To set the scene, here is an excerpt from the publication ” Surveyor n ° 2087 of December 2011 “: The file of the month Safety, reliability Underground networks by Laurent Polidori (director of ESGT) and Gille Costa (surveyor):

” *The sub-soil of our cities has become a real Gruyere whose holes serve as pathway to a growing number of networks.*

*Power supply, telephone, heating, gas, optical fiber, water … All these networks intertwine, coexist, overlap and some have been there for so long that even the memory is lost and their managers do not know the exact location.* *To open a trench on the public road becomes more and more risky.* *So much so that after very serious accidents, the MEEDTL has decided to put in place a very large reform.* *A special agency will list all the network managers, contacts and ultimately the areas of implementation.* *It will be consulted for work project declarations (DT) and declarations of intent to start a new work (Dict).*

*In the process, the regulation of these declarations is redesigned.* *All new network works will be georeferenced and subject to three accuracy classes.*

*The goal is simple: to reach by 2019 an accurate knowledge of the location of everything that runs under our feet … For more security and reliability.* “

All the operators of the various networks are required, from January 2019 to respect the obligation of setting a georeferenced map of the underground networks in urban units. For networks outside urban areas, the deadline is January 1st 2026.

The job seems simple at first glance. Three classes have been defined:

Definition of the three network classes

**Class A**

A structure or section of a structure is classified as class A if the maximum uncertainty of location indicated by its operator is less than or equal to 40 cm if it is rigid, or to 50 cm if it is flexible. The maximum uncertainty is raised to 80 cm for underground civil engineering works attached to installations intended for the circulation of rail transport vehicles or guided when these structures were built before January 1^{st}, 2011.

**Class B**

A structure or section of a structure is classified as class B if the maximum uncertainty of location indicated by its operator is greater than that relative to class A and less than or equal to 1.5 m.

**Class C**

A structure or section of a structure is classified as class C if the maximum uncertainty of location indicated by its operator is greater than 1.5 m, or if its operator is not able to provide the corresponding location

Let’s leave aside, for the time being, the technical aspects of measuring uncertainty and move on to the first major problem of this project. In short “** if the maximum uncertainty of the location cited by its operator is greater …**” .

**Definition of LOCALIZATION.**

Everyone understands this sentence without having to think about it. If I have a gas pipe under the sidewalk, parallel to the edge, I can classify this pipe in class A if its position is known with less than 40 cm of uncertainty. In front of me the sidewalk is 70cm wide, so necessarily the pipe can be classified as class A. It would be so simple, only if it were true!

First thing that should put us in the ear: why in the example above ask 40 cm of precision for a measure that everyone can do with a centimeter with a precision of at least 1cm?

The answer is much more complicated than the question. To know what the meaning of the word localization is we should dig deeper.

But I can give you part of the answer immediately: the localization of the pipe is not a function of the sidewalk, or any other remarkable element near the pipe.

First text to be aware of:

The text defines two types of objects, point objects and linear or polygon type objects. For these second, the localization concerns the identifiable points which define the lines or the polygons. The localization of a point, according to this decree, is as follows:

Locating a network point

7.1. Punctual geographical objects

If indicated by the specifications, some geographical objects can be considered as punctual. Therefore they are determined by the planimetric coordinates and if needed by the altimetric coordinates of their point of reference. The accuracy class applies to the difference between the coordinates obtained for each point by a control measure and the coordinates provided for those points; the possible support and contour points included in the survey being excluded from the points tested.

Our sidewalk has disappeared and we have to provide planimetric coordinates. In other words, we must provide the latitude / longitude of the points constituting our conduct, projected on a plane.

With regard to the accuracy of these coordinates, the text points out:

Precision measurement of the localization

6.1. Total accuracy class

The precision class defined above applies to the differences between the coordinates provided for each point and those obtained for the control measures. The total error results from the arrangement of the internal errors, the errors of attachment, and the error specific to the legal reference network. Therefore, the total error cannot be less than one of these three sources of error, and, in particular, the error of the legal reference network, as specified or as a result of the discrepancies noted when attaching.

There I feel that I’m losing you! The text speaks of three types of error:

- internal errors: these are measurement errors, for example the accuracy of the GPS used.
- the errors of attachment: these are, for example, the errors of seizure during the integration in the database of the network.
- the error specific to the legal reference network: it is the positioning error due to the projection of the geographic coordinates (latitude / longitude) in planimetric coordinates (X / Y).

The legal reference network is defined by the following decree:

Decree No. 2000-1276 of December 26^{th},2000 implementing Article 89 of Law No. 95-115 of February 4^{th}, 1995, as amended, for the planning and development of the territory relative to the conditions of execution and publication of survey plans undertaken by public services – Article 1

This article defines the planimetric coordinate system to be used by all utilities:

Planimetric reference systems

The national reference system of geographic, planimetric and altimetric coordinates cited in article 89 of the aforementioned law of February 4^{th}, 1995 is defined as follows:

- – Geographic and planimetric reference systems:

ZONE | GEODETIC SYSTEM | ELLIPSOID ASSOCIATES | PROJECTION |

Metropolitan France | RGF93 | IAG GRS 1980 | Lambert 93.
Conic compliant 9 zones. |

Guadeloupe, Martinique | WGS84 | IAG GRS 1980 | UTM North time zone 20. |

Guyana | RGFG95 | IAG GRS 1980 | UTM North time zone 22. |

Reunion | RGR92 | IAG GRS 1980 | UTM South time 40. |

Mayotte | RGM04 | IAG GRS 1980 | UTM South time 38. |

In the table above, the “9-zone compliant conic” are added to the list of projections, as far as it concerns metropolitan France.

**First trap: the change of coordinates**

The definition of the Lambert 93 projection as a reference system is not anecdotal. It is part of a process of moving from local coordinate systems to global coordinate systems. For more details on these systems, you can read Precision, uncertainty and linear alteration of geographic data (1) and (2) .

Let’s remember that the Lambert system 93 (global or 9 zones) has a network-specific error of the order of 10 cm, well below the uncertainty associated with the network class A.

On the other hand, the Lambert 1,2,3 and 4 projections as well as the UTM / WGS84 projections have a network-specific error of the order of one meter, well above the uncertainty of the network class A.

It is this difference of error that motivated the transition of all public utility data to Lambert 93 a decade ago.

The problem is that not all utilities have abandoned these reference systems internally. There are still some who have treatment networks and work with Lambert 1, 2, 3 or 4, but transform to Lambert 93 when they have to exchange with other services. As surprising as it may seem, I have already heard several geomatics managers saying that they respected the requested accuracy (<40cm) since they converted their Lambert 1 or 2 data to Lambert93.

In the articles cited above you will find numerical examples proving that this does not reflect the reality of things. Let’s take a comparison here with other types of measurement.

You use a scale calibrated in kilograms, or a thermometer in degrees. Can you guarantee a weighing to the nearest gram or a temperature of one tenth of a degree? Of course not. The uncertainty related to the Lambert 1 to 4 projections is metric, that is to say that everything to the right of the comma is false. Can you guarantee a localization to the nearest decimeter? Well, no.

As for the total error mentioned above, which cannot be less than one of the three sources of errors, in a processing chain the total error for the result cannot be less than the maximum error of one of the stages of treatment.

Warning!

Since you include a step in Lambert 1, 2, 3 or 4 in your process, the resulting processing error will be at least equal to one meter, even if you provide this result in Lambert 93.

Therefore it is impossible to classify as an A network elements using at one time or another an old Lambert projection.

**Second trap: focusing on linear alteration.**

No projection can keep all distances. We, then, introduce the notion of linear alteration to measure the distortion of distances caused by the different projections.

*Linear Alteration = (projected distance – ellipsoid distance) / ellipsoid distance*

Linear alteration is expressed in centimeters per kilometer.

For example, the 4 Lambert area projections specific to the NTF, were calculated so that the linear alteration is better than 1 per 1000, ie less than 1 meter per kilometer. For the Lambert 93, the linear alteration is from -1 m / km to +3 m / km.

The linear alteration is local and variable in each point of the map.

To avoid this quite wide range and reduce to values below 1m / km, the IGN has set up 9 areas called CC42 to 50.

These projections were introduced to reduce sharply the linear alteration induced by the large width of the Lambert application zone93.

Therefore their use assumes measures expected to be more accurate on a blueprint.

It is not justified for plans whose accuracy is lower than the linear alteration, or for the digital surveys, for which the linear alteration can be entirely corrected in a simple way.

On the contrary, the border discontinuities of the nine zones complicate digital applications and can generate significant additional costs compared to a solution using Lambert93, in particular with data in image mode.

Is linear alteration a source of uncertainty for our data in the information system? This is only the case if we do not use high-performance GIS tools. The main software used (ArcGis, QGis, …) allow to choose how to measure distances: either on the projected or the ellipsoid plan. Simply choose the second option to remove the linear alteration of our measurements.

In any case, the linear alteration introduces no uncertainty for the localization of network objects. Therefore it is completely independent of the class of objects. It intervenes on distance measurement on a blueprint but never on the localization of objects.

Thank you for this