Friday, November 9, 2007

ETL: CamptoCamp, FDO and Open Source - What about OLAP?

CamptoCamp & Talend

CampToCamp is introducing (not yet released, but anticipated), a Spatial ETL tool, that works in conjunction with Talend's Open Source ETL product Open Studio.

Once released, I'll begin to work with the product, but CamptoCamp was in Victoria presenting their solution at FOSS4G2007.

More information on their presentation can be found here.

Open Source ETL - Without Spatial

For Open Source ETL, without the Spatial, there are various Open Source solutions. Talend, being one of them.

You can take a look at:

1) Pentaho - URL:

2) Clover - URL:

3) KETL - URL:

Is there another Open Source Spatial ETL Tool?

But we do have another option as well for the Spatial side now that AutoDesk is now working in the Open Source community and they released FDO (Feature Data Objects), which is similiar to FME - but is not an FME.

FDO is a Data Access Technology that was developed to manipulate, define and analyze geospatial data regardless of where it was stored.

FDO was originally developed and included in the Autodesk Map 3D 2005 product during the spring of 2004. In this initial implementation, it was capable of working with the following geospatial types:

  • Oracle
  • SDF

The following version introduced ArcSDE.

The third verision implemented more sources, and added providers for MySQL, SQL Server, ODBC, SHP, Raster, OGC WFS, and OGC WMS.

It was then that they decide to take FDO Open Source, but would not release the Oracle version - but being Open Source, there is always an option out there and some ingenious minds to come out with some solutions.

Quoting the OSGeo FDO History site:

"The release of FDO as open source coincided with the release of MapGuide as open source in 2006. It included the SDF, SHP, MySQL, ArcSDE, ODBC, OGC WFS, and OGC WMS providers. "

FDO was now out to the Open Source World - right on schedule with their release of MapGuide Open Source.

But what about Oracle and FDO?

Much of the work for the Oracle side has been developed by SL-King in Slovenia.

King.Oracle is Open Source FDO provider for Oracle.

Through this product, which is Open Source, SL-King is providing a tool that supports Oracle Locator and Oracle Spatial. It is specifically designed for Oracle and Oracle alone and they are designing it in such a way, that it will support full Oracle Spatial functionality.

Currently the latest version (Version 0.7.3) provides:

  • Support for Oracle 10G, Oracle XE and Oracle 9i
  • Optimized for Oracle
  • Using plain Oracle tables and views
  • Can be used inside AutoCAD MAP 3D to edit and query Oracle data

For a Flash Movie on this, please look here.

Can we convert between FDO different sources?

Yes, of course! This is Open Source.

Coming from SL-King, again, we have another ingenious tool, called FDO2FDO.

FDO2FDO is an Open Source FDO client application which uses the above mentioned Open Source FDO library to manipulate, create, and define geospatial data.

Currently, the software is capable of the following:

  • Copy data from SHP files to SDF
  • From SHP to Oracle
  • Oracle to SDF...

In the end, FDO2FDO allows the user copy and modify any data from any FDO Data Store to any FDO Data Store.

There are three main parts in FDO2FDO and they are:

  1. Fdo2Fdo Api library
  2. F2Fcmd Command line utility
  3. Fdo2Fdo GUI
An introduction to FDO2FDO can be found here.

There are always solutions out there.

Can Geospatial move towards ETL and Data Warehousing?


Currently, in order to do web-mapping, you require the following:

  • database
  • web server
  • data

That is all. You can have a web-map up-and-running with MapServer or MapGuide quite easily, definitely within less than a day depending on how complicated and stylish you want to get.

But look deeper and what is it we are after? The data.

Where is the data stored? In a database.

So why don't we work on bringing OLAP into the Internet mapping and GIS worlds?

Aggregations of data can occur anywhere.

You can group data by postal/post/zip codes, populations, etc. - this is prime data for OLAP.

Take industries such as oil and gas - well production is recorded on an hourly basis. This can be summed and aggregated into data marts (OLAP) for daily, monthly, yearly.

The maps are a starting point, but there should be no disconnect between the data, databases, GIS, internet mapping, as we are only working with data and transforming it into much more usable and valuable information.

By bringing OLAP into GIS and Internet mapping, you can add more value to your client's data and this data can be fed into other applications for reporting, etc., etc..

The internet map acts as a portal to a whole other world of information.

Just a few thoughts, as I'm involved in both worlds presently.

What do you think?

Feel free to write and let me know.

Saturday, November 3, 2007

Axis Order Confusion: Software, Geodesy & Transformations

Axis Order Confusion

Not simply X, Y, Z or N, E, S, W, but how we interpret them and use them in software, geodesy and navigation - it varies and has led to confusion among many people. This is an overview of the systems, the problem and points out things to take note of.

Over time, since the early days of mathematics, and then moving into software development, GIS and internet mapping, axis play an important role, whether it be in datum transformation or even displaying a map.

Is it X,Y,Z or Z,Y,X?

As we know in mathematics, a coordinate system is a system for assigning n-tuple of numbers or scalars to each point in n-dimensional space.

We are familiar with the following coordinate sytems involved in GIS/Mapping and Geodesy:

  • Cartesian coordinate system, which may be called "rectangular", where for 3D space, it uses three numbers representing some distance

  • Polar coordinate systems

  • Curvilinear coordinates, which are based on an intersection of curves

Delving further into Polar coordinate systems, we see the following subtypes:

  • Circular coordinate systems, which is represented by a point in a plane, by an angle, and a distance from the origin

  • Cylinderical coordinate systems which require a point in space, a distance from an origin an a height

  • Spherical coordinate system, which is represented by two angles and a distance from an origin

In mapping and geodesy, we deal quite often with Spherical coordinate systems and often refer to them as Geographic Coordinate Systems.

Ordered Pairs & Coordinate Systems

In GIS software and mapping software, we have three different perspectives for an Ordered Pair (2-tuple). They are in computer science, mathematics and of course Geographical Coordinate Systems.

Let's take a quick look at how these distinct perspectives see the their world:

In computer science and computer graphics, the axis order is (X,Y), where unsigned values increase to the bottom and to the right.

Mathematics sees this world differently for the same axis order (X,Y), where we have signed values increase to the right and upwards.

In the world, where we are most involved, Geographical Coordinate Systems, the axis order varies, sometimes being (X,Y) or (Y,X). The signed values increase upwards and to the right, based on a spheroid, hence we have -180, -90, 180, and 90.

Rotation Confusion as Well - Which Sign is positive?

There are 2 different conventions in use in the survey and mapping industry for defining rotations.

This too has led to considerable confusion in the GIS and mapping world.

Both are valid when used properly.

The two conventions can be referred to as:

1) Position Vector rotation (Commonly referred to as the Busra-Wolfe)

2) Coordinate Frame rotation

This essentially comes down to the left-handed vs. right-handed rotations (see image above) for the various transforms.

But what does this mean with left vs. right? Well, this is one way of determining orientation of axes and direction of rotations.

  • Thumb = Positive X
  • Index up = Positive Y
  • Middle out = Positive Z

Clifford's Point of View

Clifford Mugnier of LSU, whom I met when I lived in Houston, gives a good explanation and way of handling rotations and coordinate systems. His reply can be found here.

My quote follows:

"Probably the best way to document a rotation method is:

use the accepted terms "coordinate frame" and "position vector".

These terms are also used in other disciplines like kinematics (robotics).

But there are more difficulties.One datum transformation method is laid down in the ISO 19111 standard.

This is an approximated 7-parameter Helmert transformation with position vectorrotation. See also ISO/IEC 18026 - Annex B.

PROJ uses about the same method, only the scaling method differs. PROJ does a scalar multiplication, ISO a matrix multiplication.

With the commonly used parameter ranges, the differences between the scaling methods are less than microns, so not important.

As far as I know, the Bursa-Wolfe transform is an approximation to theHelmert transform. The Helmert transform has sines and cosines in therotation matrices, whereas Bursa-Wolfe (and ISO 19111) use the angles themselves (since sin(a) ~ a, sin(a)*sin(b) ~ 0, and cos(a) ~ 1 for small angles).

If you read section B.6 of ISO/IEC 18026, then you'll notice that aBursa-Wolfe transform can be done with a position vector rotation model OR with a coordinate frame rotation model.

Just what one likes the best; be sure to use the correct sign of the rotation angles.


Bursa-Wolfe is NOT equivalent with this or that rotation model.

A well known expert repeatedly states that the Australians use the same datum transform rotation model as the Americans.

This is NOT true!

The order of the rotations differs (XYZ vs. ZYX).

See the Australian GDATechnical Manual.

By the way, if the rotations are approximated, then the order is not important.

Again, the differences in rotation order for real life numbers are literally microscopic."

He clearly points out, and I agree, that it is "silly to refer to a datum transformation method as an American, Australian, European, whatever regional model. If you want to document the way for instance an application transforms,givethe complete formulae, not just an ill-defined name. Why not referring to the EPSG coordinate transformation method numbers? These clearly define the most used datum transformation methods and projection methods."

A simple solution to a complex problem of rotations.

The key is to document and document and be sure to specify what is being done, what axis are being used and let your users know. Do not assume, ask questions, and your life will be easier when dealing with coordinate sytems and rotations.

Or even simplier, as Clifford points out, refer to the coordinate transformation method numbers referenced in the EPSG data and data model for defined coordinate sytems.

Friday, November 2, 2007

CS-Map, Open Source & FDO - Autodesk Speaks

This article was recently published by the Australian PC World magazine. In it they interview Autodesk's Liam Speden about CS-Map and how it will be integrated into OSGeo.

CS-Map currently supports many projections and over 3000 coordinate systems.

It is an interesting read and shows how Autodesk believes that because there are so many coordinate systems out there, Open Source can make their customers benefit from this technology and how the rapid development and implementation that takes place in the Open Source world provides a sound and stable product used by real users.

Take a look at some of the books I've listed on the side bar. They explain Open Source quite well and how innovation can happen elsewhere.

EPSG & UKOOA - Defining Co-ordinates in Digital Data Exchange Formats

Introduction to the Offshore

UKOOA and the EPSG have been working together for many years. Through their collaboration, they have developed many standards and UKOOA has been open to listening to the industry about positioning in the North Sea.

When seismic data is acquired, whether it be 2-D or 3-D seismic surveys, the shotpoints (energy source, common mid-point, etc.) need to be positioned or referenced on surface.

Over the years UKOOA has developed various formats, named via a version and a year. This is a short introduction to how these files describe positions in the oil and gas industry.


Information is described in the Header for the file. The Header records following the convention listed below:

Record Identifer "H" Column(s): 1 Format: A1
Header Record Type 2-3 I2
Header Record Type Modifier 4-5 I2
Parameter Description 6-32 A27
Parameter Data 33-80 Varies

Using the above as a basis, let us take a look at how Datum and Spheroid information is described in this file.

Header records H1600 and H1601 are required for Datum Transformation parameters used by the Bursa-Wolfe Transformation.

Reviewing the Bursa-Wolfe Transformation (as vectors), we see the following:

X DX 1 -RZ +RY X
Y = DY + SCALE * +RZ 1 -RX * Y
Z DZ -RY +RX 1 Z


X,Y,Z are geocentric cartesian coordinates defined in metres
DX,DY,DZ are the translation parameters defined in metres
RX,RY,RZ are clockwise rotations defined in arc seconds,
but are converted to radians for use in the formula

SCALE = [1+S. (1oe-6)] where S is in parts per million

The Vertical Datum, is identified by Header record H1700. Some examples of the vertical datum, in relation to offshore work are:

LAT - Lowest Astronomic Tide
MSL - Mean Sea Level
SL - Sea Level
ES - Echo Sounder

The units of measurement are specified in H2001. These should be consistent with the position data. The height unit code will be 1 for metres, 2 for any other unit of measure. Header H2002 specifies the Angular unit code to 1 for degrees, 2 for grads.

Projection Data is specified in Header records H1800 to H2509

Currently, in this older format, the following projection codes were defined and used.

001 - UTM Northern Hemisphere
002 - UTM Southern Hemisphere
003 - Transverse Mercator (North Oriented)
004 - Transverse Mercator (South Oriented)
005 - Lambert Conic Conformal with one standard parallel
006 - Lambert Conic Conformal with two standard parallels
007 - Mercator
008 - Cassini-Soldner
009 - Skew Orthomorphic
010 - Stereographic
011 - New Zealand Map Grid
999 - Any other projection or non-standard variation of the 11 listed above

Since this initial positioning file was developed with the help of surveyors, they planned ahead and answered the question: What happens when we cross the Equator?

When a survey crosses from the South to the North, and the whole survey is shot on a Southern Hemisphere UTM Zone, the coordinates will possibly exceed 9,999,999.9. This is not acceptable in the P1/90 format, so Header record H2600 must indicate that 10,000,000 must be added to the co-ordinates.

More detail about this specification can be found here.

As the industry matures, new versions were released, the next in 1994. This was called p2/94 and was derived for raw marine positioning data.


During this time, differential positioning with GPS was just being implemented and the industry was beginning to rely on this technique more and more for offshore surveying.

This format is based on UKOOA p2/91 and has extended many of the definitions needed for differential GPS.

As operators maintain and store data in these formats, P2/94 also acts as an archiving format and records information such as the satellite ephemeride, ionospheric conditions and weather/meteorological conditions of the survey.

With the move to P2/94, Geodetic information moved to new headers, and are such described as:

H0100 Magnetic Variation - General Information
H0101 Magnetic Variation - Grid Data
H011# Datum and Spheroid Definitions

where # = 1..9 and is the datum & spheroid number

H0120 Seven Parameter Cartesian Datum Shifts
H0130 Other Datum Shift Parameters
H0140 Projection Type
H0150 (Universal) Transverse Mercator Projection
H0160 Mercator Projection
H0170 Lambert Projection
H0180 Skew Orthomorphic & Oblique Mercator Projection
H0181 Skew Orthomorphic & Oblique Mercator Projection cont.
H0190 Stereographic Projection
H0199 Any other Projection

Satellite System Definitions

H600# Satellite System Description
H610# Definition of Differential Reference Stations
H620# Satellite Receiver Definition
H6300 GPS parameter recording strategy
H6301 DGPS differential recording strategy
H631# GPS clock and ephemerides parameters
H632# GPS ionospheric model & UTC parameters
H6330 Meteorological parameters
H65## DGPS differential correction source defn
H66## DGPS differential correction source defn
H67@0 GPS ellipsoid height estimate

Rotation Conventions

Note that 2 different conventions are in use in the survey industry for defining rotations. This has led to considerable confusion in the GIS and mapping world. Both are valid when used properly.

The two conventions can be referred to as:

1) Position Vector rotation (Commonly used in Europe and referred to as the Busra-Wolfe)
2) Coordinate Frame rotation (Commonly used in North America)

I will talk more about these on a later blog, as it comes into play with a lot of GIS and mapping software.

More detailed information about the P2 format can be found here.


This version came along to facilitate the exchange of position data for pipelines, flowlines, umbicals and power cables offshore.

In these cases, the data required for pipeline positions are the Latitude, Longitude, Easting, Northing, Depth, and Kilometre Point (KP), along with the standard datum and map projection parameters.

Without wanting to bore my readers with more H records, you can found out more about how the pipelines are stored in this format here.


In 1998, a new version was developed for 3D seismic surveys and binning.

This is quite complex and would make this short blog even longer, so I'll write about this format at a later date.

The main emphasis of this blog, though, is to show how formats can change over time as technology and data sharing increases. It also points out the importance of knowing the format of your data, especially if you are doing historical work over a region - do not always assume a specific data format. This is partly why the OGP has started the Joint Industry Project I mentioned in an earlier post.

UKOOA P7/2000

Well's deviate. With the advent of horizontal wells and sidetracks, and relating to seismic surveys, we enter a whole other story again.

In this story, as well (bad pun!), we have to consider height measures (such as Kelly-Bushing), and the 4 Norths (which I will explain on a later post).

As this file type would make this blog even longer, I'm going to jump ahead to what the EPSG and UKOOA are doing now in defining the Header records for this specific part of the oil and gas industry.

How the EPSG comes into Play

Turning our eyes to the EPSG in P formatted files, we want to enable integrity checking of co-ordinate system definitions in UKOOA P1, P2, P5 and P6 formats, so a provision is made to describe co-ordinate system by reference to the European Petroleum Survey Group (EPSG) database of geodetic parameters. This is the group of codes we see in use throughout the GIS field and in products such as ESRI and PROJ.4.

What this allows UKOOA to do is to adopt an industry-standard name to be quoted where the geodetic co-ordinate system used is a common system. Defining parameters and units are then as given by EPSG and are not strictly required to be explicitly given in the P-format records.

As an integrity check, it is considered good practice also to include the explicit definition .The new records which can be used as extensions within the P1/90, P2/94, P5/96 and P6/98 formats are:

H8000 EPSG Geographic CS Name
H8001 EPSG Geographic CS Code
H8002 EPSG Projected CS Name
H8003 EPSG Projected CS Code
H8004 EPSG Vertical CS Name

H8005 EPSG Vertical CS Code
H8006 EPSG Database Version

As we know, co-ordinate systems may be two- or three- dimensional.

A vertical co-ordinate system is one-dimensional.

For the P1, P2 and P5 formats:

the H8002, H8003 and H8006 records are required when latitude, longitude, easting and northing but no height or depth are given;

the H8002, H8003, H8004, H8005 and H8006 records are required when latitude, longitude, easting, northing and gravity related height or depth are given;

the H8000, H8001, H8002, H8003 and H8006 records are required when latitude, longitude, easting, northing and ellipsoidal height or depth are given.

For the P6 format, the H8002, H8003 and H8006 records are required.

That is the way UKOOA and the EPSG see the offshore world when it comes to positioning and exploration in the North Sea and elsewhere.

Exploration & Production Blog

If you are interested, I also write another blog on the oil and gas industry, mainly describing where exploration is occurring, the technology being used, history of a region, some geology, etc. and some aspects of the UN Convention on the Law of the Seas.

The blog is located here.


Thursday, November 1, 2007

Quarter Degree Grid Cells: Another way of Mapping Africa

Recently, Ragnvald Larsen of the Norwegian University of Science and Technology (NTNU) in Trondheim released some news to the Spatial Data Infrastructure for Africa (SDI-Africa) mailing list.

He has been working on project about creating Quarter Degree Grid Cells for mapping purposes for the African countries on a national level.

But what are Quarter Degree Grid Cells?

Quarter Degree Grid Cells (QDGC) are a way of dividing longitude and latitude degree square cells into smaller squares, forming in effect a system of geocodes. This is similar to the NTS system in Canada (for mapping the Northern areas of Canada) and to the way the North Sea is mapped when determining leases by the various countries involved (Norway, Denmark, UK, Germany, the Netherlands). An example of how the North Sea is subdivided by country follows:

The respective sectors are divided by median lines agreed in the late 1960s.

In the United Kingdom, the UKCS (United Kingdom Continental Shelf) is divided into quadrants of 1 degree latitude and one degree longitude. Each quadrant is divided into 30 blocks measuring 10 minutes of latitude and 12 minutes of longitude.

Norway has a similar model and is divided into quadrants of 1 degree by 1 degree. Norwegian licence blocks are larger than British blocks, being 15 minutes of latitude by 20 minutes of longitude (12 blocks in a quad).

In Denmark, the Danish sector of the North Sea is divided into 1 degree by 1 degree quadrants, and their blocks are 10 minutes latitude by 15 minutes longitude.

Germany and the Netherlands share a quadrant and block grid - quadrants are given letters rather than numbers. The blocks are 10 minutes latitude by 20 minutes longitude. The Dutch sector is located in the Southern Gas Basin and shares a grid pattern with Germany

So the theory of using grid squares has been around for quite some time.

Almost Equal Areas

QDGC represents a way of making (almost) equal area squares covering a specific area to represent specific qualities of the area covered. The squares themselves are based on the degree squares covering earth.

We know that around the equator there are 360 longitudal lines lines. For latitude, i.e. from the north to the south pole we have 180 latitudal lines. Multiplying we determine that this gives 64800 segments or tiles that can cover earth. The form of the squares becomes more rectangular the further north or south we move. At the poles they are not square or even rectangular at all, but end up in elongated triangles.

Each degree square is designated by a full reference to the main degree square.

An Example using Tanzania

Taking from the project web-site, I'll use their example, with regards to Tanzania.

S01E010 is a reference to a square in Tanzania. S means the square is south of equator, and E means it is East of the zero meridian.

The numbers refer to longitudal and latitudal degree.

A square with no sublevel reference is also called QDGC level 0.

This is square based on a full degree longitude by a full degree latitude. The QDGC level 0 squares are themselves divided into four.

A grid at this level is shown as:


Smaller squares are determined by dividing the above squares into 4 again.

So if we divide S01E010 by four again, the new grid would be S01E010AD.

The number of squares for each QDGC level can be calculated using the following formula:

number of squares = (2^d)^2 where d is QDGC level

Putting all the above theory into place, there is code out there that will allow you to compute a Quarter Degree Grid Cell, please follow the link here.

Project Information

For more information on this project and the work done by Ragnvald Larsen, please take a look at QDGC.

The attached image shows QDGC being used for mappings of the fires in Africa in the year 2000.

Monday, October 29, 2007

ETL: Fundamental to Spatial Analysis and Sharing of Data

Extract, Transform, and Load

ETL or Extract, Transform, and Load is a process in Data Warehousing. Data Warehouses are all around us - whether we are querying the Yellow Pages on-line to geo-coding our datasets, there is most often a database or data warehouse behind the scenes.

But how we get data into the warehouse, is called ETL.

This is a short introduction to ETL as it is an important part of data warehousing. I also cover a little about Spatial ETL.


Extract is where we begin this story. Essentially, in this step, we extract the data from source systems. A source system is where the data originates. It may be a well database, an address database, a MSExcel CSV file or almost anything you can think of.

A data warehouse ends up consolidating the data from different source systems. Each separate source system (in many cases) use a different data organization or format. Common data source formats are relational databases and flat files.


As our story continues, we run into the transform stage. In this chapter, we want to apply a series of rules or functions to the extracted data from the source to derive the data to be loaded to the end target.

If we are fortunate in having clean data (this rarely happens!) the data source will require very little or even no manipulation of the data. The most common scenario is that one or more of the following transformations need to be done to meet the business and technical needs of the end users.

For example, some of the transformations that may occur are (taken from Wikipedia - a good listing of transformations):

  • Selecting only certain columns to load
  • Translating coded values (e.g., if the source system stores 1 for male and 2 for female, but the warehouse stores M for male and F for female), this is called automated data cleansing; no manual cleansing occurs during ETL
  • Encoding free-form values (e.g., mapping "Male" and "1" and "Mr" into M)
  • Deriving a new calculated value (e.g., sale_amount = qty * unit_price)
  • Joining together data from multiple sources (e.g., lookup, merge, etc.)
  • Summarizing multiple rows of data (e.g., total sales for each store, and for each region)
  • Generating surrogate key values
  • Transposing or pivoting (turning multiple columns into multiple rows or vice versa)
  • Splitting a column into multiple columns (e.g., putting a comma-separated list specified as a string in one column as individual values in different columns)
  • Applying any form of simple or complex data validation; if failed, a full, partial or no rejection of the data, and thus no, partial or all the data is handed over to the next step, depending on the rule design and exception handling.


After the data has been transformed, cleansed, it is now loaded into the data warehouse.

Spatial ETL

When we apply the above principles to spatial data, we call it Spatial ETL.

As we know, spatial data can suffer tremendously in accuracy, data formats, projections, datum's, etc.

With the advent of WFS and WMS and other Web Services and definitions - knowing how accurate and clean our data is is important - especially since in Web Services we are sharing data between systems.

A common method in the Well-known text (WKT). WKT is a text markup language for representing vector geometry objects on a map. It also relates to spatial reference systems of spatial objects and of the transformations between spatial reference systems. A binary equivalent, known as well-known binary (WKB) is used to transfer and store the same information on databases, such as PostGIS. The formats are regulated by the Open Geospatial Consortium (OGC) and described in their Simple Feature Access and Coordinate Transformation Service specifications.

Frank Warmerdam, the creator and maintainer of the PRO.4 and GDAL libraries of which I've talked about before covers quite well, WKT implementations and things to be aware of in several GIS products (some of the information is out of date - most users are now using Arc 9 and above).

Quoting below (from here):

  • Oracle Spatial (WKT is used internall in MDSYS.WKT, loosely SFSQL based)
  • ESRI - The Arc8 system's projection engine uses a roughly simple features compatible description for projections. I believe ESRI provided the WKT definition for the simple features spec.
  • Cadcorp - Has the ability to read and write CT 1.0 style WKT. Cadcorp wrote the CT spec.
  • OGR/GDAL - reads/writes WKT as it's internal coordinate system description format. Attempts to support old and new forms as well as forms from ESRI.
  • FME - Includes WKT read/write capabilities built on OGR.
  • MapGuide - Uses WKT in the SDP data access API. Roughly SF compliant.
  • PostGIS - Keeps WKT in the spatial_ref_sys table, but it is up to clients to translate to
  • PROJ.4 format for actual use. I believe the spatial_ref_sys table is populated using OGR generated translations.

ETL and Spatial ETL - I'll cover more of how data warehousing and GIS and internet mapping can be tied together at a later date.

If you are really interested, take a look at the MapBender project mentioned in earlier posts. It ties together many of the concepts of ETL and data sharing quite well.

If you have ideas for Blog posts that relate to GIS, Datum's, Map Projections, Oracle, Data Warehousing, let me know. Some ideas for future blogs are:

  • The African Geoid Project
  • Map Projections of the Middle East
  • Determining Mean Sea Level
  • NTv2 files and how to create them

Let me know. Contact me via e-mail.

Friday, October 26, 2007

Joint Industry Project: Geospatial Integrity of Geoscience Software

Devon Energy, Shell, and ExxonMobil and several other major oil companies have started a Joint Industry Project (JIP) entitled "Geospatial Integrity of Geoscience Software".

This project is being financed by the oil majors and is being undertaken with the support and co-operation of the International Association of Oil and Gas Producers (OGP).

As professionals involved mapping, software development, positioning, often the co-ordinate reference systems in the code are taken for granted. This happens in the oil industry in geoscience applications and interpretation packages.

In the past, software provided defaults (such as Clarke 1866 or NAD27 - as it was software developed in North America), but with the movement into global geodetic reference systems (such as WGS84), and many local datum's still being used, software may or may not be upgraded (for various reasons) or further modified (feel that it is working fine), etc., etc., there is the distinct possibility and fact that mistakes have been made due to software errors. The errors may have occurred because of the following reasons:

  • improperly coded or cartographic algorithms

  • wrong values for embedded geodetic parameters

  • poor presentation of user input requirements by software applications

  • incorrect defaults settings (as mentioned above)

  • software processes not working as specified (take a look at the Robinson projection discussion and cs2cs and the various work-arounds to account for a spherical representation)

  • confusing or imprecise terminology (take co-ordinate reference frames and datum transformations for example)

  • lack of error trapping for user errors

  • lack of an audit trail

  • inadequate metadata

  • inadequate training and documentation for users and of users

There are three main objectives of this Joint Industry Project, and they are:

  • To transform the management of geospatial data in geoscience software applications to benefit JIP members and improve products and competencies

  • To develop and disseminate best practice tools for current software applications and future software development

  • To create a sustainable improvement process in geoscience software applications based on sound geospatial management

By the end of 2007, the JIP has already begun to take a look at Blue Marble's GeoGraphic Calculator. This application and libraries is used in commercial code (such as Oracle) and many oil and gas companies use it on a daily basis.

An example of a possible wrong vertical co-ordinate system happened November, 1999 to Chevron. The article can be found here. I've also included it below:

Chevron Mulls Options After Platform Sinks, Friday, November 12, 1999

Chevron Corp. is assessing the impact on the development timetable of its North Nemba oilfield off the Angola coast after the sinking of the production platform on route from South Korea. The $175 million dollar structure was being shipped by the vessel Mighty Servant 2 early last week when it capsized near the Indonesian island of Singkep with the loss of four crew members. The so-called topside production platform is 230 ft. long, 105 ft. wide, 150 ft. tall and took 24 months to design and build. The vessel was enroute from the South Korean port of Okpo to Angola, having fueled in Singapore, when it began taking on water and sank. Chevron spokesman Fred Gorrell said the company was fully covered by insurance to replace the platform. The vessel was lying in 35 m of water with about 5 m sticking above the surface so recovery was still being assessed. Gorrell pointed out that even if it needed to be rebuilt it would not take as long as the original because design and engineering work was already done. The North Nemba field in the prodigious Block O offshore Angola was due to come into production in the first quarter of 2000. Block O, in which Chevron has a 39 percent interest, produced 510,000 bpd in 1998. Gorrell said he wasn't sure how much North Nemba was due to add to this. Chevron owns 39.2 percent of North Nemba, while the state Angola National Oil Co. owns 41 percent, with Italy's Agip owning 9.8 percent and France's Elf Aquitaine with 10 percent.

Co-ordinates, the software we use, whether in mapping or geoscience software plays a role in many of our decisions.

This Joint Industry Project is a good start and the people involved are knowledgeable in the field (many I've worked with when I was in Houston) and through this project we can hopefully know at the end, that the software we are using is providing accurate information and maintains geospatial integrity.

More details can be found at this website.

Thursday, October 25, 2007

Molodensky: A Short History of Man's Contribution to Geodesy

As internet mapping becomes more and more prevelant and GPS is being used more we keep on hearing about the Molodensky Transformation, but who was Molodensky?
A Short History
Mikhail Sergeevich Molodenksy (1909 - 1991) was a promiennt geodesist and geophysicists who many consider a reformer in the theory of the figure of the Earth and the study of the Earth's rotation and oscillations.
He was born on June 15, 1909, in Epiphan, a small town in the Russian province of Tula. He did his initial studies at the Astronomic Department of the Mechanics and Mathematics Faculty of Moscow State University.
He was later invited by F. N. Krasovsky (there is an ellipsoid that bears this geodesist's name - more on a later blog about Russian mapping) to join the staff at the Central Research Institute of Geodesy, Aerophotogrammetry and Cartography (TsNIIGAik). It was here that he worked for over 25 years.
Molodensky's early steps in geodetic research and geodetic surveys date back to 1929 when he did some inital work for the Institute of General Geodetic Surveys (IOGR) and prior to this survey, he was given a proposal from the director of Astronomy - Geodetic Research Institute (AGNII) at State University in Moscow to do geodetic research.
There came a famous decree called the "Soviet of Labor and Defense" (May 6, 1927) which set about the establishment of a general gravimetric survey over the whole country. Lenin was laying out his vision for the country and defining a "Soviet". With this decree, there became an increase in the development of gravimetric surveying throughout the whole country.
Molodensky, who was avidly interested in gravimetry, participated in these surveys with his work at TsNIIGAik. While here and conducting these surveys, a young Molodensky, in 1933, headed up an expedition to the Crimea to perform gravimetric surveys (again under the above decree).
A Rigourous Solution
A year later, in 1934, Molodensky was beginning to make a name for himself by presenting a report at the 7th Baltic Geodetic Commission Conference in Moscow. His topic, which geodesists considered urgent at the time, is the co-swinging influence on double pendulums. Before his presentation, all solutions were seen as impossible because the accuracy of the solutions could not be determined. Molodensky provided a rigourous solution. In turn, this presentation was heard by scientists from Denmark, Finland, Germany, Poland, Sweden, the USSR and the members of the International Association of Geodesy. He essentially turned the world of geodesy upside down concerning astronomic-gravimetric leveling. His final report was published in Helsinki at the 1937 meeting of the Baltic Geodetic Commission.
Molodensky made significant developments to Soviet geodesy and gravimetry, in theory and in practice, especially when developing and applying survey methods combined with the design of gravimetric instruments. In the 1930's the only gravity measuring devices that could be found in the former Soviet Union were those of foreign manufacture. Therefore, the state saw immediately that there was an immediate task facing geodesy in the Soviet Union - the manufacture of gravity measuring instruments. A small batch were initially made, based on the German "Bamberg" instruments and several designs of original instruments had failed. It was not until 1938 that the Soviet Union had developed their own gravity measuring devices.
April, 1943, lead to the appointment of Molodensky as chief of the gravimetric laboratory at TsNIIGAik. He held this post until July 1956 when, against his will, he was appointed director of the Geophysical Institute of the Academy of Sciences (GEOFIAN). At this point he became responsible for the realization of the technical policies related to geodesy in the Soviet Union.
During this time he continued to make significant contributions to geodesy and the state wanted to recognize him for his efforts. In 1946, he was awarded the USSR State Prize, then he recieved the high degree of a Doctor of Technical Sciences and was then elected a member of the USSR Academy of Sciences.
The Geoid and Plumb-Lines
As you may recall in my previous blog, about the geoid, I discussed the "deflection of the vertical", well Molodensky's work played into this realm as well. Molodensky put forward the possibility of using gravimetric survey data for interpolation of plumb-line deflection between astronomic points of astronomic-geodetic networks. The result of this work permitted the integration of isolated sections of astronomic-geodetic networks into the main systems of co-ordinates. This made it therefore possible to map vast areas which had never been surveyed before.
Nowadays a similar process is in progress in Africa and South America and Canada with respects to gravity models which will help in determining Orthometric heights. Through Molodensky, lead to a determination of geoid heights.
In 1957, TsNIIGAik began to change direction in what it saw as important, and focused on solving more complex problems; such as the figure of the Earth, space exploration, defence problems, and the development of triangulation methods for large territories.
Famous Equations
Molodensky, though is more famous for a set of equations, that relate to datum transformation.
As we all know spatial data can have co-ordinates with different underlying ellipsoids or the underlying ellipsoids have different datums. The latter means that, apart from different ellipsoids, the centres or the rotation axes of the ellipsoids do not coincide. To relate these data one may need a so-called datum transformation.
In the early days of satellite surveying, when relationships between datums were not well defined and the data itself was not very precise, it was usual to apply a three parameter dX, dY, dZ shift to the X,Y,Z coordinate set in one datum to derive those in the second datum.
This assumed, generally erroneously, that the axial directions of the two ellipsoids involved were parallel. For localized work in a particular country or territory, the consequent errors introduced by this assumption were small and generally less than the observation accuracy of the data. As we collected more and more information about the shape and form of the Earth, and based on what Molodensky presented, among others, our knowledge and the amount of data that has been built up and as our surveying methods became more and more accurate, it became evident that a three parameter transformation is neither appropriate for world wide use, nor for widespread national use if one is seeking the maximum possible accuracy from the satellite surveying and a single set of transformation parameters.

The simplest transformation to implement involves applying shifts to the three geocentric coordinates. Molodensky developed a transformation which applies the geocentric shifts directly to geographical coordinates. This method assumes that the axes of the source and target systems are parallel to each other.
From a mathematical point of view a datum transformation is possible via 3 dimensional geocentric co-ordinates, thus implying a 3D similarity transformation defined by 7 parameters: 3 shifts, 3 rotations and a scale difference. This transformation is combined with transformations between the geocentric co-ordinates and ellipsoidal latitude and longitude co-ordinates in both datum systems.

The transformation from the latitude and longitude co-ordinates into the geocentric co-ordinates is rather straightforward and turns ellipsoidal latitude , longitude and height into X,Y and Z, using 3 direct equations that contain the ellipsoidal parameters a and e.

The inverse equations are more complicated and require either an iterative calculation of the latitude and ellipsoidal height.
A very good approximation of this datum transformations makes use of the Molodensky and the regression equations, relating directly the ellipsoidal latitude and longitude, and in case of Molodensky also the height, of both datum systems.
Various software uses the formulation put forward by Molodensky, whether used in cs2cs and ESRI software, or even in Oracle, the foundations where laid out by this man who has made significant contribution to our understanding of the shape and form of the Earth.

Monday, October 22, 2007

The Geoid - An Equipotential Description with Gravity

The Geoid is a surface that is not often talked about on blogs or mentioned on the web - so this may be a first.

The Geoid surface is irregular, unlike reference ellipsoids (such as Clarke 1866, Bessel, Hayford, etc.) which have been used to approximate the shape of the physical Earth at a local point. The geoid is considerably smoother than Earth's physical surface.

In looking for a good description that makes sense to many people, I stumbled upon this one on Wikipedia:

"In geodetic surveying, the computation of the geodetic coordinates of points is commonly performed on a reference ellipsoid closely approximating the size and shape of the Earth in the area of the survey. The actual measurements made on the surface of the Earth with certain instruments are however referred to the geoid. The ellipsoid is a mathematically defined regular surface with specific dimensions. The geoid, on the other hand, coincides with that surface to which the oceans would conform over the entire Earth if free to adjust to the combined effect of the Earth's mass attraction (gravitation) and the centrifugal force of the Earth's rotation. As a result of the uneven distribution of the Earth's mass, the geoidal surface is irregular and, since the ellipsoid is a regular surface, the separations between the two, referred to as geoid undulations, geoid heights, or geoid separations, will be irregular as well."

and further it states:

"The geoid is a surface along which the gravity potential is everywhere equal and to which the direction of gravity is always perpendicular. The latter is particularly important because optical instruments containing levelling devices are commonly used to make geodetic measurements. When properly adjusted, the vertical axis of the instrument coincides with the direction of gravity and is, therefore, perpendicular to the geoid. The angle between the plumb line which is perpendicular to the geoid (sometimes called "the vertical") and the perpendicular to the ellipsoid (sometimes called "the ellipsoidal normal") is defined as the deflection of the vertical. It has two components: an east-west and a north-south component."

The reference surface for heights is traditionally taken as Mean Sea Level (MSL).

The geoid, as described above, is a surface of equal gravity potential which closely approximates mean sea level.

With GPS becoming more and more relevant in our daily lives, what is the height measurement we get?
The heights derived from GPS are relative to the GPS reference ellipsoid (WGS84). The separation between the geoid and an ellipsoid is known as the geoid-ellipsoid separation, or N value.

In a mathematical sense, we have the following then:

H = h - N

where H = Orthometric Height

h = Ellipsoidal Height (for example, the height above the ellipsoid WGS84)

N = Geoid-Ellipsoid Height (this is also called the Geoid Undulation)

Note that with N, that if the geoid is above the ellipsoid, N is positive. If the geoid is below the ellipsoid, N is negative.

How does mass effect the geoid and the ellipsoid?

Where a mass deficiency exists, the geoid will dip below the mean ellipsoid and where a mass surplus exists, the geoid will rise above the mean ellipsoid.

Where are the largest undulations?

Well, the largest undulations known, with the minimum in the Indian Ocean at a value of N = -100 metres and the maximum in the northern part of the Atlantic Ocean with N = +70 metres.

So how do we describe the shape and size of the Earth?

There are three surfaces to be considered:

  • The topography - the physical surface of the earth.

  • The Geoid - the level surface (also a physical reality).

  • The Ellipsoid - the mathematical surface for computations.

Mean Sea Level (MSL) points, an approximation to the geoid, and can be used as reference surfaces for height measurements (i.e. orthometric heights).

Ellipsoidal heights (such as those derived by GPS) have to be adjusted before they can be compared to the orthometric heights given on topographic maps.

The deviation between the geoid and an reference ellipsoid is called Geoid undulation (N). Geoid undulations can be used to adjust the ellipsoidal heights (H = h +/- N).

This is an introduction to the Geoid and the science of Geodesy. It hopefully clears up some questions about this surface.

I'll explain in more detail some of the formulations of the Geoid and how geodesists over time have tried to model it and some of the efforts being conducted presently to come up with a global gravity model to aid in height determination at a later date.

There are some very interesting projects going on in Africa, South America, and Canada.

Sunday, October 21, 2007

The Robinson Projection: Not shaped like an Egg

A Pleasing View of the World

The Robinson Projection came into being in 1963 and was introduced by Dr. Arthur H. Robinson.

This projection can be classified as a pseudo-cylindrical projection because of its straight parallels, along each of which the meridians are spaced evenly. The central meridian is also a straight line and all other meridians are curved.

The projection is neither equal-area nor conformal, therefore abandoning both for a compromise for creating what Dr. Robinson felt produced a better overall view of the world. This was the first map projection to be developed for commercial interests. Rand McNally felt that many of the map projections in use did not present the earth as a whole very well. With Mercator the poles were distorted. Robinson, was essentially contracted to develop a map projection that did not maintain angle, direction, or limit distortion, but was sanctioned to produce a map projection that "looked good" for books and atlases.

Remember maps are designed for one of the following 4 reasons:

  • Conformality - the shapes of places are accurate
  • Distance - measured distances are accurate
  • Area/Equivalence - the areas represented on the map are proportional to their area on the earth
  • Direction - angles of direction are portrayed accurately

Dr. Robinson specified the projection to be constructed by referring to a table of cartesian coordinate values at specific intersections of latitude and longitude. The intermediate locations are to be found by interpolation. Dr. Robinson developed the projection through a series of trials, continually iterating till he settled upon the meridian shapes and parallel spacing most pleasing to the eye. In comparison with other Map Projections, they are mainly developed or are formulated as mathematical equations.

Parallels are straight parallel lines, equally spaced between latitudes 38 degrees north and south. Space decreases beyond these limits. The Equator is 0.8487 times as long as the circumference of a sphere of equal area. The central meridian is a straight line 0.5072 as long as the Equator. Other meridians are equally spaced elliptical arcs and concave toward the central meridian. The scale is true along latitudes 38 degrees north and south, constant along any given latitude, and the same for the latitude of opposite sign (Robinson 1974; Snyder and Voxland 1989).

This map projection is also based on a sphere, not an ellipsoid. This is an important point to remember, as the earth is being modelled differently.

What is the true shape of the Earth?

The Earth, in actual fact, is shaped more like an egg, hence, even an ellipsoid is not the best model. In the past, when datum's were more local (such as NAD27, SAD69, Cape Datum, etc.), various ellipsoids were tied to local points on Earth. For NAD27, this was Meades Ranch, Kansas.

But back to the Earth's shape; it is very close to an oblate spheroid — a rounded shape with a bulge around the equator — although the precise shape (the geoid) varies from this by up to 100 metres.

The rotation of the Earth creates the equatorial bulge so that the equatorial diameter is 43 km larger than the pole to pole diameter.

What about height? A whole other story.

Interesting, eh? There are so many different ways to see the Earth. When we look at height systems and describe the geoid, we are describing an equipotential surface. But height is a whole other story, as gravity is involved and it is not as simple as getting the "Zed" or "Zee" measurement from your GPS.

I'll explain height later and how we can determine MSL (and where the "mean" actually comes from).

Thursday, October 18, 2007

Google Maps: Is the Earth a Sphere or Ellipsoid?

Google Maps sees the Earth as a Spheroid, not an Ellipsoid. This came up through a discussion on the PROJ mailing list and I thought it was interesting to point out how Open Source can even handle projected lat/long systems (such as Google Maps) using a very familiar tool called cs2cs.

Christoper Schmidt wrote about it on his blog and also on his blog he points out the EPSG code to use. The magical number for the Google Mercator Projection (of a lat/long grid based on a sphere) is: 900913

Now onto the fun, showing how we can use Open Source to have our data show within a KML project and Google Maps. Quoting from Frank's FAQ, he provides an excellent example, we see the following the use of cs2cs:

"cs2cs +proj=latlong +datum=WGS84 +to +proj=merc +a=6378137 +b=6378137 +lat_ts=0.0 +lon_0=0.0 +x_0=0.0 +y_0=0 +k=1.0 +units=m +no_defs"

Notice the sphere is being used? a=b

Because we are dealing with a sphere, the Y values will be greatly different from those on an ellipsoid (30 to 100 metres or more).

Quoting Frank again:

"In this case, and many other cases using spherical projections, the desired approach is to actually treat the lat/long locations on the sphere as if they were on WGS84 without any adjustments when using them for converting to other coordinate systems. The solution is to "trick" PROJ.4 into applying no change to the lat/long values when going to (and through) WGS84. This can be accomplished by asking PROJ to use a null grid shift file for switching from your spherical lat/long coordinates to WGS84.

cs2cs +proj=latlong +datum=WGS84 +to +proj=merc +a=6378137 +b=6378137 +lat_ts=0.0 +lon_0=0.0 +x_0=0.0 +y_0=0 +k=1.0 +units=m +nadgrids=@null +no_defs

Note the strategic addition of +nadgrids=@null to the spherical projection definition"

As you can see the value of Open Source and the mailing list and Open Source software is that people are sharing knowledge - whether it be via blogs, lists, or some other means of communication. There is a community out there that supports each other. These are actual users facing everyday problems and looking for solutions. The answers do exist, just the question has to be asked, and the community comes together to help.

Thursday, October 11, 2007

Is WGS84 really WGS84? Is it correctly defined?

While doing some research on things that geodesists like - questioning MSL and the geoid, questioning how exact our definitions of ellipsoids and the earth are, I stumbled upon a very interesting article, written by Muneendra Kumar, PhD (Retired, National GeoSpatial Intelligence Agency) and James P Reilly, PhD (New Mexico State University) and they were asking:

Is definition of WGS 84 correct?

The following is written by these two distinguished gentlemen and I hope it proves to be as interesting to everyone as it was to me.

In the end, though, for most mapping purposes, WGS84 is still WGS84 and your latitude and longitude, or your Northing and Easting will remain the same.

As a side note, the North Pole is moving south and Sea Level is not level!

More on that little bit of geodesy in a later blog.

Enjoy and feel free to write me if you have any questions or comments.

Is Definition of WGS84 Correct?



A Geodetic Analysis

The first and original version of the "WGS 84", defined by a special committee of the Defense Mapping Agency (DMA), was released in September 1987.

As this task of updating the WGS 72 was concurrent with development of the North
American Datum (NAD) 1983, the committee members always had many in-depth
discussions with the members of the special committee of the National Geodetic
Survey (NGS). This approach ensured the; correct geodetic definition both for
WGS 84 and NAD 83. Around 1992, it was decided by DMA that, in future update(s)
of the "WGS 84" for accuracy enhancement, the academia and other satellite
geodesy experts would be associated. However, that scientific participation was
not followed and three subsequent updates were carried out without in-depth
discussions of satellite geodetic theory and/or correct statistical evaluation.
The non-scientific procedure(s) allowed definition deficiencies to creep in.
This paper outlines the geodetic details of the three updated versions of 1994,
1996, and 2001 and brings out in "open" the definition deficiencies in the
current version WGS 84 (G1150), which otherwise will remain hidden within the
National Geospatial- Intelligence Agency (NGA).The correctly defined "WGS 84",
the coordinate system used in GPS, is a critical requirement for the geodetic
integrity and accurate GPS positioning.

1984 "Original" Definition

The WGS 84 was originally defined with BIH Conventional Terrestrial System (CTS) for Reference Epoch "RE (84.0)". The main satellite data sets used were from the
Navy Navigation satellite System (NNSS). At the time of release in 1987, the
accuracy achieved was in the order of ± 1 - 2 meter and as such the tidal
effects, as specified in the International Association of Geodesy (IAG)
Resolution 16 of 1983 were not considered.

The "Three" WGS 84 Updates

1994 "WGS 84 (G730)"

This version was updated with the International Earth Rotation Service(IERS) realized International Terrestrial Reference Frame (ITRF) 19921, RE (88.0). During this update, NGA moved the RE (88.0) of the defining
ITRF to RE (94.0), which is incorrect. For this "change", DMA geodesists did not
have the capability and expertise. And, they did not have the authority to
override IERS. Note: With a new origin and orientation of its three axes, WGS 84
(G730) is geodetically a different coordinate system than the original WGS 84.
For mapping, the two could be considered the same. 1 First six ITRF solutions,
viz., ITRF 1988, ITRF 1989, ITRF 1990, ITRF 1991, ITRF 1992, and ITRF 1993, were realized for the RE (88.0). As the ITRF 1993 was based on all the data sets
available up to the end of year 1993 and thus realized in 1994, it would not
have been possible for DMA to define the WGS 84 (G730), which was realized using
the GPS data for the week starting 2 January 1994.

1996 "WGS 84 (G873)"

At the time of this update, the ITRF 1994, RE (93.0) was used (Note: ITRF96 (93.0) was not available). But, DMA geodesists again incorrectly moved the epoch of the
defining "RF" to RE (97.0). And, for geodetic application, they created the
third WGS 84. In addition, ignoring IAG Resolution No. 16 of 1983 and bypassing
IERS Conventions (IERS, 96), which recommend the "Zero-tide" model, National
Imagery and Mapping Agency (NIMA) geodesists adopted an "arbitrary" practice to
use "Tide-free" model. Note: According to IERS, the positions in the "Tide-free"
environ are non-realistic and not observable.

2001 Current "WGS 84 (G1150)"

During the updating of this version, the ITRF00, RE (97.0) was used.
But, like the 1994 and 1996 versions, NIMA geodesists incorrectly moved the RE
of the defining RF from (97.0) to (01.0), They also kept the 1996 practice for
"Tide-free" model, even after being alerted that the world's eminent geodesists
support the "Zerotide" of the IAG' standing Resolution No. 16 of 1983.
Furthermore, during the adjustment of the GPS tracking stations network, about
65% stations were held fixed (Note: An objection by the first author was not
even discussed). This over constrained adjustment is statistically incorrect and
not acceptable. Note: For geodetic positioning, this is the fourth version of
WGS 84.

The "Version" Identifiers

The "G730", "G873", and "G1150" indicate the GPS-week, of which the data sets were used to realize the three updates. As these "identifiers" do NOT specifically identify any definite time epoch, they do NOT have any geodetic significance.

Important "Contrast" To Note In SIRGAS 2000, the "RE" of the defining ITRF has NOT been "moved".

Analytical Conclusion

The current "WGS 84 (G1150)" is incorrectly defined, does not
comply with IAG Resolution No. 16 of 1983, and its time epoch is not definitive.
Furthermore, the adjustment of the GPS tracking station network is statistically


IERS, 96 IERS Conventions, Tech Note 21, July 1996.