New Modern Height Determination Techniques
by Michel Kasser
The surveyor, thanks to the rapid evolutions of the available
equipments, has today a wide range of possibilities opened to him when
he has to perform altimetric determinations. The present paper
presents the possibilities opened to him, with special attention paid
to the use of GPS methodology.
Methodes Modernes de Mesures Altimetriques
Le géomètre dispose actuellement d'une grande
variété de procédés de mesure des altitudes et des dénivelées.
Le présent article présente une analyse comparative des solutions
qui apparaissent les plus adaptées pour quelques cas courants, avec
un approfondissement particulier de l'emploi du GPS.
Prof. Michel Kasser
2 Av. Pasteur
F-94 165 Saint-Mandé Cedex
Tel. + 33 1 4398 8331
Fax + 33 1 4398 8450
E-mail : firstname.lastname@example.org
New Modern Height Determination Techniques
1. A SHORT REVIEW OF AVAILABLE METHODOLOGIES FOR
The different techniques for altimetric
determination are wellknown. For each of them we shall recall their
specific advantages and drawbacks.
1.1 Direct (or Geometric, or Geodetic) Levelling
Direct levelling is performed with a level and one
or two graduated rods. The various errors are described in many papers
and will not be presented here.
- The level may be opto-mechanical or digital, which implies
different levels of security regarding possible blunders, and also
different levels of precision. The precision may range from 0.3
(in exceptional conditions, with very specific instruments and
field procedures) to 3 mm.km-1/2 and more. Today it appears that
the best digital levels do not allow for an accuracy equivalent to
the one provided by high precision older levels (automatic levels,
or spirit levels as well). But their ease of use is considerably
better, and blunders are quite unlikely to occur.
- The equipment has to be used at least by 1 observer + 1 helper
for the rod. For maximal precision it requires 1 observer and 2
helpers for the staffs. When the team works along roads, it is
often mandatory to have one extra worker to protect from the
traffic. And the equipment may be mounted on vehicles to improve
the efficiency (motorised levelling). Thus the team varies from 2
to 4 people.
- The daily production depends strongly on the equipment and the
composition of the team, from 4 km/day to more than 30 km/day.
1.2 Indirect (or Trigonometric) Levelling
It relies upon the use of theodolites and EDM, in
order to measure the zenith angle and the slope distance from one
station to another. This methodology is generally much faster than
direct levelling and of lesser accuracy due to refraction effects. An
exception is the trigonometric levelling using simultaneous reciprocal
measurements. This method can be motorised and has been widely
developed and used at IGN-France since 1982 for the national levelling
network (NGF). Its main features include:
- the possibility to have a large variation of production cost
between low and high accuracy measures. The specification of
maximum sight line length has a very important impact on the
accuracy and on the daily production.
- the possibility to achieve the same precision standards as the
direct levelling, with a quite different error model. The standard
deviation is generally higher (due to the much better aiming
capability of levels with a parallel plate micrometer), and on the
other hand the bias are generally much smaller (the line of sight
being more or less statistically normal to the refraction index
gradient, which is not the case with direct levelling).
- a productivity that stays at a high level even in mountainous
The use of a tacheometer allows for rapid levelling
operations with a limited accuracy if the ranges used are long. And if
the tacheometer includes a reflectorless EDM, this will provide a very
convenient situation for a 0.5 to 1 cm accuracy height determination
of natural topographic details close to the station. This feature is
very useful in urban areas.
1.3 Use of GPS
GPS may be used for heighting. Its main features
for such operations are:
- The benchmarks do not have to be along roads, but require an
open sky above them, which is not suitable in dense urban areas.
And we shall remember that most surveying works are performed in
- The error determination is comparably very large and depends
from the duration of the measurements, hardly better than 2 cm rms
(one should not assimilate the internal consistency provided by
computations with the accuracy), and the dependence with distance
between stations is very low. The error increases with the height
difference, and depends strongly of the observations duration and
type of computation.
- An excellent knowledge is required of the Zero-Altitude Surface
ZAS (close to the geoid and often wrongly presented as the same
thing), as GPS provides only geometric observations, and height is
a geopotential information. Only in a limited number of countries
(among which most of European countries) is this information
available with a precision comparable with GPS vertical
component's one for 2 hours long sessions.
If the ZAS is not available, the surveyor will have
the possibility to use GPS on a limited zone by measuring the
discrepancy between the official altitude and the ellipsoidal height.
For that he will get GPS measurements over a set of benchmarks from
the national network, with a density as homogeneous as possible in the
zone (typically 1 benchmark every 3 / 4 km may be correct if the area
is not too mountainous; if the area is mountainous, the precision
requirement will probably be lower so that such a density may also be
acceptable). If the discrepancy has only a variation of a few cm, a
simple mathematical interpolation model between the benchmarks will
provide the necessary correction, with an accuracy compatible with the
2 cm rms of the GPS vertical component.
The use of GPS for topographic applications is now
sometimes proposed in real-time differential configuration, which
means a more expensive equipment, but no post processing work. The
main feature of this configuration will be the possibility to have a
correct radio-link (emission authorisations, topography allowing a
correct reception far from the emitting station). But it must be taken
into consideration that post-processing GPS data allows sometimes to
benefit a posteriori from data that in real-time did not work properly
(ambiguity resolution after an interruption of reception), which means
that real-time applications must be used only when it is requested,
and sometimes may not be the best choice.
Permanent stations provide now an interesting
situation for the surveyor, as they allow to reach the national
altimetric reference (within a short observation time in a radius of
10-15 km around the station) with only one GPS receiver used. Such
stations are now installed, either by national agencies (e. g.
Swedesurvey in Sweden, L+T in Switzerland, IGNF in France, ...), or by
city technical administrations to lower their own production costs, or
by scientific groups (for example to monitor tectonic activities). The
observer will go back to its office after field observations, and he
will download (generally through Internet, in Rinex format) the
observations at the nearest permanent stations before processing with
his preferred software.
2. TYPICAL HEIGHT DETERMINATION SITUATIONS FOR
Almost in all cases, high precision altimetric
operations are requested as soon as, at least potentially in some part
of the area, water has to flow driven by gravity only (e.g. sewerage,
irrigation, drainage). Moreover, all national levelling networks have
been set up for these reasons too.
We shall select typical works where surveyors are
requested to perform levelling production.
2.1 Fundamental Levelling of the National Network
Although such an activity is generally done
directly by a national office, it may be in some countries at least
partially observed under the control of this office, and this highly
specialised activity is interesting to analyse. The goal is to provide
benchmarks everywhere in the country, with a variation of density for
benchmarks close to the population density, a millimetric local
precision and a long range error figure as low as possible. This
network must be observed at the lowest cost (compatible with this
precision) possible, and regularly checked because of benchmarks
destruction. The information about altitudes must be widely accessible
at the lowest cost possible, every surveyor being encouraged to use
this unique national height system so as to maximise national economy
and synergy between various public and private surveying operations.
2.2 Urban Densification Network
The goal is to provide levelling over a large
number of marks, some of them being often natural ones (sewer plates,
sidewalk borders, etc.), the other ones being benchmarks with special
attention paid to their conservation. The applications are mostly
related to water driven by gravity (sewerage systems for example). In
most cases, the requested accuracy is high (1 mm to 5 mm relatively to
the national levelling network). The client is the technical service
of the town, and generally he will look much more at the density, the
cost and the conservation rather than the precision.
2.3 Semi-Urban Network
Such networks will be requested for the preparation
of new works, town housing developments, implantation of a new plant,
extension of sewerage network, setting up new benchmarks for a new
road, highway, or fast train (TGV) line, etc. The required accuracy
will be of the same type (0.5 to 1 cm relatively to the national
network), but the density of the benchmarks will be low, using
2.4 Rural Height Determinations
They may be requested because the national network
is not dense enough, if some new water organisation is planned (e.g.
in flat areas, for drainage, in villages for water supplies, etc.).
The density will be low, but the references will be perhaps very far
from the site.
2.5 Stability Monitoring
In order to check the movements or deformations of
a bridge, a dam, a high building, or for common buildings during an
underground tunnel boring, the main point will be the highest accuracy
possible, with local references established only for these works,
possibly with no link to the national network.
2.6 Control and Real Time Guidance of Construction
This goal appears more and more important for
future productivity gains in civil engineering, and especially for the
construction of roads, highways or train lines. There are many
possible specifications of precision. The base layer thickness for
roads should be monitored within 5 cm, and the last layers, that are
formed with quite expensive materials, should have a thickness control
to within 5 mm. Increasingly it is requested that any geometric
control be permanent, without any interruption for setting up the
instruments elsewhere in a new section, and be perfectly reliable
whatever the profiles to achieve.
3. WHAT TECHNIQUE IS OPTIMAL TODAY FOR THESE
For the case A, a large part (if not all) of
the network should be observed with motorised levelling or
trigonometric motorised levelling for sections in mountainous areas.
But the question arises about the possibility to use GPS in parts. One
must remember that the various "orders" for levelling are
due to the enormous difficulties that geodesists experienced in the
past with the least square adjustments of even modest systems of
equations. The "first order" goal was to provide the
national reference system with a density acceptable for letting the
further densification in user-oriented benchmarks not too demanding in
terms of observations and computations. The first order was up to now
a technical necessity, but its benchmarks were not particularly
valuable for the normal users. In some countries, these benchmarks may
even be quite difficult to exploit: in France up to 20 years ago, most
of them were along railways lines, and thus became quite dangerous to
use at the era of the TGV. If there exists in the country a good
geoidal computation providing a centimetric or sub-centimetric ZAS, we
should now consider that the first order notion be replaced by an
equivalent notion of reference national height network based on
stations observed with GPS and the highest precision methodology
possible, of course with ZAS corrections, but these stations being
regularly spaced without any terrestrial observations between them.
The mean distance between them could be from 50 to 100 km, their
global precision being around 2 cm (with a much better repeatability,
around 3 to 5 mm, but who cares really about repeatability?). This
would provide a zero surface much more horizontal than commonly
achieved with classical methods, and thus very low bias, at the cost
of a higher standard deviation. But the general goals of the national
network would be fulfilled at a much better cost than today.
For the case B, GPS will not be profitable:
too many situations exist where the sky is not fully visible (close to
buildings, trees, etc.), and too many benchmarks impossible to pick up
directly with the antenna, so that an auxiliary tacheometer will be
requested, limiting the benefit of the GPS advantages. And the
real-time differential equipment will generally not work properly
between the buildings, with their shadow zones. Our opinion is that
trigonometric levelling with a tacheometer using a reflectorless EDM
will be the best device, as:
- it allows to measure natural objects (sewer plates, marks on
concrete borders, etc.) which is often required, if necessary with
only 1 people,
- the accuracy obtained will be acceptable,
- the cost of the equipment is compatible with the economic
activity of surveyors, tacheometers being the everyday tools of
most of them.
- The use of a very high tripod (> 2.2 m for example) or
of mural benchmarks set up very high on the walls is a very useful
feature, due to the difficulty to get the optical axis
unobstructed by passing-by people, trucks or cars.
Another solution would be the use of a digital
level with one cheap fibreglass rod (invar rods are much more
expensive), but this will prove less efficient if the density of
points to survey is high.
For the case C, considering the low density
requested, we may consider the use of digital levels because of their
low cost, or the use of high precision tacheometers with reciprocal
simultaneous angle measurements if the equipment is available. The
latter would be preferable if the area is large (or very long), and/or
with difficulties of communications (for example for a new highway
where there are no roads to go from a station to the next one).
For the case D, the GPS will generally be
the best economical solution, as soon as the work to be performed is
not too small an area. Of course the use of real-time differential GPS
may be considered if the topography allows for it: it will provide a
better security for the quality of satellite measurements and the
integrity of the collected data will be tested before leaving the
zone. Thus it will be more interesting in situations where the cost of
a remeasurement due to a lack of data integrity would be high.
For the case E, the use of optico-mechanical
levels should probably be preferred for their unsurpassed precision.
And as a complement we may note that for stability controls, digital
levels and GPS receivers may be used as automatic continuous
- For digital levels, the required length of rod may be fixed, for
example to a building, and monitored automatically by the digital
level controlled by a PC. Multiple targets may be surveyed if the
digital level is motorised (one command for the direction, one
command for the focus), and the accuracy of such measurement
reaches easily the 0.1 mm level, even for distances ranging beyond
- For GPS, the requested receiver will have at least a single
frequency capability, but of course phase measurement and if
possible a large internal memory. Such an equipment may then be
permanently installed on a given device, with a reference station
not too far away (e. g. less than 1 km when monitoring a bridge),
a power supply and if necessary a data link. Considering the
possibility to filter the results, even vertical movements as
small as 2 to 5 mm may be detected over periods of several days.
For the case F, three methods may be
considered: GPS, laser equipment and automatic (unmanned) tacheometers.
All of these have been tested, but clearly the "pros and
cons" are not the same for each of them. For example:
- GPS, in real-time differential mode with multiple antennas on
the machine and its blade, may provide an excellent permanent
control as long as there is no problems of "shadow"
zones where the satellites cannot be received (high trees, high
buildings, bridges or tunnel sections). But generally its accuracy
is not sufficient for the last layers, as it cannot guarantee
better than 1 cm (and in good situations!), and up to now the cost
of the equipment is high. But it will be perfectly compatible with
even very complicated profiles.
- Motorised automatic tacheometers provide a much better
precision, and may achieve millimetre accuracy, even in zones with
"shadows" where GPS could not be used. But new stations
have to be set up every 50 to 200 m (depending upon the
topography, as from the stations nothing must limit the sight on
the machine), and the continuity of the work requires at least two
fully operational equipment. But the cost of the equipment is
probably lower than for the GPS, and it is much more versatile and
usable on many different situations, not only in guidance of
- Laser equipment also allow to achieve a millimetre accuracy, and
their ease of setting up is quite appreciated
("2-slopes" configuration, an improper terminology but
an efficient technique), and their cost is low but they do not
allow for complicated slope or profile variations and their range
is limited, which requires the permanent management of at least
two instruments (and more generally three) if the continuity of
the guidance service is requested.
In any case, a careful estimation of the effects of
refraction should be performed, as tacheometers and laser equipment
may be sometimes used on very long ranges (more than 500 m is an
achievable range for some lasers, and an automatic tacheometer may
easily work much farther). Thus it must be pointed out that on such
ranges, the errors induced by refraction are often larger than
Each given type of work requires a careful
analysis, as usual, and a regular re-evaluation to the method that is
optimal at a given date. But surveyors will have noticed that since a
few years, "precise height determinations" are not always
equivalent to "direct levelling". Here we have presented a
few examples: the relevance of the analysis presented is probably
quite dependent on the economic conditions in each country. But we
consider that sometimes the GPS may be used, sometimes not. The same
applies for the use of tacheometers. Thus we encourage the surveyors (i)
not to overestimate the accuracy of GPS (this paper does not want to
emphasise this classical question of the vertical precision of GPS,
but any surveyor must be aware of the large discrepancy between the
repeatability of GPS - a few mm - and its real precision - generally
more than 2 cm rms -) and underestimate the problems posed by the
different reference frames of GPS and national levelling network, and
(ii) to have in mind for each work a clear and regularly updated idea
about the economic and precision aspects relative to the methods
Prof. Michel Kasser
18 April 2000