the \newold{apparent area 
(called ``space angle'' in the language of mathematics)}
{space angle [bef. Dec 5]} 
of the light-sending (emitting,
reflecting, refracting, dispersing) parts of it remains small also
from views going just slightly upwards, being proportional to the
departure from the horizontal direction. Of course, keeping the
luminance low within this \newold{area}{space angle [bef. Dec 5]} 
by a suitable optical
construction can help as well, this is where the quality of different
fully shielded luminaires appears.

However, the advocates of perpetuating the use of non-FS luminaires
claim that using non-FS luminaires helps combating the light
pollution. Sounds incredible? 

Their argument is that to achieve a sufficient luminance of the road as
demanded by some standards, more light is needed using the FS
luminaires, hence more light disperses to the atmosphere from the road
and the light pollution inevitably rises.

The error in this reasoning is a misperception what the light
pollution is. In many cases, it is no measurable quantity. An
interpretation, that the luminous flux upward is the measure, is
completely unuseful. There are no cases where this quantity would
matter. Let us discuss it. 

\section{Which upward light matters}

Are the birds affected by this light? Not very much, what disturbs
them most are the bright or even glaring points, i.e., the direct
light from the lamps: just FS ones do no harm. 
Any spots of large artificial luminance in
their field of view may play a role, apart from luminaires themselves
they may be windows, lit billboars or even facades, 
but the lit terrain below is
irrelevant.

Are the stargazers affected by this light? In some extent yes, but it
depends. They do not see this light. What they see, is the light from
the sky, going downward. This is the light pollution in the narrowest
old sense: \emph{an artificial increase of the luminance of a
cloudless night sky}. 

Such an artificially made part of the sky luminance is not simply
proportional to the amount of light going upward. A proportionality
holds just for one single elevation angle of the upward going
radiation. The constant of proportionality depends on the turbidity of
the air, and of course, on the elevation angle itself. It quickly
declines with the elevation. No wonder, there is less air on the path
of the skyward light. As we know, the air is mostly transparent, so
most of the upward going radiation never turns back and escapes into
the space without doing any harm. This is true for all light going
steeply upwards. What matters much more, is the light which goes just
very slightly upwards. Almost all of it is dispersed at last, half of
it upwards into the space, half of it downwards, contributing to the
artificial increase of the sky luminance. Even without computation
everybody knows that, when remembers how the setting Sun looks like.
Just a very tiny fraction of its light remains undispersed, so little,
that it does not heat us at all, and sometimes even so little, that it
can be viewed comfortably without any sunglasses. 

So, the unwanted increase of the night sky luminance is caused mainly
by the artificially produced light going in shallow elevation angles
upwards. Counting all the upward light together is like counting all
the money together, not regarding if they are liras, marks, dollars or
pounds (or euros, pesos, rupies). The exchange rates are to be
regarded!

For an air with neither aerosols nor
absorption (it does not exist in reality) 
the fraction of the downward scattered light would be some
five per cent per ``one air mass'' (the same amount would be dispersed
upwards). It means, that the light travelling at 30 degrees elevation,
going through twice the amount of air as the light going to zenith,
would be dispersed downwards from some 10, 17\,\% would
return back to the ground from the light going to 15 degrees, 33\,\%
cent from 6 degrees and 44\,\% from the directions below 3
degrees. So, this almost horizontal light is nine times more
polluting, in the terms of the sky luminance, than the vertical one,
isn't it?

No, it is not. It's even worse. Such a calculation holds for uniformly
populated (or artificially lit) landscape. With villages a couple of
kilometres or even more from each other, everybody who is seeking a
wonderful natural night would go in the middle between them. There the
increase of sky luminance due to the artificially emitted light is
even more caused by the low-elevation light from the villages. To the
air above such remote places, no other light can get. And as regards
observation of aurorae, which are mostly quite low above horizon in
our central European latitudes (or comets, which are usually low
everywhere), the light caps above villages make the main obstacle,
caused by the shallow elevation light mostly. So does the almost
horizontal light twenty or fifty times more harm than the
steep-up-going light? Something like that. 

Then there is the aerosol content in the atmosphere, always present in
some extent, and mostly predominant in the forward scatter of the
light, with a steep maximum around the original direction of the light
(the Rayleigh scatter on the gases themselves is dumbbell-like shaped,
with a minimum perpendicular to the original direction). The light
caps above lit areas are caused then mainly by the forward scatter of
the low-elevation light on the aerosols. We know such a scatter
maximum from our daytime experience as well: this is the reason why
the sky around the Sun, even with a rather clean air, is much brighter
then elsewhere, often so bright, that it cannot be comfortably viewed
even when we shade the Sun itself by our hand. 

On the other side, aerosol content diminishes the role of the light
going horizontally, making the total scatter including ``downscatter'' 
larger at large elevations (for
the lowest ones, even the cleanest air scatters almost half of the light
downwards, as we know already). So, inside the large lit areas (like
urban aglomerations) with badly transparent air it lowers the relative
importance of almost horizontal light to perhaps a factor of four
instead of nine. There is also some absorption of the light even by
the clear air (visible as dark bands in the spectrum of the setting
Sun), it reduces the importance of shallow angles even a bit more, but
these are per cents rather then a factor of two.  

But at the best nights with low turbidity of the air, when the natural
sky would sparkle by thousands of stars, the low elevation component
is by far the most harmful one everywhere, with an exception of a
centre of one single small town in the middle of the ocean (just there
the steep light contributes overwhelmingly to the sky luminance
directly overhead, it's being of course just one of the many 
adverse effects of the light pollution).

\section{Going quantitatively}

This could do perhaps. But some people might like to know how much
exactly is the sky luminance increased by each way of artificial
lighting of our homes, ways and working places. For an as accurate
answer as possible, they have to study the works of Pierantonio
Cinzano and his collaborators (starting perhaps from the famous
Atlas \cite{C2}), or even reproduce their computations
with many possible angular distributions of emitted light,
of location of the light sources, shapes of the terrain etc.
For some Italian situations it has been done already \cite{C4}. The angular
distribution of the light from real settlements is poorly known,
however \cite{C1}.

In fact, we are not so much interested in just this question. The
prevention of all the light pollution is the ultimate goal, not a mere
reduction of the luminance of the sky in some places. But let us make
a couple of remarks on the luminance of the sky, for those who are
still curious. 

I have written a programme handling the photometric data on
luminaires, the so-called \emph{ies} photometric files.\footnote
 {it handles also the \emph{eulumdat} format now}
The original goal had
been just to get a human-readable table from the standard data. Then I
added a computation of further quantities, step after step, and
eventually I've included some estimate of the obsolete increase of the
sky luminance by the direct light from the luminaires. 

The program itself and a lot of its results is available in \cite{H1},
some old comments on it and this issue in \cite{H2}.

The model I use is the simplest possible. 

The upward light from a lit terrain is considered to be
lambertian-distributed, i.e., the luminance of the terrain is the same
from any direction and the amount of light is then simply proportional
to the cosine of the viewing angle (looking vertically down the angle is zero
an the cosine is one). Such a source is called cosine source as well,
a graphical representation is a sphere lying on the ground. No real
terrain is like that, esp. when illuminated obliquely. There may be
also some mirror component, like from an old asphalt road polished by
the tyres of millions of cars. If the luminaires
produce large luminous intensities far from the nadir, at 75 degrees
or even higher, then there is some reflected component at these
shallow angles even in the light dispersed from the road. The more
when the road is wet. However, lambertian distribution is the simplest
model and it would be hardly possible to chose a better one for a
general case.

For the computation of dispersed light, 
all the downward scattered light is taken as a whole,
\oldnew{and just single scattering is
considered in its}{in the} default variant.

Taking a simplified part of the Pascal code of the programme, the function
describing the angular dependence of the scatter (called the
indicatrix) can have several shapes, x being the angle of scattering (in
degrees):

\begin{verbatim}
   cx:=cos(x);
   sx:=sin(x);
   y:=sqr(x);
     if Sky=0 then
       if x<=10 then
         y:=7.5*exp(-0.1249*y/(1+0.04996*y))
       else
         if x<=124 then
         y:=1.88*exp(-0.07226*x+0.0002406*y)
       else y:=0.025 + 0.015*sin(2.25*x-369)
     else
       y:=1+cSky[Sky]*(exp(dSky[Sky]*x*pi/180)-exp(dSky[Sky]*pi/2))
         + eSky[Sky]* cx*cx;
\end{verbatim}

where the coefficients are 

\begin{verbatim}
 cSky:array[4..6] of real=
 (10,16,24); 
 dSky:array[4..6] of real=
 (-3,-3,-2.8);
 eSky:array[4..6] of real=
 (0.45,0.30,0.15);
\end{verbatim}
       
The amount of total scatter is given by the extinction of direct
vertical light, measured conventionally in magnitudes (\verb"ZenExt", as a
default, the programme uses a value of 0.30 mag), for the computation
it is necessary to normalise all the values to get the correct
extinction. 

The first formula (for \verb"Sky=0",
before the last ``else'' in the piece of code above) 
is used in the works of Cinzano (e.g., \cite{C2}), 
taken from Garstang \cite{G}
 and describes just the aerosol part of the scatter (Mie scatter).
The gas itself sends simply half of the scattered light into each
half-space, i.e. the scatter is centrally symmetric. The 
gaseous part is taken as if the vertical extinction caused by it would be
always just 0.1 mag, the rest is considered to be the aerosol part:
 \verb"AerosFr:=(ZenExt-0.1)/ZenExt". 

The other three alternatives are standard CIE skies got from the many
measurements of the daytime sky luminance of cloudless skies, as
published by Kittler \cite{K}, not distinguishing the mechanisms of the
scatter. They involve multiple scattering as well.


To speed up the computation, the proportion of the downward-scattered
light as a function of the elevation angle \emph{h} expressed in
degrees is approximated by the following functions (these are my formulas,
for \verb"Sky=0" it is valid for single scattering only):  
       
\begin{verbatim}
 case Sky of
  0: FluxX:=(0.08+0.4*exp(-h/24))*AerosFr + 0.5*(1-AerosFr);
  4: FluxX:= 0.342+0.158*exp(-h/27);
  5: FluxX:= 0.275+0.225*exp(-h/27);
  6: FluxX:= 0.184+0.316*exp(-h/29);
\end{verbatim}

You can notice that for a horizontal case \verb"h=0" the downward fraction is
almost exactly one half.

What the programme does is just comparing the luminance of the sky
caused by the direct light from the luminaire (i.e., an avoidable
light, using the proper shielding) and the (unavoidable) light dispersed
from the terrain. The terrain is considered lambertian and flat. The
first assumption (cosine distribution from the lit surface) can be a
good approximation of the reality, whereas the latter is not in many
cases. The almost horizontal light from the lit ground is absorbed by
trees, houses etc., whereas the lamps on high poles are obstructed far
less in most cases. Then the influence of the direct light from the
lamps may be still twice larger. On the other side, in tall narrow
streets, the horizontal light from lamps may be blocked as well and
the influence of the steep light from the pavement may be larger (but
anyway, such narrow deep streets contribute to the sky luminance very
little). 

The exact numbers given by the programme are of a limited value. But
one thing is obvious from the results for many luminaires: 
\emph{one per cent of light going almost horizontally from the lamps themselves 
adds some another thirty per cent to the increase of the
sky luminance caused by the lit ground}, a very serious penalty!
Penalty about three per cent could be perhaps tolerable, if they were
some valid reasons to use a non-FS luminaire, but it would demand just
0.1\,\% of light just above horizon. The tolerability would be
relative, however, as those three per cent describe just the overall
rise of the sky luminance. For the places we'd love to keep
near-natural, the influence would be still too 
large\old{:
considering the roughness of the terrain, it may contribute easily
more than half of the artificial increase of the sky luminance there,
as caused by the outdoor lighting in all the municipalities around}.

\new{version 3}
{Thanks to an idea by Cinzano, \cite{C5}, I've included the computation 
of ``distant pollution'' into my programme recently. If
you are say 50~km from the town, just its rays going at most 5 degrees
above horizon are hitting the lower 5~km of atmosphere above you, where 
half of the gas and vast majority of the aerosols is contained. If the
town would use non-FS luminaires sending just one per cent of its light
above horizon, they would cast seven times more light into the air 
above you than the illuminated townscape itself.\footnote
 {such a number gives eg the luminaire used in an example 
 by David Keith \cite{DK}, when the programme \cite{H1} is run with parameters
 \texttt{ies2tab -l -c -la5 samp0195.ies}. A large contrast to the result for 
 the same luminaire if just the overall sky luminance 
 is concerned as I've published earlier in \cite{H2}.}
As the aerosols are  
mostly lower than 3 km, the artificial part of the luminance of
zenith would be increased rather twelve times than eight times, in 
comparison with a town using just fully shielded luminaires. So, even 
having a flat terrain and just 0.1\,\%  of the light from lamps going
(just) over horizon, this ``negligible fraction'' 
would contribute half of this type of pollution, easily avoidable 100\,\%  
over the ``inevitable'' one...\footnote
 {considering the roughness of the terrain, it may contribute even
 more than half of the artificial increase of the sky luminance there,
 on the other side, including the ``tertiary light source'', 
 namely the illuminated air over the city, would set it back to one
 half again}.
}

\section{Non-FS luminaires help nobody}

The advantage of the non-FS luminaires over the FS ones cited by some
lighting experts stems from the fact, that extreme luminous
intensities can be reached even at 80 degrees from the nadir with
non-FS lamps. Neglecting the horrible glare from such lamps, the
simplistic computation of the luminance of the road (with assumptions
on its reflectivity which may be far from reality and are never
checked) gives a possibility to install these lamps further apart,
casting in fact less light on the terrain and getting sometimes lower
total upward light fluxes.

This approach makes use of the light reflected from the glossy asphalt
road at very low angles -- namely, the road standard assumes
observation of the road at an angle of just one degree from
horizontal! It may be a sound approximation for a highway, but we do
not illuminate highways in Czechia very often (fortunately). To compute the
lighting tasks this way in a municipality 
with a legal upper speed limit of 50 km/h seems
to be rather queer, luminance in such a very distant point is scarcely
the most important value. Making use of the grazing illumination angles
means inevitably lots of glare in the same time. It's difficult to
quantify, but more fatigue for the drivers is a consensus
already and a higher danger of overlooking a traffic signal is
obvious. A danger of overlooking a pedestrian
when a million times more conspicuous glare bomb is visible near to him,
is much more fatal however. 

Not just the \emph{light above horizon} causes pollution -- it's just 
that it is agreed to be called
pollution by everybody. Even the \emph{not-enough-steep-down
light} below horizon is horrible and dangerous pollution, and it is
mostly plentiful by those ``more efficient'' non-FS luminaires, being
a synonym for their ``efficiency''.

In fact, a responsible lighting project should not be limited to
comparing two refractors for the otherwise same luminaire, or just two
or three luminaires more. It should take advantage of the free market
and choose the best suiting, least-polluting lamps from all the world.
Of course just among the FS ones, perhaps with a large and precise reflector
system, if the task really demands it, with the least possible amount
of light above 80 degrees (and usually above 75 degrees already,
definitely inside a city at least). In many cases, a very important
parameter should be, how well is the light confined to the target
property to be illuminated, avoiding illumination of gardens, windows, or
sometimes water surfaces (the artificial light damages 
both marine and freshwater life
especially seriously). 

Of course, nothing \emph{above} the lamps is illuminated by FS
luminaires, but also some things \emph{below} the bulbs should be protected by
choosing or adapting the luminaires as needed. 
When the cone of light is not asymmetric in
itself enough, a mirror-like aluminium sheet houseside (waterside, ...)
helps, adding more light streetside. It's fine that some producers
have such option by their fixtures from the beginning already. Of
course, for a perfect control of the light cone, the bulb itself might
be shielded by small mirrors, avoiding direct light from the bulb
going far away from the target area. I hope it will become usual with
shallow luminaires in the future -- for the deep ones, the cone can be
controlled simply by the opening of the fixture.

\section{Measures of the light pollution: what to avoid}

So, is there a measure of the light pollution? Yes, but not a single one.
There are several important measures of pollution, concerning the
emissions from the lamps. 

First, the amount of light going from the luminaires above horizon,
esp. almost horizontally (the quantity given by my programme is a fair
approximation, even if understating the damage by near horizontal
light), completely evitable by a suitable geometry of the luminaire,
confining all the light to the bottom half-space. It needs not be
measured in such a case, as the FS-property is visible 
on the luminaire at the first glance. 

Second, the amount of light going, say, over 75 degrees from the
nadir, producing glare and compromising visibility and safety. 
(And it's this glare which prevents the people to notice
even bright planets with a Moon crescent just over horizon.)

Third, the amount of direct light going in another inappropriate
directions, outside the property to be illuminated.
(It's this light that deprives us of the beauty of the heavens
in adition to the artificial luminance of the sky itself.)

Fourth, the amount of light going unused from the lit surfaces. This
cannot be zero of course.
Sometimes the lit surfaces can be dark to lower this amount, e.g., boards
with white letters. But generally, the amount of incident light should
be kept on the lowest possible levels all the time, always choosing the
lower one if in doubt.\footnote
 {There is an accepted upper limit of an average luminance 
of any lit surface outdoor,
in absence of any safety standards demanding more, namely 1~cd\pms{}, this
is far enough at night -- see e.g. \cite{visual}.}
 Avoiding pollution should be a strong motive for that.
It may easily mean to have the lights off for most of the time. Motion
detectors are a sound option, when they don't start in vain (and when
the switched lights are not too strong). 

Fifth, some surfaces need not be lit at all at night. \emph{Not to light} is
the option most favourable to the environment, most cheap and most
responsible in many cases. After all, don't we have small lamps (with
very cheap and reliable alkaline accumulators nowadays) when the night
seems too dark before we adapt to it or when the way goes through a dense forest
(and we don't know it and are in a hurry?). Don't we have headlamps in
our cars, when riding quickly? There is no obligation to illuminate
anything outdoors. Night is a natural phenomenon and our eyes have
evolved to work well in such conditions. A street or a road is not a
corridor inside a windowless building, there is never a true darkness
outside. \emph{Not lighting} some areas means to educate people about the
advantages of letting some things to nature alone. This pays off in many
cases, not just as regards lighting. People have been often afraid of
the nature in the past, now they
should be afraid of losing their healing contact with it altogether. Night is
a possibility to refresh our links with it, with a multitude of gains. 
Now it is the most endangered part of our world -- fortunately, the
most easy to rescue as well. Let's do it. 

\begin{thebibliography}{9}

\bibitem{czechsite} IDA Czechia, 2002: an English-version web site, 
\h{www.astro.cz/darksky}

\bibitem{C1} Cinzano, P.  2001: private comm., 
 \h{amper.ped.muni.cz/jenik/letters/public/msg00022.html} 
\bibitem{C2} Cinzano, P. -- Falchi, F. -- Elvidge, C. D. 2000: 
 The first world atlas of the
 artificial night sky brightness, Monthly Not. of Royal Astron. Soc, 328,
 689-707,  see also \h{www.lightpollution.it} (also for further papers
 of Cinzano) 
\bibitem{G} Garstang, R. H. 1991: ..., Publ. Astr. Soc. Pacific, 103, 1109
 (see \h{physics.colorado.edu/directory/faculty/garstang_r.html} as well)
\bibitem{C3} Cinzano, P. 2000: 
 The growth of light pollution in north-eastern Italy from 1960 to 1995,
 in Measuring and Modelling Light Pollution, ed. P. Cinzano, Mem. Soc.
 Astro. It., vol.71, 159-166 (2000) - submitted April 1998
\bibitem{C4} Cinzano, P. 2000:
The Propagation of Light Pollution in Diffusely Urbanised
Areas, in Measuring and Modelling Light Pollution, ed. P. Cinzano,
Mem. Soc. Astro. It., vol.71, 93-112 (2000) - submitted May 1998

\bibitem{C5} Cinzano, P. 2002: drafts of papers on the Roadpollution programme
 and its results (priv. comm.)

\bibitem{DK} Keith, D. 2001, presentation at 
Street and Area Lighting Conference 2001, the quoted photometric file 
is available at \h{resodance.com/mdi/SALC_exs.html}.  

\bibitem{K}
 Kittler, R. 1993: Relative scattering indicatrix: Derivation from regular
radiance/luminance sky scans. Light Res. and Technol., 25, 125-127.

\bibitem{H1} Hollan, J. 2002: 
 \amper{light/ies2}, a programme extracting an information
from the ies photometric files and some its results (files and
directories).

\bibitem{H2} Hollan, J. 2002: FS fixtures are vital for reducing sky
luminance, a letter to the DarkSky-list, \ampjl{public/msg00059.html}.

\bibitem{visual} Cielobuio, 2001, Visual Regolamento, in
 \h{www.vialattea.net/cielobuio/arc-lrl17.htm}, either
 \h{www.vialattea.net/cielobuio/lrl17/visualreg17.htm}
or preferrably the typeset pdf version in  
 \h{www.vialattea.net/cielobuio/lrl17/visualreg17.zip}

\end{thebibliography}

\end{document}
