Specification Version: 1.7

Last Modified: 13 July, 1995

GENERAL

1 Introduction

1.1 About this Specification

1.1.1 Background

1.1.2 History

1.1.3 Scope

1.1.4 Features

1.2 Revision Notes

1.2.1 Revision Nomenclature

1.2.2 New Features

1.2.3 Clarifications

1.2.4 Organizational changes

1.2.5 Changes in Requirements

1.2.6 Agenda for Future Development

1.3 Administration

1.3.1 Information and Support

1.3.2 Private Keys and Codes

1.3.3 Proposed Revisions to GeoTIFF

2 Baseline GeoTIFF

2.1 Notation

2.2 GeoTIFF Design Considerations

2.3 GeoTIFF Software Requirements

2.4 GeoTIFF File and "Key" Structure

2.5 Coordinate Systems in GeoTIFF

2.5.1 Device Space and GeoTIFF

2.5.2 Raster Coordinate Systems

2.5.2.1 Raster Data

2.5.2.2 Raster Space

2.5.3 Model Coordinate Systems

2.5.3.1 Geographic Coordinate Systems

2.5.3.2 Geocentric Coordinate Systems

2.5.3.3 Projected Coordinate Systems

2.5.3.4 Vertical Coordinate Systems

2.5.4 Reference Parameters

2.6 Coordinate Transformations

2.6.1 GeoTIFF Tags for Coordinate Transformations

2.6.2 Cookbook for Defining Transformations

2.7 Geocoding Raster Data

2.7.1 General Approach

2.7.2 GeoTIFF GeoKeys for Geocoding

2.7.3 Cookbook for Geocoding Data

3 Examples

3.1 Common Examples

3.1.1. UTM Projected Aerial Photo

3.1.2. Standard State Plane

3.1.3. Lambert Conformal Conic Aeronautical Chart

3.1.4. DMA ADRG Raster Graphic Map

3.2 Less Common Examples

3.2.1. Unrectified Aerial photo, known tiepoints, in degrees.

3.2.2. Rotated Scanned Map

3.2.3. Digital Elevation Model

4 Extended GeoTIFF

5 References

6 Appendices

6.1 Tag ID Summary

6.2 Key ID Summary

6.2.1 GeoTIFF Configuration Keys

6.2.2 Geographic CS Parameter Keys

6.2.3 Projected CS Parameter Keys

6.2.4 Vertical CS Keys

6.3 Key Code Summary

6.3.1 GeoTIFF General Codes

6.3.1.1 Model Type Codes

6.3.1.2 Raster Type Codes

6.3.1.3 Linear Units Codes

6.3.1.4 Angular Units Codes

6.3.2 Geographic CS Codes

6.3.2.1 Geographic CS Type Codes

6.3.2.2 Geodetic Datum Codes

6.3.2.3 Ellipsoid Codes

6.3.2.4 Prime Meridian Codes

6.3.3 Projected CS Codes

6.3.3.1 Projected CS Type Codes

6.3.3.2 Projection Codes

6.3.3.3 Coordinate Transformation Codes

6.3.4 Vertical CS Codes

6.3.4.1 Vertical CS Type Codes

6.3.4.2 Vertical CS Datum Codes

7 Glossary

GENERAL

Authors:

Niles Ritter, Jet Propulsion Laboratory

Cartographic Applications Group

4800 Oak Grove Dr.

Pasadena, CA 91109

email:ndr@tazboy.jpl.nasa.gov

Mike Ruth, SPOT Image Corp

Product Development Group

1897 Preston White Dr.

Reston, VA 22091

email:ruth@spot.com

Acknowledgements:

GeoTIFF Working Group:

Mike Ruth, Niles Ritter, Ed Grissom, Brett Borup, George Galang,

John Haller, Gary Stephenson, Steve Covington, Tim Nagy,

Jamie Moyers, Jim Stickley, Joe Messina, Yves Somer.

Additional advice from discussions with Tom Lane, Sam Leffler regarding TIFF implementations.

Roger Lott, Fredrik Lundh, and Jarle Land provided valuable information

regarding projections, projection code databases and geodetics.

GeoTIFF Mailing list:

Posting: geotiff@tazboy.jpl.nasa.gov

Subscription: geotiff-request@tazboy.jpl.nasa.gov

(send message "subscribe geotiff your-name-here").

Disclaimers and Notes for This Version:

This proposal has not been approved by SPOT, JPL, or any other organization. This represents a proposal, which derives from many discussions between an international body of TIFF users and developers.

The authors and their sponsors assume no liability for any special, incidental, indirect or consequences of any kind, or any damages whatsoever resulting from loss of use, data or profits, whether or not advised of the possibility of damage, and on any theory of of liability, arising out of or in connectionwith the use of this specification.

Copyright

Portions of this specification are copyrighted by Niles Ritter and Mike Ruth. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct or commercial advantage and this copyright notice appears.

Licenses and Trademarks

Aldus and Adobe are registered trademarks, and TIFF is a registered trademark of Aldus Corp, now owned by Adobe. SPOT Image, ESRI, ERDAS, ARC/Info, Intergraph and Softdesk are registered trademarks. Concurrence

The following members of the GeoTIFF working group have reviewed and approved of this revision.

Name Organization Representing

-------------------- ----------------------- ------------

Niles Ritter Jet Propulsion Labs JPL Carto Group

Mike Ruth SPOT Image Corp (USA) SPOT Image Corp (USA)

1 Introduction

1.1 About this Specification

This is a description of a proposal to specify the content and structure of a group of industry-standard tag sets for the management of georeference or geocoded raster imagery using Aldus-Adobe's public domain Tagged-Image File Format (TIFF).

This specification closely follows the organization and structure of the TIFF specification document.

1.1.1 Background

TIFF has emerged as one of the world's most popular raster file formats. But TIFF remains limited in cartographic applications, since no publicly available, stable structure for conveying geographic information presently exists in the public domain.

Several private solutions exist for recording cartographic information in TIFF tags. Intergraph has a mature and sophisticated geotie tag implementation, but this remains within the private TIFF tagset registered exclusively to Intergraph. Other companies (such as ESRI, and Island Graphics) have geographic solutions which are also proprietary or limited by specific application to their software's architecture.

Many GIS companies, raster data providers, and their clients have requested that the companies concerned with delivery and exploitation of raster geographic imagery develop a publicly available, platform interoperable standard for the support of geographic TIFF imagery. Such TIFF imagery would originate from satellite imaging platforms, aerial platforms, scans of aerial photography or paper maps, or as a result of geographic analysis. TIFF images which were supported by the public "geotie" tagset would be able to be read and positioned correctly in any GIS or digital mapping system which supports the "GeoTIFF" standard, as proposed in this document.

The savings to the users and providers of raster data and exploitation softwares are potentially significant. With a platform interoperable GeoTIFF file, companies could stop spending excessive development resource in support of any and all proprietary formats which are invented. Data providers may be able to produce off-the-shelf imagery products which can be delivered in the "generic" TIFF format quickly and possibly at lower cost. End-users will have the advantage of developed software that exploits the GeoTIFF tags transparently. Most importantly, the same raster TIFF image which can be read and modified in one GIS environment may be equally exploitable in another GIS environment without requiring any file duplication or import/export operation.

1.1.2 History

The initial efforts to define a TIFF "geotie" specification began under the leadership of Ed Grissom at Intergraph,and others in the early 1990's. In 1994 a formal GeoTIFF mailing-list was created and maintained by Niles Ritter at JPL, which quickly grew to over 140 subscribers from government and industry. The purpose of the list is to discuss common goals and interests in developing an industry-wide GeoTIFF standard, and culminated in a conference in March of 1995 hosted by SPOT Image, with representatives from USGS, Intergraph, ESRI, ERDAS, SoftDesk, MapInfo, NASA/JPL, and others, in which the current working proposal for GeoTIFF was outlined. The outline was condensed into a prerelease GeoTIFF specification document by Niles Ritter, and Mike Ruth of SPOT Image.Following discussions with Dr. Roger Lott of the European Petroleum Survey Group (EPSG), the GeoTIFF projection parametrization method was extensively modified, and brought into compatibility with both the POSC Epicentre model, and the Federal Geographic Data Committee (FGDC) metadata approaches.

1.1.3 Scope

The GeoTIFF spec defines a set of TIFF tags provided to describe all "Cartographic" information associated with TIFF imagery that originates from satellite imaging systems, scanned aerial photography, scanned maps, digital elevation models, or as a result of geographic analyses. Its aim is to allow means for tying a raster image to a known model space or map projection, and for describing those projections.

GeoTIFF does not intend to become a replacement for existing geographic data interchange standards, such as the USGS SDTS standard or the FGDC metadata standard. Rather, it aims to augment an existing popular raster-data format to support georeferencing and geocoding information.

The tags documented in this spec are to be considered completely orthogonal to the raster-data descriptions of the TIFF spec, and impose no restrictions on how the standard TIFF tags are to be interpreted, which color spaces or compression types are to be used, etc.

1.1.4 Features

GeoTIFF fully complies with the TIFF 6.0 specifications, and its extensions do not in any way go against the TIFF recommendations, nor do they limit the scope of raster data supported by TIFF.

GeoTIFF uses a small set of reserved TIFF tags to store a broad range of georeferencing information, including UTM, US State Plane, National Grids, ARC, as well as the underlying projection types such as Transverse Mercator, Geographic, Lambert Conformal Conic, etc. No information is stored in private structures, IFD's or other mechanisms which would hide information from naive TIFF reading software.

GeoTIFF uses a "MetaTag" (GeoKey) approach to encode dozens of information elements into just 6 tags, taking advantage of TIFF platform-independent data format representation to avoid cross-platform interchange difficulties. These keys are designed in a manner parallel to standard TIFF tags, and closely follow the TIFF discipline in their structure and layout. New keys may be defined as needs arise, within the current framework, and without requiring the allocation of new tags from Aldus/Adobe.

GeoTIFF uses numerical codes to describe projection types, coordinate systems, datums, ellipsoids, etc. The projection, datums and ellipsoid codes are derived from the EPSG list compiled by the Petrotechnical Open Software Company (POSC), and mechanisms for adding further international projections,datums and ellipsoids has been established. The GeoTIFF information content is designed to be compatible with the data decomposition approach used by the National Spatial Data Infrastructure (NSDI) of the U.S. Federal Geographic Data Committee (FGDC).

While GeoTIFF provides a robust framework for specifying a broad class of existing Projected coordinate systems, it is also fully extensible, permitting internal, private or proprietary information storage. However, since this standard arose from the need to avoid multiple proprietary encoding systems, use of private implementations is to be discouraged.

1.2 Revision Notes

This is the second (beta) release of GeoTIFF Revision 0.2, supporting the new EPSG 2.1 codes.

1.2.1 Revision Nomenclature

A Revision of GeoTIFF specifications will be denoted by two integers separated by a decimal, indicating the Major and Minor revision numbers. GeoTIFF stores most of its information using a "Key-Code" pairing system; the Major revision number will only be incremented when a substantial addition or modification is made to the list of information Keys, while the Minor Revision number permits incremental augmentation of the list of valid codes.

1.2.2 New Features

New EPSG 2.1 Codes installed.

1.2.3 Clarifications

o GeoTIFF-writers shall store the GeoKey entries in key-sorted order

within the GeoKeyDirectoryTag. This is a change from preliminary

discussions which permitted arbitrary order, and more closely follows

the TIFF discipline.

o The third value "ScaleZ" in ModelPixelScaleTag = (ScaleX, ScaleY,

ScaleZ) shall by default be set to 0, not 1, as suggested in preliminary

discussions. This is because most standard model spaces are

2-dimensional (flat), and therefore its vertical shape is

independent of the pixel-value.

o The code 32767 shall be used to imply "user-defined", rather than

16384. This avoids breaking up the reserved public GeoKey code space

into two discontiguous ranges, 0-16383 and 16385-32767.

o If a GeoKey is coded "undefined", then it is exactly that; no

parameters should be provided (e.g. EllipsoidSemiMajorAxis, etc).

To provide parameters for a non-coded attribute, use "user-defined".

1.2.4 Organizational changes

None.

1.2.5 Changes in Requirements

Changes to this preliminary revision:

o South Oriented Gauss Conformal is now a distinct code.

1.2.6 Agenda for Future Development

A three-phase development of GeoTIFF approach is proposed in this document, which will be implemented with three Major Revisions: 0.x, 1.x and 2.x. Further revisions may occur as the need arises, though most will be in the form of incremental (minor) revisions.

Revision 0.1, representing the first "Beta" revision implementation, was released in June 1995 and is subject to the first beta implementation in code. An incremental 0.2 revision has been made. Incremental 0.x changes may also occur, and lists of additional Keys for the next Major revision will be collected by the GeoTIFF mailing list. The goal is to make 0.x as close to the baseline requirements as possible.

Revision 1.0, will be the first true "Baseline" revision, and is proposed to support well-documented, public, relatively simple Projected Coordinate Systems (PCS), including most commonly used and supported in the international public domains today, together with their underlying map-projection systems. Following the critiques of the 0.x Revision phase, the 1.0 Revision spec will be released in July 95 timeframe. As before, incremental 1.x augmentations to the "codes" list will be established, as well as discussions regarding the future "2.0" requirements.

The Revision 2.0 phase is proposed to extend the capability of the GeoTIFF tagsets beyond PCS projections into more complex map projection geometries, including single-project, single-vendor, or proprietary cartographic solutions.

TBD: Sounding Datums and related parameters for Digital Elevation Models (DEM's) and bathymetry -- Revision 2?

1.3 Administration

1.3.1 Information and Support:

The most recent version of the GeoTIFF spec is available via anonymous FTP at:

ftp://mtritter.jpl.nasa.gov/pub/tiff/geotiff/

and is mirrored at the USGS:

ftp://ftpmcmc.er.usgs.gov/release/geotiff/

Information and a hypertext version of the GeoTIFF spec is available via

WWW at the following site:

http://www-mipl.jpl.nasa.gov/~ndr/cartlab/geotiff/

A mailing-list is currently active to discuss the on-going development of this standard. To subscribe to this list, send e-mail to:

GeoTIFF-request@tazboy.jpl.nasa.gov

with no subject and the body of the message reading:

subscribe geotiff your-name-here

To post inquiries directly to the list, send email to:

geotiff@tazboy.jpl.nasa.gov

1.3.2 Private Keys and Codes:

As with TIFF, in GeoTIFF private "GeoKeys" and codes may be used, starting with 32768 and above. Unlike the TIFF spec, however, these private key-spaces will not be reserved, and are only to be used for private, internal purposes.

1.3.3 Proposed Revisions to GeoTIFF

Should a feature arise which is not currently supported, it should be formally proposed for addition to the GeoTIFF spec, through the official mailing-list.

The current maintainer of the GeoTIFF specification is Niles Ritter, though this may change at a later time. Projection codes are maintained through EPSG/POSC, and a mechanism for change/additions will be established through the GeoTIFF mailing list.

2 Baseline GeoTIFF

2.1 Notation

This spec follows the notation remarks of the TIFF 6.0 spec, regarding "is", "shall", "should", and "may"; the first two indicate mandatory requirements, "should" indicates a strong recommendation, while "may" indicates an option.

2.2 GeoTIFF Design Considerations

Every effort has been made to adhere to the philosophy of TIFF data abstraction. The GeoTIFF tags conform to a hierarchical data structure of tags and keys, similar to the tags which have been implemented in the "basic" and "extended" TIFF tags already supported in TIFF Version 6 specification. The following are some points considered in the design of GeoTIFF:

o Private binary structures, while permitted under the TIFF spec, are in

general difficult to maintain, and are intrinsically platform-

dependent. Whenever possible, information should be sorted into their

intrinsic data-types, and placed into appropriately named tags. Also,

implementors of TIFF readers would be more willing to honor a new tag

specification if it does not require parsing novel binary structures.

o Any Tag value which is to be used as a "keyword" switch or modifier

should be a SHORT type, rather than an ASCII string. This avoids common

mistakes of mis-spelling a keyword, as well as facilitating an

implementation in code using the "switch/case"features of most

languages. In general, scanning ASCII strings for keywords

(CaseINSensitiVE?) is a hazardous (not to mention slower and more

complex) operation.

o True "Extensibility" strongly suggests that the Tags defined have a

sufficiently abstract definition so that the same tag and its values may

be used and interpreted in different ways as more complex information

spaces are developed. For example, the old SubFileType tag (255) had to

be obsoleted and replaced with a NewSubFileType tag, because images

began appearing which could not fit into the narrowly defined classes

for that Tag. Conversely, the YCbCrSubsampling Tag has taken on new

meaning and importance as the JPEG compression standard for TIFF becomes

finalized.

2.3 GeoTIFF Software Requirements

GeoTIFF requires support for all documented TIFF 6.0 tag data-types, and in particular requires the IEEE double-precision floating point "DOUBLE" type tag. Most of the parameters for georeferencing will not have sufficient accuracy with single-precision IEEE, nor with RATIONAL format storage. The only other alternative for storing high-precision values would be to encode as ASCII, but this does not conform to TIFF recommendations for data encoding.

It is worth emphasizing here that the TIFF spec indicates that TIFF-compliant readers shall honor the 'byte-order' indicator, meaning that 4-byte integers from files created on opposite order machines will be swapped in software, and that 8-byte DOUBLE's will be 8-byte swapped.

A GeoTIFF reader/writer, in addition to supporting the standard TIFF tag types, must also have an additional module which can parse the "Geokey" MetaTag information. A public-domain software package for performing this function will soon be available.

2.4 GeoTIFF File and "Key" Structure

This section describes the abstract file-format and "GeoKey" data storage mechanism used in GeoTIFF. Uses of this mechanism for implementing georeferencing and geocoding is detailed in section 2.6 and section 2.7.

A GeoTIFF file is a TIFF 6.0 file, and inherits the file structure as described in the corresponding portion of the TIFF spec. All GeoTIFF specific information is encoded in several additional reserved TIFF tags, and contains no private Image File Directories (IFD's), binary structures or other private information invisible to standard TIFF readers.

The number and type of parameters that would be required to describe most popular projection types would, if implemented as separate TIFF tags, likely require dozens or even hundred of tags, exhausting the limited resources of the TIFF tag-space. On the other hand, a private IFD, while providing thousands of free tags, is limited in that its tag-values are invisible to non-savvy TIFF readers (which don't know that the IFD_OFFSET tag value points to a private IFD).

To avoid these problems, a GeoTIFF file stores projection parameters in a set of "Keys" which are virtually identical in function to a "Tag", but has one more level of abstraction above TIFF. Effectively, it is a sort of "Meta-Tag". A Key works with formatted tag-values of a TIFF file the way that a TIFF file deals with the raw bytes of a data file. Like a tag, a Key has an ID number ranging from 0 to 65535, but unlike TIFF tags, all key ID's are available for use in GeoTIFF parameter definitions.

The Keys in GeoTIFF (also call "GeoKeys") are all referenced from the GeoKeyDirectoryTag, which defined as follows:

GeoKeyDirectoryTag:

Tag = 34735 (87AF.H)

Type = SHORT (2-byte unsigned short)

N = variable, >= 4

Alias: ProjectionInfoTag, CoordSystemInfoTag

Owner: SPOT Image, Inc.

This tag may be used to store the GeoKey Directory, which defines and references the "GeoKeys", as described below.

The tag is an an array of unsigned SHORT values, which are primarily grouped into blocks of 4. The first 4 values are special, and contain GeoKey directory header information. The header values consist of the following information, in order:

Header={KeyDirectoryVersion, KeyRevision, MinorRevision, NumberOfKeys}

where

"KeyDirectoryVersion" indicates the current version of Key

implementation, and will only change if this Tag's Key

structure is changed. (Similar to the TIFFVersion (42)).

The current DirectoryVersion number is 1. This value will

most likely never change, and may be used to ensure that

this is a valid Key-implementation.

"KeyRevision" indicates what revision of Key-Sets are used.

"MinorRevision" indicates what set of Key-codes are used. The

complete revision number is denoted .

"NumberOfKeys" indicates how many Keys are defined by the rest

of this Tag.

This header is immediately followed by a collection of KeyEntry sets, each of which is also 4-SHORTS long. Each KeyEntry is modeled on the "TIFFEntry" format of the TIFF directory header, and is of the form:

KeyEntry = { KeyID, TIFFTagLocation, Count, Value_Offset }

where

"KeyID" gives the key-ID value of the Key (identical in function

to TIFF tag ID, but completely independent of TIFF tag-space),

"TIFFTagLocation" indicates which TIFF tag contains the value(s)

of the Key: if TIFFTagLocation is 0, then the value is SHORT,

and is contained in the "Value_Offset" entry. Otherwise, the type

(format) of the value is implied by the TIFF-Type of the tag

containing the value.

"Count" indicates the number of values in this key.

"Value_Offset" Value_Offset indicates the index-

offset *into* the TagArray indicated by TIFFTagLocation, if

it is nonzero. If TIFFTagLocation=0, then Value_Offset

contains the actual (SHORT) value of the Key, and

Count=1 is implied. Note that the offset is not a byte-offset,

but rather an index based on the natural data type of the

specified tag array.

Following the KeyEntry definitions, the KeyDirectory tag may also contain additional values. For example, if a Key requires multiple SHORT values, they shall be placed at the end of this tag, and the KeyEntry will set TIFFTagLocation=GeoKeyDirectoryTag, with the Value_Offset pointing to the location of the value(s).

All key-values which are not of type SHORT are to be stored in one of the following two tags, based on their format:

GeoDoubleParamsTag:

Tag = 34736 (87BO.H)

Type = DOUBLE (IEEE Double precision)

N = variable

Owner: SPOT Image, Inc.

This tag is used to store all of the DOUBLE valued GeoKeys, referenced by the GeoKeyDirectoryTag. The meaning of any value of this double array is determined from the GeoKeyDirectoryTag reference pointing to it. FLOAT values should first be converted to DOUBLE and stored here.

GeoAsciiParamsTag:

Tag = 34737 (87B1.H)

Type = ASCII

Owner: SPOT Image, Inc.

N = variable

This tag is used to store all of the ASCII valued GeoKeys, referenced by the GeoKeyDirectoryTag. Since keys use offsets into tags, any special comments may be placed at the beginning of this tag. For the most part, the only keys that are ASCII valued are "Citation" keys, giving documentation and references for obscure projections, datums, etc.

Note on ASCII Keys:

Special handling is required for ASCII-valued keys. While it is true that TIFF 6.0 permits multiple NULL-delimited strings within a single ASCII tag, the secondary strings might not appear in the output of naive "tiffdump" programs. For this reason, the null delimiter of each ASCII Key value shall be converted to a "|" (pipe) character before being installed back into the ASCII holding tag, so that a dump of the tag will look like this.

AsciiTag="first_value|second_value|etc...last_value|"

A baseline GeoTIFF-reader must check for and convert the final "|" pipe character of a key back into a NULL before returning it to the client software.

GeoKey Sort Order:

In the TIFF spec it is required that TIFF tags be written out to the file in tag-ID sorted order. This is done to avoid forcing software to perform N-squared sort operations when reading and writing tags.

To follow the TIFF philosophy, GeoTIFF-writers shall store the GeoKey entries in key-sorted order within the CoordSystemInfoTag.

Example:

GeoKeyDirectoryTag=( 1, 1, 2, 6,

1024, 0, 1, 2,

1026, 34737,12, 0,

2048, 0, 1, 32767,

2049, 34737,14, 12,

2050, 0, 1, 6,

2051, 34736, 1, 0 )

GeoDoubleParamsTag(34736)=(1.5)

GeoAsciiParamsTag(34737)=("Custom File|My Geographic|")

The first line indicates that this is a Version 1 GeoTIFF GeoKey directory, the keys are Rev. 1.2, and there are 6 Keys defined in this tag.

The next line indicates that the first Key (ID=1024 = GTModelTypeGeoKey) has the value 2 (Geographic), explicitly placed in the entry list (since TIFFTagLocation=0).

The next line indicates that the Key 1026 (the GTCitationGeoKey) is listed in the GeoAsciiParamsTag (34737) array, starting at offset 0 (the first in array), and running for 12 bytes and so has the value "Custom File" (the "|" is converted to a null delimiter at the end).

Going further down the list, the Key 2051 (GeogLinearUnitSizeGeoKey) is located in the GeoDoubleParamsTag (34736), at offset 0 and has the value 1.5; the value of key 2049 (GeogCitationGeoKey) is "My Geographic".

The TIFF layer handles all the problems of data structure, platform independence, format types, etc, by specifying byte-offsets, byte-order format and count, while the Key describes its key values at the TIFF level by specifying Tag number, array-index, and count. Since all TIFF information occurs in TIFF arrays of some sort, we have a robust method for storing anything in a Key that would occur in a Tag.

With this Key-value approach, there are 65536 Keys which have all the flexibility of TIFF tag, with the added advantage that a TIFF dump will provide all the information that exists in the GeoTIFF implementation.

This GeoKey mechanism will be used extensively in section 2.7, where the numerous parameters for defining Coordinate Systems and their underlying projections are defined.

2.5 Coordinate Systems in GeoTIFF

Geotiff has been designed so that standard map coordinate system definitions can be readily stored in a single registered TIFF tag. It has also been designed to allow the description of coordinate system definitions which are non-standard, and for the description of transformations between coordinate systems, through the use of three or four additional TIFF tags.

However, in order for the information to be correctly exchanged between various clients and providers of GeoTIFF, it is important to establish a common system for describing map projections.

In the TIFF/GeoTIFF framework, there are essentially three different spaces upon which coordinate systems may be defined. The spaces are:

1) The raster space (Image space) R, used to reference the pixel values

in an image,

2) The Device space D, and

3) The Model space, M, used to reference points on the earth.

In the sections that follow we shall discuss the relevance and use of each of these spaces, and their corresponding coordinate systems, from the standpoint of GeoTIFF.

2.5.1 Device Space and GeoTIFF

In standard TIFF 6.0 there are tags which relate raster space R with device space D, such as monitor, scanner or printer. The list of such tags consists of the following:

ResolutionUnit (296)

XResolution (282)

YResolution (283)

Orientation (274)

XPosition (286)

YPosition (287)

In Geotiff, provision is made to identify earth-referenced coordinate systems (model space M) and to relate M space with R space. This provision is independent of and can co-exist with the relationship between raster and device spaces. To emphasize the distinction, this spec shall not refer to "X" and "Y" raster coordinates, but rather to raster space "J" (row) and "I" (column) coordinate variables instead, as defined in section 2.5.2.2.

2.5.2 Raster Coordinate Systems

2.5.2.1 Raster Data

Raster data consists of spatially coherent, digitally stored numerical data, collected from sensors, scanners, or in other ways numerically derived. The manner in which this storage is implemented in a TIFF file is described in the standard TIFF specification.

Raster data values, as read in from a file, are organized by software into two dimensional arrays, the indices of the arrays being used as coordinates. There may also be additional indices for multispectral data, but these indices do not refer to spatial coordinates but spectral, and so of not of concern here.

Many different types of raster data may be georeferenced, and there may be subtle ways in which the nature of the data itself influences how the coordinate system (Raster Space) is defined for raster data. For example, pixel data derived from imaging devices and sensors represent aggregate values collected over a small, finite, geographic area, and so it is natural to define coordinate systems in which the pixel value is thought of as filling an area. On the other hand, digital elevations models may consist of discrete "postings", which may best be considered as point measurements at the vertices of a grid, and not in the interior of a cell.

2.5.2.2 Raster Space

The choice of origin for raster space is not entirely arbitrary, and depends upon the nature of the data collected. Raster space coordinates shall be referred to by their pixel types, ie, as "PixelIsArea" or "PixelIsPoint".

Note: For simplicity, both raster spaces documented below use a fixed pixel size and spacing of 1. Information regarding the visual representation of this data, such as pixels with non-unit aspect ratios, scales, orientations, etc, are best communicated with the TIFF 6.0 standard tags.

"PixelIsArea" Raster Space

The "PixelIsArea" raster grid space R, which is the default, uses coordinates I and J, with (0,0) denoting the upper-left corner of the image, and increasing I to the right, increasing J down. The first pixel-value fills the square grid cell with the bounds:

top-left = (0,0), bottom-right = (1,1)

and so on; by extension this one-by-one grid cell is also referred to as a pixel. An N by M pixel image covers an are with the mathematically defined bounds (0,0),(N,M).

(0,0)

+---+---+-> I

| * | * |

+---+---+ Standard (PixelIsArea) TIFF Raster space R,

| (1,1) (2,1) showing the areas (*) of several pixels.

|

J

"PixelIsPoint" Raster Space

The PixelIsPoint raster grid space R uses the same coordinate axis names as used in PixelIsArea Raster space, with increasing I to the right, increasing J down. The first pixel-value however, is realized as a point value located at (0,0). An N by M pixel image consists of points which fill the mathematically defined bounds (0,0),(N-1,M-1).

(0,0) (1,0)

*-------*------> I

| |

| (1,1)

J

If a point-pixel image were to be displayed on a display device with pixel cells having the same size as the raster spacing, then the upper-left corner of the displayed image would be located in raster space at (-0.5, -0.5).

2.5.3 Model Coordinate Systems

The following methods of describing spatial model locations (as opposed to raster) are recognized in Geotiff:

Geocentric coordinates

Geographic coordinates

Projected coordinates

Vertical coordinates

Geographic, geocentric and projected coordinates are all imposed on models of the earth. To describe a location uniquely, a coordinate set must be referenced to an adequately defined coordinate system. If a coordinate system is from the Geotiff standard definitions, the only reference required is the standard coordinate system code/name. If the coordinate system is non-standard, it must be defined. The required definitions are described below.

Projected coordinates, local grid coordinates, and (usually) geographical coordinates, form two dimensional horizontal coordinate systems (i.e., horizontal with respect to the earth's surface). Height is not part of these systems. To describe a position in three dimensions it is necessary to consider height as a second one-dimensional vertical coordinate system.

To georeference an image in GeoTIFF, you must specify a Raster Space coordinate system, choose a horizontal model coordinate system, and a transformation between these two, as will be described in section 2.6

2.5.3.1 Geographic Coordinate Systems

Geographic Coordinate Systems are those that relate angular latitude and longitude (and optionally geodetic height) to an actual point on the earth. The process by which this is accomplished is rather complex, and so we describe the components of the process in detail here.

Ellipsoidal Models of the Earth

The geoid - the earth stripped of all topography - forms a reference surface for the earth. However, because it is related to the earth's gravity field, the geoid is a very complex surface; indeed, at a detailed level its description is not well known. The geoid is therefore not used in practical mapping.

It has been found that an oblate ellipsoid (an ellipse rotated about its minor axis) is a good approximation to the geoid and therefore a good model of the earth. Many approximations exist: several hundred ellipsoids have been defined for scientific purposes and about 30 are in day to day use for mapping. The size and shape of these ellipsoids can be defined through two parameters. Geotiff requires one of these to be

the semi-major axis (a),

and the second to be either

the inverse flattening (1/f)

or

the semi-minor axis (b).

Historical models exist which use a spherical approximation; such models are not recommended for modern applications, but if needed the size of a model sphere may be defined by specifying identical values for the semimajor and semiminor axes; the inverse flattening cannot be used as it becomes infinite for perfect spheres.

Other ellipsoid parameters needed for mapping applications, for example the square of the eccentricity, can easily be calculated by an application from the two defining parameters. Note that Geotiff uses the modern geodesy convention for the symbol (b) for the semi-minor axis. No provision is made for mapping other planets in which a tri-dimensional (triaxial) ellipsoid might be required, where (b) would represent the semi-median axis and (c) the semi-minor axis.

Numeric codes for ellipsoids regularly used for earth-mapping are included in the Geotiff reference lists.

Latitude and Longitude

The coordinate axes of the system refererencing points on an ellipsoid are called latitude and longitude. More precisely, geodetic latitude and longitude are required in this Geotiff standard. A discussion of the several other types of latitude and longitude is beyond the scope of this document as they are not required for conventional mapping.

Latitude is defined to be the angle subtended with the ellipsoid's equatorial plane by a perpendicular through the surface of the ellipsoid from a point. Latitude is positive if north of the equator, negative if south.

Longitude is defined to be the angle measured about the minor (polar) axis of the ellipsoid from a prime meridian (see below) to the meridian through a point, positive if east of the prime meridian and negative if west. Unlike latitude which has a natural origin at the equator, there is no feature on the ellipsoid which forms a natural origin for the measurement of longitude. The zero longitude can be any defined meridian. Historically, nations have used the meridian through their national astronomical observatories, giving rise to several prime meridians. By international convention, the meridian through Greenwich, England is the standard prime meridian. Longitude is only unambiguous if the longitude of its prime meridian relative to Greenwich is given. Prime meridians other than Greenwich which are sometimes used for earth mapping are included in the Geotiff reference lists.

Geodetic Datums

As well as there being several ellipsoids in use to model the earth, any one particular ellipsoid can have its location and orientation relative to the earth defined in different ways. If the relationship between the ellipsoid and the earth is changed, then the geographical coordinates of a point will change.

Conversely, for geographical coordinates to uniquely describe a location the relationship between the earth and the ellipsoid must be defined. This relationship is described by a geodetic datum. An exact geodetic definition of geodetic datums is beyond the current scope of Geotiff. However the Geotiff standard requires that the geodetic datum being utilized be identified by numerical code. If required, defining parameters for the geodetic datum can be included as a citation.

Defining Geographic Coordinate Systems

In summary, geographic coordinates are only unique if qualified by the code of the geographic coordinate system to which they belong. A geographic coordinate system has two axes, latitude and longitude, which are only unambiguous when both of the related prime meridian and geodetic datum are given, and in turn the geodetic datum definition includes the definition of an ellipsoid. The Geotiff standard includes a list of frequently used geographic coordinate systems and their component ellipsoids, geodetic datums and prime meridians. Within the Geotiff standard a geographic coordinate system can be identified either by

the code of a standard geographic coordinate system

or by

a user-defined system.

The user is expected to provide geographic coordinate system code/name, geodetic datum code/name, ellipsoid code (if in standard) or ellipsoid name and two defining parameters (a) and either (1/f) or (b), and prime meridian code (if in standard) or name and longitude relative to Greenwich.

2.5.3.2 Geocentric Coordinate Systems

A geocentric coordinate system is a 3-dimensional coordinate system with its origin at or near the center of the earth and with 3 orthogonal axes. The Z-axis is in or parallel to the earth's axis of rotation (or to the axis around which the rotational axis precesses). The X-axis is in or parallel to the plane of the equator and passes through its intersection with the Greenwich meridian, and the Y-axis is in the plane of the equator forming a right-handed coordinate system with the X and Z axes.

Geocentric coordinate systems are not frequently used for describing locations, but they are often utilized as an intermediate step when transforming between geographic coordinate systems. (Coordinate system transformations are described in section 2.6 below).

In the Geotiff standard, a geocentric coordinate system can be identified, either

through the geographic code (which in turn implies a datum),

or

through a user-defined name.

2.5.3.3 Projected Coordinate Systems

Although a geographical coordinate system is mathematically two dimensional, it describes a three dimensional object and cannot be represented on a plane surface without distortion. Map projections are transformations of geographical coordinates to plane coordinates in which the characteristics of the distortions are controlled. A map projection consists of a coordinate system transformation method and a set of defining parameters. A projected coordinate system (PCS) is a two dimensional (horizontal) coordinate set which, for a specific map projection, has a single and unambiguous transformation to a geographic coordinate system.

In GeoTIFF PCS's are defined using the POSC/EPSG system, in which the PCS planar coordinate system, the Geographic coordinate system, and the transformation between them, are broken down into simpler logical components. Here are schematic formulas showing how the Projected Coordinate Systems and Geographic Coordinates Systems are encoded:

Projected_CS = Geographic_CS + Projection

Geographic_CS = Angular_Unit + Geodetic_Datum + Prime_Meridian

Projection = Linear Unit + Coord_Transf_Method + CT_Parameters

Coord_Transf_Method = { TransverseMercator | LambertCC | ...}

CT_Parameters = {OriginLatitude + StandardParallel+...}

(See also the Reference Parameters documentation in section 2.5.4). Notice that "Transverse Mercator" is not referred to as a "Projection", but rather as a "Coordinate Transformation Method"; in GeoTIFF, as in EPSG/POSC, the word "Projection" is reserved for particular, well-defined systems in which both the coordinate transformation method, its defining parameters, and their linear units are established.

Several tens of coordinate transformation methods have been developed. Many are very similar and for practical purposes can be considered to give identical results. For example in the Geotiff standard Gauss-Kruger and Gauss-Boaga projection types are considered to be of the type Transverse Mercator. Geotiff includes a listing of commonly used projection defining parameters.

Different algorithms require different defining parameters. A future version of Geotiff will include formulas for specific map projection algorithms recommended for use with listed projection parameters.

To limit the magnitude of distortions of projected coordinate systems, the boundaries of usage are sometimes restricted. To cover more extensive areas, two or more projected coordinate systems may be required. In some cases many of the defining parameters of a set of projected coordinate systems will be held constant.

The Geotiff standard does not impose a strict hierarchy onto such zoned systems such as US State Plane or UTM, but considers each zone to be a discrete projected coordinate system; the ProjectedCSTypeGeoKey code value alone is sufficient to identify the standard coordinate systems.

Within the Geotiff standard a projected coordinate system can be identified either by

the code of a standard projected coordinate system

or by

a user-defined system.

User-define projected coordinate systems may be defined by defining the Geographic Coordinate System, the coordinate transformation method and its associated parameters, as well as the planar system's linear units.

2.5.3.4 Vertical Coordinate Systems

Many uses of Geotiff will be limited to a two-dimensional, horizontal, description of location for which geographic coordinate systems and projected coordinate systems are adequate. If a three-dimensional description of location is required Geotiff allows this either through the use of a geocentric coordinate system or by defining a vertical coordinate system and using this together with a geographic or projected coordinate system.

In general usage, elevations and depths are referenced to a surface at or close to the geoid. Through increasing use of satellite positioning systems the ellipsoid is increasingly being used as a vertical reference surface. The relationship between the geoid and an ellipsoid is in general not well known, but is required when coordinate system transformations are to be executed.

2.5.4 Reference Parameters

Most of the numerical coding systems and coordinate system definitions are based on the hierarchical system developed by EPSG/POSC. The complete set of EPSG tables used in GeoTIFF is available via FTP to

ftp://ftpmcmc.er.usgs.gov/release/geotiff/tables

or:

ftp://mtritter.jpl.nasa.gov/pub/geotiff/tables

Appended below is the README.TXT file that accompanies the tables of defining parameters for those codes:

+-----------------------------------+

| EPSG Geodesy Parameters |

| version 2.1, 2nd June 1995. |

+-----------------------------------+

The European Petroleum Survey Group (EPSG) has compiled and is distrubuting this set of parameters defining various geodetic and cartographic coordinate systems to encourage standardisation across the Exploration and Production segment of the oil industry. The data is included as reference data in the Geotiff data exchange specification, in Iris21 the Petroconsultants data model, and in Epicentre, the POSC data model. Parameters map directly to the POSC Epicentre model v2.0, except for data item codes which are included in the files for data management purposes. Geodetic datum parameters are embedded within the geographic coordinate system file. This has been done to ease parameter maintenance as there is a high correlation between geodetic datum names and geographic coordinate system names. The Projected Coordinate System v2.0 tabulation consists of systems associated with locally used projections. Systems utilising the popular UTM grid system have also been included.

Criteria used for material in these lists include:

- information must be in the public domain: "private" data

is not included.

- data must be in current use.

- parameters are given to a precision consistent with

coordinates being to a precision of one centimetre.

The user assumes the entire risk as to the accuracy and the use of this data. The data may be copied and distributed

subject to the following conditions:

1) All data must then be copied without modification

and all pages must be included;

2) All components of this data set must be distributed

together;

3) The data may not be distributed for profit by any

third party; and

4) Acknowledgement to the original source must be

given.

INFORMATION PROVIDED IN THIS DOCUMENT IS PROVIDED "AS IS"

WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR

IMPLIED, INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES

OF MERCHANTABILITY AND/OR FITNESS FOR A PARTICULAR PURPOSE.

Data is distributed on MS-DOS formatted diskette in comma-

separated record format. Additional copies may be obtained

from Jean-Patrick Girbig at the address below at a cost of

US$100 to cover media and shipping, payment to be made in

favour of Petroconsultants S.A at Union Banque Suisses,

1211 Geneve 11, Switzerland (compte number 403 458 60 K).

The data is to be made available on a bulletin board shortly.

Shipping List

-------------

This data set consists of 8 files:

PROJCS.CSV Tabulation of Projected Coordinate Systems to

which map grid coordinates may be referenced.

GEOGCS.CSV Tabulation of Geographic Coordinate Systems to

which latitude and longitude coordinates may be

referenced. This table includes the equivalent

geocentric coordinate systems and also the

geodetic datum, reference to which allows latitude

and longitude or geocentric XYZ to uniquely

describe a location on the earth.

VERTCS.CSV Tabulation of Vertical Coordinate Systems to which heights or depths may be referenced. This table is currently in an early form.

PROJ.CSV Tabulation of transformation methods and parameters through which Projected Coordinate Systems are defined and related to Geographic Coordinate Systems.

ELLIPS.CSV Tabulation of reference ellipsoids upon which geodetic datums are based.

PMERID.CSV Tabulation of prime meridians upon which geodetic datums are based.

UNITS.CSV Tabulation of length units used in Projected and Vertical Coordinate Systems and angle units used in Geographic Coordinate Systems.

README.TXT This file.

The data files (.CSV) have a heirarchical structure:

+---------------------------+ +----------------------------+

| VERTCS | | PROJCS |

+---------------------------+ +----------------------------+

|Vertical Coordinate Systems| |Projected Coordinate Systems|

+-------------+-------------+ +------------+---------------+

| |

+--------+ |

| |

| +--------------------------+

| | |

| | +-------------+---------------+

| | | GEOGCS |

| | +-----------------------------+

| | |Geographic Coordinate Systems|

| | |Geocentric Coordinate Systems|

| | +-----------------------------+

| | | Geodetic Datums |

| | +-------------+---------------+

| | |

| | +--------+-------+

| | | |

| +------+-----+ +------+-----+ +------+-------+

| | PROJ | | ELLIPS | | PMERID |

| +------------+ +------------+ +--------------+

| | Projection | | Ellipsoid | |Prime Meridian|

| | Parameters | | Parameters | | Parameters |

| +------+-----+ +------+-----+ +------+-------+

| | | |

+------------+-----------+-----+----------------+

|

+-------------+------------+

| UNITS |

+--------------------------+

| Linear and Angular Units |

+--------------------------+

The parameter listings are "living documents" and will be updated by the EPSG from time to time. Any comment or

suggestions for improvements should be directed to:

Jean-Patrick Girbig, or Roger Lott,

Manager Cartography, Head of Survey,

Petroconsultants S.A., BP Exploration,

PO Box 152, Uxbridge One,

24 Chemin de la Marie, Harefield Road,

1258 Perly-Geneva, Uxbridge,

Switzerland. Middlesex UB8 1PD,

England.

Internet:

lottrj@txpcap.hou.xwh.bp.com

Requests for the inclusion of new data should include supporting documentation. Requests for changing existing data should include reference to both the name and code of the item.

10th June 1995.

2.6 Coordinate Transformations

The purpose of Geotiff is to allow the definitive identification of georeferenced locations within a raster dataset. This is generally accomplished through tying raster space coordinates to a model space coordinate system, when no further information is required. In the GeoTIFF nomenclature, "georeferencing" refers to tying raster space to a model space M, while "geocoding" refers to defining how the model space M assigns coordinates to points on the earth.

The three tags defined below may be used for defining the relationship between R and M, and the relationship may be diagrammed as:

ModelPixelScaleTag

ModelTiepointTag

R ------------ OR --------------> M

(I,J,K) ModelTransformationTag (X,Y,Z)

The next section describes these Baseline georeferencing tags in detail.

2.6.1 GeoTIFF Tags for Coordinate Transformations

For most common applications, the transformation between raster and model space may be defined with a set of raster-to-model tiepoints and scaling parameters. The following two tags may be used for this purpose:

ModelTiepointTag:

Tag = 33922 (8482.H)

Type = DOUBLE (IEEE Double precision)

N = 6*K, K = number of tiepoints

Alias: GeoreferenceTag

Owner: Intergraph

This tag stores raster->model tiepoint pairs in the order

ModelTiepointTag = (...,I,J,K, X,Y,Z...),

where (I,J,K) is the point at location (I,J) in raster space with pixel-value K, and (X,Y,Z) is a vector in model space. In most cases the model space is only two-dimensional, in which case both K and Z should be set to zero; this third dimension is provided in anticipation of future support for 3D digital elevation models and vertical coordinate systems.

A raster image may be georeferenced simply by specifying its location, size and orientation in the model coordinate space M. This may be done by specifying the location of three of the four bounding corner points. However, tiepoints are only to be considered exact at the points specified; thus defining such a set of bounding tiepoints does not imply

that the model space locations of the interior of the image may be exactly computed by a linear interpolation of these tiepoints.

However, since the relationship between the Raster space and the model space will often be an exact, affine transformation, this relationship can be defined using one set of tiepoints and the "ModelPixelScaleTag", described below, which gives the vertical and horizontal raster grid cell size, specified in model units.

If possible, the first tiepoint placed in this tag shall be the one establishing the location of the point (0,0) in raster space. However, if this is not possible (for example, if (0,0) is goes to a part of model space in which the projection is ill-defined), then there is no particular order in which the tiepoints need be listed.

For orthorectification or mosaicking applications a large number of tiepoints may be specified on a mesh over the raster image. However, the definition of associated grid interpolation methods is not in the scope of the current GeoTIFF spec.

Remark: As mentioned in section 2.5.1, all GeoTIFF information is independent of the XPosition, YPosition, and Orientation tags of the standard TIFF 6.0 spec.

The next two tags are optional tags provided for defining exact affine transformations between raster and model space; baseline GeoTIFF files may use either, but shall never use both within the same TIFF image directory.

ModelPixelScaleTag:

Tag = 33550

Type = DOUBLE (IEEE Double precision)

N = 3

Owner: SoftDesk

This tag may be used to specify the size of raster pixel spacing in the model space units, when the raster space can be embedded in the model space coordinate system without rotation, and consists of the following 3 values:

ModelPixelScaleTag = (ScaleX, ScaleY, ScaleZ)

where ScaleX and ScaleY give the horizontal and vertical spacing of raster pixels. The ScaleZ is primarily used to map the pixel value of a digital elevation model into the correct Z-scale, and so for most other purposes this value should be zero (since most model spaces are 2-D, with Z=0).

A single tiepoint in the ModelTiepointTag, together with this tag, completely determine the relationship between raster and model space; thus they comprise the two tags which Baseline GeoTIFF files most often will use to place a raster image into a "standard position" in model space.

Like the Tiepoint tag, this tag information is independent of the XPosition, YPosition, Resolution and Orientation tags of the standard TIFF 6.0 spec. However, simple reversals of orientation between raster and model space (e.g. horizontal or vertical flips) may be indicated by reversal of sign in the corresponding component of the ModelPixelScaleTag. GeoTIFF compliant readers must honor this sign-reversal convention.

This tag must not be used if the raster image requires rotation or shearing to place it into the standard model space. In such cases the transformation shall be defined with the more general ModelTransformationTag, defined below.

ModelTransformationTag

Tag = 33920 (8480.H)

Type = DOUBLE

N = 16

Owner: Intergraph

This tag may be used to specify the transformation matrix between the raster space (and its dependent pixel-value space) and the (possibly 3D) model space. If specified, the tag shall have the following organization:

ModelTransformationTag = (a,b,c,d,e....m,n,o,p).

where

model image

coords = matrix * coords

|- -| |- -| |- -|

| X | | a b c d | | I |

| | | | | |

| Y | | e f g h | | J |

| | = | | | |

| Z | | i j k l | | K |

| | | | | |

| 1 | | m n o p | | 1 |

|- -| |- -| |- -|

By convention, and without loss of generality, the following parameters are currently hard-coded and will always be the same (but must be specified nonetheless):

m = n = o = 0, p = 1.

For Baseline GeoTIFF, the model space is always 2-D, and so the matrix will have the more limited form:

|- -| |- -| |- -|

| X | | a b 0 d | | I |

| | | | | |

| Y | | e f 0 h | | J |

| | = | | | |

| Z | | 0 0 0 0 | | K |

| | | | | |

| 1 | | 0 0 0 1 | | 1 |

|- -| |- -| |- -|

Values "d" and "h" will often be used to represent translations in X and Y, and so will not necessarily be zero. All 16 values should be specified, in all cases. Only the raster-to-model transformation is defined; if the inverse transformation is required it must be computed by the client, to the desired accuracy.

This matrix tag should not be used if the ModelTiepointTag and the ModelPixelScaleTag are already defined. If only a single tiepoint (I,J,K,X,Y,Z) is specified, and the ModelPixelScale = (Sx, Sy, Sz) is specified, then the corresponding transformation matrix may be computed from them as:

|- -|

| Sx 0.0 0.0 Tx |

| | Tx = X - I/Sx

| 0.0 -Sy 0.0 Ty | Ty = Y + J/Sy

| | Tz = Z - K/Sz (if not 0)

| 0.0 0.0 Sz Tz |

| |

| 0.0 0.0 0.0 1.0 |

|- -|

where the -Sy is due the reversal of direction from J increasing- down in raster space to Y increasing-up in model space.

Like the Tiepoint tag, this tag information is independent of the XPosition, YPosition, and Orientation tags of the standard TIFF 6.0 spec.

2.6.2 Cookbook for Defining Transformations

Here is a 4-step guide to producing a set of Baseline GeoTIFF tags for defining coordinate transformation information of a raster dataset.

Step 1: Establish the Raster Space coordinate system used:

RasterPixelIsArea or RasterPixelIsPoint.

Step 2: Establish/define the model space Type in which the image is

to be georeferenced. Usually this will be a Projected

Coordinate system (PCS). If you are geocoding this data

set, then the model space is defined to be the corresponding

geographic, geocentric or Projected coordinate system (skip

to the "Cookbook" section 2.7.3 first to do determine this).

Step 3: Identify the nature of the transformations needed to tie

the raster data down to the model space coordinate system:

Case 1: The model-location of a raster point (x,y) is known, but not

the scale or orientations:

Use the ModelTiepointTag to define the (X,Y,Z) coordinates

of the known raster point.

Case 2: The location of three non-collinear raster points are known

exactly, but the linearity of the transformation is not known.

Use the ModelTiepointTag to define the (X,Y,Z) coordinates

of all three known raster points. Do not compute or define the

ModelPixelScale or ModelTransformation tag.

Case 3: The position and scale of the data is known exactly, and

no rotation or shearing is needed to fit into the model space.

Use the ModelTiepointTag to define the (X,Y,Z) coordinates

of the known raster point, and the ModelPixelScaleTag to

specify the scale.

Case 4: The raster data requires rotation and/or lateral shearing to

fit into the defined model space:

Use the ModelTransformation matrix to define the transformation.

Case 5: The raster data cannot be fit into the model space with a

simple affine transformation (rubber-sheeting required).

Use only the ModelTiepoint tag, and specify as many

tiepoints as your application requires. Note, however, that

this is not a Baseline GeoTIFF implementation, and should

not be used for interchange; it is recommended that the image be

geometrically rectified first, and put into a standard projected

coordinate system.

Step 4: Install the defined tag values in the TIFF file and close it.

2.7 Geocoding Raster Data

2.7.1 General Approach

A geocoded image is a georeferenced image as described in section 2.6, which also specifies a model space coordinate system (CS) between the model space M (to which the raster space has been tied) and the earth. The relationship can be diagrammed, including the associated TIFF tags, as follows:

ModelPixelScaleTag

ModelTiepointTag GeoKeyDirectoryTag CS

R -------- OR ---------------> M --------- AND -----------> Earth

ModelTransformationTag GeoDoubleParamsTag

GeoAsciiParamsTag

The geocoding coordinate system is defined by the GeoKeyDirectoryTag, while the Georeferencing information (T) is defined by the ModelTiepointTag and the ModelPixelScale, or ModelTransformationTag. Since these two systems are independent of each other, the tags used to store the parameters are separated from each other in the GeoTIFF file to emphasize the orthogonality.

2.7.2 GeoTIFF GeoKeys for Geocoding

As mentioned above, all information regarding the Model Coordinate System used in the raster data is referenced from the GeoKeyDirectoryTag, which stores all of the GeoKey entries. In the Appendix, section 6.2 summarizes all of the GeoKeys defined for baseline GeoTIFF, and their corresponding codes are documented in section 6.3. Only the Keys themselves are documented here.

Common Features

Public and Private Key and Code Ranges

GeoTIFF GeoKey ID's may take any value between 0 and 65535. Following TIFF general approach, the GeoKey ID's from 32768 and above are available for private implementations. However, no registry will be established for these keys or codes, so developers are warned to use them at their own risk.

The Key ID's from 0 to 32767 are reserved for use by the official GeoTIFF spec, and are broken down into the following sub-domains:

[ 0, 1023] Reserved

[ 1024, 2047] GeoTIFF Configuration Keys

[ 2048, 3071] Geographic/Geocentric CS Parameter Keys

[ 3072, 4095] Projected CS Parameter Keys

[ 4096, 5119] Vertical CS Parameter Keys

[ 5120, 32767] Reserved

[32768, 65535] Private use

GeoKey codes, like keys and tags, also range from 0 to 65535. Following the TIFF approach, all codes from 32768 and above are available for private user implementation. There will be no registry for these codes, however, and so developers must be sure that these tags will only be used internally. Use private codes at your own risk.

The codes from 0 to 32767 for all public GeoKeys are reserved by this GeoTIFF specification.

Common Public Code Values

For consistency, several key codes have the same meaning in all implemented GeoKeys possessing a SHORT numerical coding system:

0 = undefined

32767 = user-defined

The "undefined" code means that this parameter is intentionally omitted, for whatever reason. For example, the datum used for a given map may be unknown, or the accuracy of a aerial photo is so low that to specify a particular datum would imply a higher accuracy than is in the data.

The "user-defined" code means that a feature is not among the standard list, and is being explicitly defined. In cases where this is meaningful, Geokey parameters have been supplied for the user to define this feature.

"User-Defined" requirements: In each section below a specification of the additional GeoKeys required for the "user-defined" option is given. In all cases the corresponding "Citation" key is strongly recommended, as per the FGDC Metadata standard regarding "local" types.

GeoTIFF Configuration GeoKeys

These keys are to be used to establish the general configuration of this file's coordinate system, including the types of raster coordinate systems, model coordinate systems, and citations if any.

GTModelTypeGeoKey

Key ID = 1024

Type: SHORT (code)

Values: Section 6.3.1.1 Codes

This GeoKey defines the general type of model Coordinate system used, and to which the raster space will be transformed:unknown, Geocentric (rarely used), Geographic, Projected Coordinate System, or user-defined. If the coordinate system is a PCS, then only the PCS code need be specified. If the coordinate system does not fit into one of the standard registered PCS'S, but it uses one of the standard projections and datums, then its should be documented as a PCS model with "user-defined" type, requiring the specification of projection parameters, etc.

GeoKey requirements for User-Defined Model Type (not advisable):

GTCitationGeoKey

GTRasterTypeGeoKey

Key ID = 1025

Type = Section 6.3.1.2 codes

This establishes the Raster Space coordinate system used; there are currently only two, namely RasterPixelIsPoint and RasterPixelIsArea. No user-defined raster spaces are currently supported. For variance in imaging display parameters, such as pixel aspect-ratios, use the standard TIFF 6.0 device-space tags instead.

GTCitationGeoKey

Key ID = 1026

Type = ASCII

As with all the "Citation" GeoKeys, this is provided to give an ASCII reference to published documentation on the overall configuration of this GeoTIFF file.

Geographic CS Parameter GeoKeys

In general, the geographic coordinate system used will be implied by the projected coordinate system code. If however, this is a user-defined PCS, or the ModelType was chosen to be Geographic, then the system must be explicitly defined here, using the Horizontal datum code.

GeographicTypeGeoKey

Key ID = 2048

Type = SHORT (code)

Values = Section 6.3.2.1 Codes

This key may be used to specify the code for the geographic coordinate system used to map lat-long to a specific ellipsoid over the earth.

GeoKey Requirements for User-Defined geographic CS:

GeogCitationGeoKey

GeogGeodeticDatumGeoKey

GeogAngularUnitsGeoKey (if not degrees)

GeogPrimeMeridianGeoKey (if not Greenwich)

GeogCitationGeoKey

Key ID = 2049

Type = ASCII

Values = text

General citation and reference for all Geographic CS parameters.

GeogGeodeticDatumGeoKey

Key ID = 2050

Type = SHORT (code)

Values = Section 6.3.2.2 Codes

This key may be used to specify the horizontal datum, defining the size, position and orientation of the reference ellipsoid used in user-defined geographic coordinate systems.

GeoKey Requirements for User-Defined Horizontal Datum:

GeogCitationGeoKey

GeogEllipsoidGeoKey

GeogPrimeMeridianGeoKey

Key ID = 2051

Type = SHORT (code)

Units: Section 6.3.2.4 code

Allows specification of the location of the Prime meridian for user-defined geographic coordinate systems. The default standard is Greenwich, England.

GeogLinearUnitsGeoKey

Key ID = 2052

Type = DOUBLE

Values: Section 6.3.1.3 Codes

Allows the definition of geocentric CS linear units for user-defined GCS.

GeogLinearUnitSizeGeoKey

Key ID = 2053

Type = DOUBLE

Units: meters

Allows the definition of user-defined linear geocentric units, as measured in meters.

GeogAngularUnitsGeoKey

Key ID = 2054

Type = SHORT (code)

Values = Section 6.3.1.4 Codes

This key may be used to specify the angular units of measurement used in user-defined geographic coordinate system.

GeoKey Requirements for "user-defined" units:

GeogCitationGeoKey

GeogAngularUnitSizeGeoKey

GeogAngularUnitSizeGeoKey

Key ID = 2055

Type = DOUBLE

Units: radians

Allows the definition of user-defined angular geographic units, as measured in radians.

GeogEllipsoidGeoKey

Key ID = 2056

Type = SHORT (code)

Values = Section 6.3.2.3 Codes

This key may be used to specify the coded ellipsoid used in the geodetic datum of the Geographic Coordinate System.

GeoKey Requirements for User-Defined Ellipsoid:

GeogCitationGeoKey

[GeogSemiMajorAxisGeoKey,

[GeogSemiMinorAxisGeoKey | GeogInvFlatteningGeoKey] ]

GeogSemiMajorAxisGeoKey

Key ID = 2057

Type = DOUBLE

Units: Geocentric CS Linear Units

Allows the specification of user-defined Ellipsoid Semi-Major Axis (a).

GeogSemiMinorAxisGeoKey

Key ID = 2058

Type = DOUBLE

Units: Geocentric CS Linear Units

Allows the specification of user-defined Ellipsoid Semi-Minor Axis (b).

GeogInvFlatteningGeoKey

Key ID = 2059

Type = DOUBLE

Units: none.

Allows the specification of the inverse of user-defined Ellipsoid's flattening parameter (f). The eccentricity-squared e^2 of the ellipsoid is related to the non-inverted f by:

e^2 = 2*f - f^2

Note: if the ellipsoid is spherical the inverse-flattening becomes infinite; use the GeogSemiMinorAxisGeoKey instead, and set it equal to the semi-major axis length.

GeogAzimuthUnitsGeoKey

Key ID = 2060

Type = SHORT (code)

Values = Section 6.3.1.4 Codes

This key may be used to specify the angular units of measurement used to defining azimuths, in geographic coordinate systems. These may be used for defining azimuthal parameters for some projection algorithms, and may not necessarily be the same angular units used for lat-long.

GeogPrimeMeridianLongGeoKey

Key ID = 2061

Type = DOUBLE

Units = GeogAngularUnits

This key allows definition of user-defined Prime Meridians, the location of which is defined by its longitude relative to Greenwich.

Projected CS Parameter GeoKeys

The PCS range of GeoKeys includes the projection and coordinate transformation keys as well. The projection keys are included in this block since they can only be used to define projected coordinate systems.

ProjectedCSTypeGeoKey

Key ID = 3072

Type = SHORT (codes)

Values: Section 6.3.3.1 codes

This code is provided to specify the projected coordinate system.

GeoKey requirements for "user-defined" PCS families:

PCSCitationGeoKey

ProjectionGeoKey

PCSCitationGeoKey

Key ID = 3073

Type = ASCII

As with all the "Citation" GeoKeys, this is provided to give an ASCII reference to published documentation on the Projected Coordinate System particularly if this is a "user-defined" PCS.

Projection Definition GeoKeys

With the exception of the first two keys, these are mostly projection-specific parameters, and only a few will be required for any particular projection type. Projected coordinate systems automatically imply a specific projection type, as well as specific parameters for that projection, and so the keys below will only be necessary for user-defined projected coordinate systems.

ProjectionGeoKey

Key ID = 3074

Type = SHORT (code)

Values: Section 6.3.3.2 codes

Allows specification of the coded projection used. Note: this does not include the definition of the corresponding Geographic Coordinate System to which the projected CS is related; only the projection is defined here.

GeoKeys Required for "user-defined" Projections:

PCSCitationGeoKey

ProjCoordTransGeoKey

ProjLinearUnitsGeoKey

(additional parameters depending on ProjCoordTransGeoKey).

ProjCoordTransGeoKey

Key ID = 3075

Type = SHORT (code)

Values: Section 6.3.3.3 codes

Allows specification of the coordinate transformation method used. Note: this does not include the definition of the corresponding Geographic Coordinate System to which the projected CS is related; only the transformation method is defined here.

GeoKeys Required for "user-defined" Coordinate Transformations:

PCSCitationGeoKey

ProjLinearUnitsGeoKey

Key ID = 3076

Type = SHORT (code)

Values: Section 6.3.1.3 codes

Defines linear units used by this projection.

ProjLinearUnitSizeGeoKey

Key ID = 3077

Type = DOUBLE

Units: meters

Defines size of user-defined linear units in meters.

ProjStdParallelGeoKey

Key ID = 3078

Type = DOUBLE

Units: GeogAngularUnit

Latitude of primary Standard Parallel.

ProjStdParallel2GeoKey

Key ID = 3079

Type = DOUBLE

Units: GeogAngularUnit

Latitude of second Standard Parallel, if required.

ProjOriginLongGeoKey

Key ID = 3080

Type = DOUBLE

Units: GeogAngularUnit

Longitude of map-projection origin.

ProjOriginLatGeoKey

Key ID = 3081

Type = DOUBLE

Units: GeogAngularUnit

Latitude of map-projection origin.

ProjFalseEastingGeoKey

Key ID = 3082

Type = DOUBLE

Units: ProjLinearUnit

Gives the false easting coordinate of the map projection origin.

ProjFalseNorthingGeoKey

Key ID = 3083

Type = DOUBLE

Units: ProjLinearUnit

Gives the false northing coordinate of the map projection origin.

ProjFalseOriginLongGeoKey

Key ID = 3084

Type = DOUBLE

Units: GeogAngularUnit

Gives the longitude of the false origin.

ProjFalseOriginLatGeoKey

Key ID = 3085

Type = DOUBLE

Units: GeogAngularUnit

Gives the latitude of the false origin.

ProjFalseOriginEastingGeoKey

Key ID = 3086

Type = DOUBLE

Units: ProjLinearUnit

Gives the easting coordinate of the false origin. This is NOT the False Easting.

ProjFalseOriginNorthingGeoKey

Key ID = 3087

Type = DOUBLE

Units: ProjLinearUnit

Gives the northing coordinate of the false origin. This is NOT the False Northing.

ProjCenterLongGeoKey

Key ID = 3088

Type = DOUBLE

Units: GeogAngularUnit

Longitude of Center of Projection. Note that this is not necessarily the origin of the projection.

ProjCenterLatGeoKey

Key ID = 3089

Type = DOUBLE

Units: GeogAngularUnit

Latitude of Center of Projection. Note that this is not necessarily the origin of the projection.

ProjCenterEastingGeoKey

Key ID = 3090

Type = DOUBLE

Units: ProjLinearUnit

Gives the easting coordinate of the center. This is NOT the False Easting.

ProjFalseOriginNorthingGeoKey

Key ID = 3091

Type = DOUBLE

Units: ProjLinearUnit

Gives the northing coordinate of the center. This is NOT the False Northing.

ProjScaleAtOriginGeoKey

Key ID = 3092

Type = DOUBLE

Units: none

Scale at Origin. This is a ratio, so no units are required.

ProjScaleAtCenterGeoKey

Key ID = 3093

Type = DOUBLE

Units: none

Scale at Center. This is a ratio, so no units are required.

ProjAzimuthAngleGeoKey

Key ID = 3094

Type = DOUBLE

Units: GeogAzimuthUnit

Azimuth angle east of true north of the central line passing through the projection center (for elliptical (Hotine) Oblique Mercator). Note that this is the standard method of measuring azimuth, but is opposite the usual mathematical convention of positive indicating counter-clockwise.

ProjStraightVertPoleLongGeoKey

Key ID = 3095

Type = DOUBLE

Units: GeogAngularUnit

Longitude at Straight Vertical Pole. For polar stereographic.

Vertical CS Parameter Keys

Note: Vertical coordinate systems are not yet implemented. These sections are provided for future development, and any vertical coordinate systems in the current revision must be defined using the VerticalCitationGeoKey.

VerticalCSTypeGeoKey

Key ID = 4096

Type = SHORT (code)

Values = Section 6.3.4.1 Codes

This key may be used to specify the vertical coordinate system.

VerticalCitationGeoKey

Key ID = 4097

Type = ASCII

Values = text

This key may be used to document the vertical coordinate system used, and its parameters.

VerticalDatumGeoKey

Key ID = 4098

Type = SHORT (code)

Values = Section 6.3.4.2 codes

This key may be used to specify the vertical datum for the vertical coordinate system.

VerticalUnitsGeoKey

Key ID = 4099

Type = SHORT (code)

Values = Section 6.3.1.3 Codes

This key may be used to specify the vertical units of measurement used in the geographic coordinate system, in cases where geographic CS's need to reference the vertical coordinate. This, together with the Citation key, comprise the only fully implemented keys in this section, at present.

2.7.3 Cookbook for Geocoding Data

Step 1: Determine the Coordinate system type of the raster data, based on

the nature of the data: pixels derived from scanners or other

optical devices represent areas, and most commonly will use the

RasterPixelIsArea coordinate system. Pixel data such as digital

elevation models represent points, and will probably use

RasterPixelIsPoint coordinates.

Store in: GTRasterTypeGeoKey

Step 2: Determine which class of model space coordinates are most natural

for this dataset:Geographic, Geocentric, or Projected Coordinate

System. Usually this will be PCS.

Store in: GTModelTypeGeoKey

Step 3: This step depends on the GTModelType:

case PCS: Determine the PCS projection system. Most of the

PCS's used in standard State Plane and national grid systems

are defined, so check this list first. UTM is not defined at

this level, given the number of different GCS/datums used with

UTM, and so it must be defined at the level of a Projection

instead.

Store in: ProjectedCSTypeGeoKey, ProjectedCSTypeGeoKey

If coded, it will not be necessary to specify the Projection

datum, etc for this case, since all of those parameters

are determined by the ProjectedCSTypeGeoKey code. Skip to

step 4 from here.

If none of the coded PCS's match your system, then this is a

user-defined PCS. Use the Projection code list to check for

standard projection systems (UTM may be handled at this level).

Store in: ProjectionGeoKey and skip to Geographic CS case.

If none of the Projection codes match your system, then this

is a user-defined projection. Use the ProjCoordTransGeoKey to

specify the coordinate transformation method (e.g. Transverse

Mercator), and all of the associated parameters of that method.

Also define the linear units used in the planar coordinate

system.

Store in: ProjCoordTransGeoKey, ProjLinearUnitsGeoKey

Now continue on to define the Geographic CS, below.

case GEOCENTRIC:

case GEOGRAPHIC: Check the list of standard GCS's and use the

corresponding code. To use a code both the Datum, Prime

Meridian, and angular units must match those of the code.

Store in: GeographicTypeGeoKey and skip to Step 4.

If none of the coded GCS's match exactly, then this is a

user-defined GCS. Check the list of standard datums,

Prime Meridians, and angular units to define your system.

Store in: GeogGeodeticDatumGeoKey, GeogAngularUnitsGeoKey,

GeogPrimeMeridianGeoKey and skip to Step 4.

If none of the datums match your system, you have a

user-defined datum, which is an odd system, indeed. Use

the GeogEllipsoidGeoKey to select the appropriate ellipsoid

or use the GeogSemiMajorAxisGeoKey, GeogInvFlatteningGeoKey to

define, and give a reference using the GeogCitationGeoKey.

Store in: GeogEllipsoidGeoKey, etc. and go to Step 4.

Step 4: Install the GeoKeys/codes into the GeoKeyDirectoryTag, and the

DOUBLE and ASCII key values into the corresponding value-tags.

Step 5: Having completely defined the Raster & Model coordinate system,

go to Cookbook section 2.6.2 and use the Georeferencing Tags

to tie the raster image down onto the Model space.

3 Examples

Here are some examples of how GeoTIFF may be implemented at the Tag and GeoKey level, following the general "Cookbook" approach above.

3.1 Common Examples

3.1.1. UTM Projected Aerial Photo

We have an aerial photo which has been orthorectified and resampled to a UTM grid, zone 60, using WGS84 datum; the coordinates of the upper-left corner of the image is are given in easting/northing, as 350807.4m, 5316081.3m. The scanned map pixel scale is 100 meters/pixels (the actual dpi scanning ratio is irrelevant).

ModelTiepointTag = (0, 0, 0, 350807.4, 5316081.3, 0.0)

ModelPixelScaleTag = (100.0, 100.0, 0.0)

GeoKeyDirectoryTag:

GTModelTypeGeoKey = 1 (ModelTypeProjected)

GTRasterTypeGeoKey = 1 (RasterPixelIsArea)

ProjectedCSTypeGeoKey = 32660 (PCS_WGS84_UTM_zone_60N)

PCSCitationGeoKey = "UTM Zone 60 N with WGS84"

Notes:

1) We did not need to specify the GCS lat-long, since the

PCS_WGS84_UTM_zone_60N codes implies particular GCS and

units already (WGS_84 and meters). The citation was added just

for documentation.

2) The "GeoKeyDirectoryTag" is expressed using the "GeoKey"

structure defined above. At the TIFF level the tags look like

this:

GeoKeyDirectoryTag=( 1, 0, 1, 4,

1024, 0, 1, 1,

1025, 0, 1, 1,

3072, 0, 1, 32660,

3073, 34737, 25, 0 )

GeoAsciiParamsTag(34737)=("UTM Zone 60 N with WGS84|")

For the rest of these examples we will only show the GeoKey-level

dump, with the understanding that the actual TIFF-level tag

representation can be determined from the documentation.

3.1.2. Standard State Plane

We have a USGS State Plane Map of Texas, Central Zone, using NAD83, correctly oriented. The map resolution is 1000 meters/pixel, at origin. There is a grid intersection line in the image at pixel location (50,100), and corresponds to the projected coordinate system easting/northing of (949465.0, 3070309.1).

ModelTiepointTag = ( 50, 100, 0, 949465.0, 3070309.1, 0)

ModelPixelScaleTag = (1000, 1000, 0)

GeoKeyDirectoryTag:

GTModelTypeGeoKey = 1 (ModelTypeProjected)

GTRasterTypeGeoKey = 1 (RasterPixelIsArea)

ProjectedCSTypeGeoKey = 32139 (PCS_NAD83_Texas_Central)

Notice that in this case, since the PCS is a standard code, we

do not need to define the GCS, datum, etc, since those are implied

by the PCS code. Also, since this is NAD83, meters are used rather

than US Survey feet (as in NAD 27).

3.1.3. Lambert Conformal Conic Aeronautical Chart

We have a 500 x 500 scanned aeronautical chart of Seattle, WA, using Lambert Conformal Conic projection, correctly oriented. The central meridian is at 120 degrees west. The map resolution is 1000 meters/pixel, at origin, and uses NAD27 datum. The standard parallels of the projection are at 41d20m N and 48d40m N. The latitude of the origin

is at 45 degrees North, and occurs in the image at the raster coordinates (80,100). The origin is given a false easting and northing of 200000m, 1500000m.

ModelTiepointTag = ( 80, 100, 0, 200000, 1500000, 0)

ModelPixelScaleTag = (1000, 1000, 0)

GeoKeyDirectoryTag:

GTModelTypeGeoKey = 1 (ModelTypeProjected)

GTRasterTypeGeoKey = 1 (RasterPixelIsArea)

GeographicTypeGeoKey = 4267 (GCS_NAD27)

ProjectedCSTypeGeoKey = 32767 (user-defined)

ProjectionGeoKey = 32767 (user-defined)

ProjLinearUnitsGeoKey = 1 (Linear_Meter)

ProjCoordTransGeoKey = 8 (CT_LambertConfConic)

ProjStdParallelGeoKey = 41.333

ProjStdParallel2GeoKey = 48.666

ProjCenterLongGeoKey =-120.0

ProjOriginLatGeoKey = 45.0

ProjFalseEastingGeoKey, = 200000.0

ProjFalseNorthingGeoKey, = 1500000.0

Notice that the Tiepoint takes the false easting and northing into

account when tying the raster point (50,100) to the projection origin.

3.1.4. DMA ADRG Raster Graphic Map

The U.S. Defense Mapping Agency produces ARC digitized raster graphics datasets by scanning maps and geometrically resampling them into an equirectangular projection, so that they may be directly indexed with WGS84 geographic coordinates. The scale for one map is 0.2 degrees per pixel horizontally, 0.1 degrees per pixel vertically. If stored in a GeoTIFF file it contains the following information:

ModelTiepointTag=(0.0, 0.0, 0.0, -120.0, 32.0, 0.0)

ModelPixelScale = (0.2, 0.1, 0.0)

GeoKeyDirectoryTag:

GTModelTypeGeoKey = 2 (ModelTypeGeographic)

GTRasterTypeGeoKey = 1 (RasterPixelIsArea)

GeographicTypeGeoKey = 4326 (GCS_WGS_84)

3.2 Less Common Examples

3.2.1. Unrectified Aerial photo, known tiepoints, in degrees.

We have an aerial photo, and know only the WGS84 GPS location of several points in the scene: the upper left corner is 120 degrees West, 32 degrees North, the lower-left corner is at 120 degrees West, 30 degrees 20 minutes North, and the lower-right hand corner of the image is at 116 degrees 40 minutes West, 30 degrees 20 minutes North. The photo is not geometrically corrected, however, and the complete projection is therefore not known.

ModelTiepointTag=( 0.0, 0.0, 0.0, -120.0, 32.0, 0.0,

0.0, 1000.0, 0.0, -120.0, 30.33333, 0.0,

1000.0, 1000.0, 0.0, -116.6666667, 30.33333, 0.0)

GeoKeyDirectoryTag:

GTModelTypeGeoKey = 1 (ModelTypeGeographic)

GTRasterTypeGeoKey = 1 (RasterPixelIsArea)

GeographicTypeGeoKey = 4326 (GCS_WGS_84)

Remark: Since we have not specified the ModelPixelScaleTag, clients

reading this GeoTIFF file are not permitted to infer that there

is a simple linear relationship between the raster data and the

geographic model coordinate space. The only points that are know

to be exact are the ones specified in the tiepoint tag.

3.2.2. Rotated Scanned Map

We have a scanned standard British National Grid, covering the 100km grid zone NZ. Consulting documentation for BNG we find that the southwest corner of the NZ zone has an easting,northing of 400000m, 500000m, relative to the BNG standard false origin. This scanned map has a resolution of 100 meter pixels, and was rotated 90 degrees to fit onto the scanner, so that the southwest corner is now the northwest corner. In this case we must use the ModelTransformation tag rather than the tiepoint/scale pair to map the raster data into model space:

ModelTransformationTag = ( 0, 100.0, 0, 400000.0,

100.0, 0, 0, 500000.0,

0, 0, 0, 0,

0, 0, 0, 1)

GeoKeyDirectoryTag:

GTModelTypeGeoKey = 1 ( ModelTypeProjected)

GTRasterTypeGeoKey = 1 (RasterPixelIsArea)

ProjectedCSTypeGeoKey = 27700 (PCS_British_National_Grid)

PCSCitationGeoKey = "British National Grid, Zone NZ"

Remark: the matrix has 100.0 in the off-diagonals due to the 90 degree rotation; increasing I points north, and increasing J points east.

3.2.3. Digital Elevation Model

The DMA stores digital elevation models using an equirectangular projection, so that it may be indexed with WGS84 geographic coordinates. Since elevation postings are point-values, the pixels should not be considered as filling areas, but as point-values at grid vertices. To accommodate the base elevation of the Angeles Crest forest, the pixel value of 0 corresponds to an elevation of 1000 meters relative to WGS84 reference ellipsoid. The upper left corner is at 120 degrees West, 32 degrees North, and has a pixel scale of 0.2 degrees/pixel longitude, 0.1 degrees/pixel latitude.

ModelTiepointTag=(0.0, 0.0, 0.0, -120.0, 32.0, 1000.0)

ModelPixelScale = (0.2, 0.1, 1.0)

GeoKeyDirectoryTag:

GTModelTypeGeoKey = 2 (ModelTypeGeographic)

GTRasterTypeGeoKey = 2 (RasterPixelIsPoint)

GeographicTypeGeoKey = 4326 (GCS_WGS_84)

VerticalCSTypeGeoKey = 5030 (VertCS_WGS_84_ellipsoid)

VerticalCitationGeoKey = "WGS 84 Ellipsoid"

VerticalUnitsGeoKey = 1 (Linear_Meter)

Remarks:

1) Note the "RasterPixelIsPoint" raster space, indicating that

the DEM posting of the first pixel is at the raster point

(0,0,0), and therefore corresponds to 120W,32N exactly.

2) The third value of the "PixelScale" is 1.0 to indicate

that a single pixel-value unit corresponds to 1 meter,

and the last tiepoint value indicates that base value

zero indicates 1000m above the reference surface.

4 Extended GeoTIFF

This section is for future development TBD.

Possible additional GeoKeys for Revision 2.0:

PerspectHeightGeoKey (General Vertical Nearsided Perspective)

SOMInclinAngleGeoKey (SOM)

SOMAscendLongGeoKey (SOM)

SOMRevPeriodGeoKey (SOM)

SOMEndOfPathGeoKey (SOM) ? is this needed ? SHORT

SOMRatioGeoKey (SOM)

SOMPathNumGeoKey (SOM) SHORT

SOMSatelliteNumGeoKey (SOM) SHORT

OEAShapeMGeoKey (Oblated Equal Area)

OEAShapeNGeoKey (Oblated Equal Area)

OEARotationAngleGeoKey (Oblated Equal Area)

Other items for consideration:

o Digital Elevation Model information, such as Vertical Datums, Sounding Datums.

o Accuracy Keys for linear, circular, and spherical errors, etc.

o Source information, such as details of an original coordinate system and of transformations between it and the coordinate system in which data is being exchanged.

5 References

1. EPSG/POSC Projection Coding System Tables. Available via FTP to:

ftp://ftpmcmc.er.usgs.gov/release/geotiff/tables

or:

ftp://mtritter.jpl.nasa.gov/pub/geotiff/tables

2. TIFF Revision 6.0 Specification: A PDF formatted version

is available via FTP to:

ftp://ftp.adobe.com/pub/adobe/DeveloperSupport/TechNotes/PDFfiles/TIFF6.pdf

PostScript formatted text versiona available at:.

ftp://sgi.com/graphics/tiff/TIFF6.ps.Z (compressed)

ftp://sgi.com/graphics/tiff/TIFF6.ps (uncompressed)

3. LIBTIFF -- Public Domain TIFF library, available via anonymous

FTP to:

ftp://sgi.com/graphics/tiff/

4. Spatial Data Transfer Standard (SDTS) of the USGS.

(Federal Information Processing Standard (FIPS) 173):

ftp://sdts.er.usgs.gov/pub/sdts/

SDTS Task Force

U.S. Geological Survey

526 National Center

Reston, VA 22092

E-mail: sdts@usgs.gov

5. Map use: reading, analysis, interpretation.

Muehrcke, Phillip C. 1986. Madison, WI: JP Publications.

6. Map projections: a working manual. Snyder, John P. 1987.

USGS Professional Paper 1395.

Washington, DC: United States Government Printing Office.

7. Notes for GIS and The Geographer's Craft at U. Texas, on the World Wide Web (WWW) (current as of 10 April 1995):

http://wwwhost.cc.utexas.edu/ftp/pub/grg/gcraft/notes/notes.html

8. Digital Geographic Information Exchange Standard (DIGEST).

Allied Geographic Publication No 3, Edition 1.2 (AGeoP-3)

(NATO Unclassified).

6. Appendices

6.1 Tag ID Summary

Here are all of the TIFF tags (and their owners) that are used to store GeoTIFF information of any type. It is very unlikely that any other tags will be necessary in the future (since most additional information will be encoded as a GeoKey).

ModelPixelScaleTag = 33550 (SoftDesk)

ModelTransformationTag = 33920 (Intergraph)

ModelTiepointTag = 33922 (Intergraph)

GeoKeyDirectoryTag = 34735 (SPOT)

GeoDoubleParamsTag = 34736 (SPOT)

GeoAsciiParamsTag = 34737 (SPOT)

6.2 Key ID Summary

6.2.1 GeoTIFF Configuration Keys

GTModelTypeGeoKey = 1024 /* Section 6.3.1.1 Codes */

GTRasterTypeGeoKey = 1025 /* Section 6.3.1.2 Codes */

GTCitationGeoKey = 1026 /* documentation */

6.2.2 Geographic CS Parameter Keys

GeographicTypeGeoKey = 2048 /* Section 6.3.2.1 Codes */

GeogCitationGeoKey = 2049 /* documentation */

GeogGeodeticDatumGeoKey = 2050 /* Section 6.3.2.2 Codes */

GeogPrimeMeridianGeoKey = 2051 /* Section 6.3.2.4 codes */

GeogLinearUnitsGeoKey = 2052 /* Section 6.3.1.3 Codes */

GeogLinearUnitSizeGeoKey = 2053 /* meters */

GeogAngularUnitsGeoKey = 2054 /* Section 6.3.1.4 Codes */

GeogAngularUnitSizeGeoKey = 2055 /* radians */

GeogEllipsoidGeoKey = 2056 /* Section 6.3.2.3 Codes */

GeogSemiMajorAxisGeoKey = 2057 /* GeogLinearUnits */

GeogSemiMinorAxisGeoKey = 2058 /* GeogLinearUnits */

GeogInvFlatteningGeoKey = 2059 /* ratio */

GeogAzimuthUnitsGeoKey = 2060 /* Section 6.3.1.4 Codes */

GeogPrimeMeridianLongGeoKey = 2061 /* GeogAngularUnit */

6.2.3 Projected CS Parameter Keys

ProjectedCSTypeGeoKey = 3072 /* Section 6.3.3.1 codes */

PCSCitationGeoKey = 3073 /* documentation */

ProjectionGeoKey = 3074 /* Section 6.3.3.2 codes */

ProjCoordTransGeoKey = 3075 /* Section 6.3.3.3 codes */

ProjLinearUnitsGeoKey = 3076 /* Section 6.3.1.3 codes */

ProjLinearUnitSizeGeoKey = 3077 /* meters */

ProjStdParallelGeoKey = 3078 /* GeogAngularUnit */

ProjStdParallel2GeoKey = 3079 /* GeogAngularUnit */

ProjOriginLongGeoKey = 3080 /* GeogAngularUnit */

ProjOriginLatGeoKey = 3081 /* GeogAngularUnit */

ProjFalseEastingGeoKey = 3082 /* ProjLinearUnits */

ProjFalseNorthingGeoKey = 3083 /* ProjLinearUnits */

ProjFalseOriginLongGeoKey = 3084 /* GeogAngularUnit */

ProjFalseOriginLatGeoKey = 3085 /* GeogAngularUnit */

ProjFalseOriginEastingGeoKey = 3086 /* ProjLinearUnits */

ProjFalseOriginNorthingGeoKey = 3087 /* ProjLinearUnits */

ProjCenterLongGeoKey = 3088 /* GeogAngularUnit */

ProjCenterLatGeoKey = 3089 /* GeogAngularUnit */

ProjCenterEastingGeoKey = 3090 /* ProjLinearUnits */

ProjCenterNorthingGeoKey = 3091 /* ProjLinearUnits */

ProjScaleAtOriginGeoKey = 3092 /* ratio */

ProjScaleAtCenterGeoKey = 3093 /* ratio */

ProjAzimuthAngleGeoKey = 3094 /* GeogAzimuthUnit */

ProjStraightVertPoleLongGeoKey = 3095 /* GeogAngularUnit */

6.2.4 Vertical CS Keys

VerticalCSTypeGeoKey = 4096 /* Section 6.3.4.1 codes */

VerticalCitationGeoKey = 4097 /* documentation */

VerticalDatumGeoKey = 4098 /* Section 6.3.4.2 codes */

VerticalUnitsGeoKey = 4099 /* Section 6.3.1.3 codes */

6.3 Key Code Summary

6.3.1 GeoTIFF General Codes

This section includes the general "Configuration" key codes, as well as general codes which are used by more than one key (e.g. units codes).

6.3.1.1 Model Type Codes

Ranges:

0 = undefined

[ 1, 32766] = GeoTIFF Reserved Codes

32767 = user-defined

[32768, 65535] = Private User Implementations

GeoTIFF defined CS Model Type Codes:

ModelTypeProjected = 1 /* Projection Coordinate System */

ModelTypeGeographic = 2 /* Geographic latitude-longitude System */

ModelTypeGeocentric = 3 /* Geocentric (X,Y,Z) Coordinate System */

Notes:

1. ModelTypeGeographic and ModelTypeProjected

correspond to the FGDC metadata Geographic and

Planar-Projected coordinate system types.

6.3.1.2 Raster Type Codes

Ranges:

0 = undefined

[ 1, 1023] = Raster Type Codes (GeoTIFF Defined)

[1024, 32766] = Reserved

32767 = user-defined

[32768, 65535]= Private User Implementations

Values:

RasterPixelIsArea = 1

RasterPixelIsPoint = 2

Note: Use of "user-defined" or "undefined" raster codes is not recommended.

6.3.1.3 Linear Units Codes

There are several different kinds of units that may be used in geographically related raster data: linear units, angular units, units of time (e.g. for radar-return), CCD-voltages, etc. For this reason there will be a single, unique range for each kind of unit, broken down into the following currently defined ranges:

Ranges:

0 = undefined

[ 1, 2000] = Obsolete GeoTIFF codes

[2001, 8999] = Reserved by GeoTIFF

[9000, 9099] = EPSG Linear Units.

[9100, 9199] = EPSG Angular Units.

32767 = user-defined unit

[32768, 65535]= Private User Implementations

Linear Unit Values (See the ESPG/POSC tables for definition):

Linear_Meter = 9001

Linear_Foot = 9002

Linear_Foot_US_Survey = 9003

Linear_Foot_Modified_American = 9004

Linear_Foot_Clarke = 9005

Linear_Foot_Indian = 9006

Linear_Link = 9007

Linear_Link_Benoit = 9008

Linear_Link_Sears = 9009

Linear_Chain_Benoit = 9010

Linear_Chain_Sears = 9011

Linear_Yard_Sears = 9012

Linear_Yard_Indian = 9013

Linear_Fathom = 9014

Linear_Mile_International_Nautical = 9015

6.3.1.4 Angular Units Codes

These codes shall be used for any key that requires specification of an angular unit of measurement.

Angular Units

Angular_Radian = 9101

Angular_Degree = 9102

Angular_Arc_Minute = 9103

Angular_Arc_Second = 9104

Angular_Grad = 9105

Angular_Gon = 9106

Angular_DMS = 9107

Angular_DMS_Hemisphere = 9108

6.3.2 Geographic CS Codes

6.3.2.1 Geographic CS Type Codes

Note: A Geographic coordinate system consists of both a datum and a Prime Meridian. Some of the names are very similar, and differ only in the Prime Meridian, so be sure to use the correct one. The codes beginning with GCSE_xxx are unspecified GCS which use ellipsoid (xxx); it is recommended that only the codes beginning with GCS_ be used if possible.

Ranges:

0 = undefined

[ 1, 1000] = Obsolete EPSG/POSC Geographic Codes

[ 1001, 3999] = Reserved by GeoTIFF

[ 4000, 4199] = EPSG GCS Based on Ellipsoid only

[ 4200, 4999] = EPSG GCS Based on EPSG Datum

[ 5000, 32766] = Reserved by GeoTIFF

32767 = user-defined GCS

[32768, 65535] = Private User Implementations

Values:

Note: Geodetic datum using Greenwich PM have codes equal to the corresponding Datum code - 2000.

GCS_Adindan = 4201

GCS_AGD66 = 4202

GCS_AGD84 = 4203

GCS_Ain_el_Abd = 4204

GCS_Afgooye = 4205

GCS_Agadez = 4206

GCS_Lisbon = 4207

GCS_Aratu = 4208

GCS_Arc_1950 = 4209

GCS_Arc_1960 = 4210

GCS_Batavia = 4211

GCS_Barbados = 4212

GCS_Beduaram = 4213

GCS_Beijing_1954 = 4214

GCS_Belge_1950 = 4215

GCS_Bermuda_1957 = 4216

GCS_Bern_1898 = 4217

GCS_Bogota = 4218

GCS_Bukit_Rimpah = 4219

GCS_Camacupa = 4220

GCS_Campo_Inchauspe = 4221

GCS_Cape = 4222

GCS_Carthage = 4223

GCS_Chua = 4224

GCS_Corrego_Alegre = 4225

GCS_Cote_d_Ivoire = 4226

GCS_Deir_ez_Zor = 4227

GCS_Douala = 4228

GCS_Egypt_1907 = 4229

GCS_ED50 = 4230

GCS_ED87 = 4231

GCS_Fahud = 4232

GCS_Gandajika_1970 = 4233

GCS_Garoua = 4234

GCS_Guyane_Francaise = 4235

GCS_Hu_Tzu_Shan = 4236

GCS_HD72 = 4237

GCS_ID74 = 4238

GCS_Indian_1954 = 4239

GCS_Indian_1975 = 4240

GCS_Jamaica_1875 = 4241

GCS_JAD69 = 4242

GCS_Kalianpur = 4243

GCS_Kandawala = 4244

GCS_Kertau = 4245

GCS_KOC = 4246

GCS_La_Canoa = 4247

GCS_PSAD56 = 4248

GCS_Lake = 4249

GCS_Leigon = 4250

GCS_Liberia_1964 = 4251

GCS_Lome = 4252

GCS_Luzon_1911 = 4253

GCS_Hito_XVIII_1963 = 4254

GCS_Herat_North = 4255

GCS_Mahe_1971 = 4256

GCS_Makassar = 4257

GCS_EUREF89 = 4258

GCS_Malongo_1987 = 4259

GCS_Manoca = 4260

GCS_Merchich = 4261

GCS_Massawa = 4262

GCS_Minna = 4263

GCS_Mhast = 4264

GCS_Monte_Mario = 4265

GCS_M_poraloko = 4266

GCS_NAD27 = 4267

GCS_NAD_Michigan = 4268

GCS_NAD83 = 4269

GCS_Nahrwan_1967 = 4270

GCS_Naparima_1972 = 4271

GCS_GD49 = 4272

GCS_NGO_1948 = 4273

GCS_Datum_73 = 4274

GCS_NTF = 4275

GCS_NSWC_9Z_2 = 4276

GCS_OSGB_1936 = 4277

GCS_OSGB70 = 4278

GCS_OS_SN80 = 4279

GCS_Padang = 4280

GCS_Palestine_1923 = 4281

GCS_Pointe_Noire = 4282

GCS_GDA94 = 4283

GCS_Pulkovo_1942 = 4284

GCS_Qatar = 4285

GCS_Qatar_1948 = 4286

GCS_Qornoq = 4287

GCS_Loma_Quintana = 4288

GCS_Amersfoort = 4289

GCS_RT38 = 4290

GCS_SAD69 = 4291

GCS_Sapper_Hill_1943 = 4292

GCS_Schwarzeck = 4293

GCS_Segora = 4294

GCS_Serindung = 4295

GCS_Sudan = 4296

GCS_Tananarive = 4297

GCS_Timbalai_1948 = 4298

GCS_TM65 = 4299

GCS_TM75 = 4300

GCS_Tokyo = 4301

GCS_Trinidad_1903 = 4302

GCS_TC_1948 = 4303

GCS_Voirol_1875 = 4304

GCS_Voirol_Unifie = 4305

GCS_Bern_1938 = 4306

GCS_Nord_Sahara_1959 = 4307

GCS_Stockholm_1938 = 4308

GCS_Yacare = 4309

GCS_Yoff = 4310

GCS_Zanderij = 4311

GCS_MGI = 4312

GCS_Belge_1972 = 4313

GCS_DHDN = 4314

GCS_Conakry_1905 = 4315

GCS_WGS_72 = 4322

GCS_WGS_72BE = 4324

GCS_WGS_84 = 4326

GCS_Bern_1898_Bern = 4801

GCS_Bogota_Bogota = 4802

GCS_Lisbon_Lisbon = 4803

GCS_Makassar_Jakarta = 4804

GCS_MGI_Ferro = 4805

GCS_Monte_Mario_Rome = 4806

GCS_NTF_Paris = 4807

GCS_Padang_Jakarta = 4808

GCS_Belge_1950_Brussels = 4809

GCS_Tananarive_Paris = 4810

GCS_Voirol_1875_Paris = 4811

GCS_Voirol_Unifie_Paris = 4812

GCS_Batavia_Jakarta = 4813

GCS_ATF_Paris = 4901

GCS_NDG_Paris = 4902

Ellipsoid-Only GCS:

Note: the numeric code is equal to the code of the correspoding EPSG ellipsoid, minus 3000.

GCSE_Airy1830 = 4001

GCSE_AiryModified1849 = 4002

GCSE_AustralianNationalSpheroid = 4003

GCSE_Bessel1841 = 4004

GCSE_BesselModified = 4005

GCSE_BesselNamibia = 4006

GCSE_Clarke1858 = 4007

GCSE_Clarke1866 = 4008

GCSE_Clarke1866Michigan = 4009

GCSE_Clarke1880_Benoit = 4010

GCSE_Clarke1880_IGN = 4011

GCSE_Clarke1880_RGS = 4012

GCSE_Clarke1880_Arc = 4013

GCSE_Clarke1880_SGA1922 = 4014

GCSE_Everest1830_1937Adjustment = 4015

GCSE_Everest1830_1967Definition = 4016

GCSE_Everest1830_1975Definition = 4017

GCSE_Everest1830Modified = 4018

GCSE_GRS1980 = 4019

GCSE_Helmert1906 = 4020

GCSE_IndonesianNationalSpheroid = 4021

GCSE_International1924 = 4022

GCSE_International1967 = 4023

GCSE_Krassowsky1940 = 4024

GCSE_NWL9D = 4025

GCSE_NWL10D = 4026

GCSE_Plessis1817 = 4027

GCSE_Struve1860 = 4028

GCSE_WarOffice = 4029

GCSE_WGS84 = 4030

GCSE_GEM10C = 4031

GCSE_OSU86F = 4032

GCSE_OSU91A = 4033

GCSE_Clarke1880 = 4034

GCSE_Sphere = 4035

6.3.2.2 Geodetic Datum Codes

Note: these codes do not include the Prime Meridian; if possible use the GCS codes above if the datum and Prime Meridian are on the list. Also, as with the GCS codes, the codes beginning with DatumE_xxx refer only to the specified ellipsoid (xxx); if possible use instead the named datums beginning with Datum_xxx

Ranges:

0 = undefined

[ 1, 1000] = Obsolete EPSG/POSC Datum Codes

[ 1001, 5999] = Reserved by GeoTIFF

[ 6000, 6199] = EPSG Datum Based on Ellipsoid only

[ 6200, 6999] = EPSG Datum Based on EPSG Datum

[ 6322, 6327] = WGS Datum

[ 6900, 6999] = Archaic Datum

[ 7000, 32766] = Reserved by GeoTIFF

32767 = user-defined GCS

[32768, 65535] = Private User Implementations

Values:

Datum_Adindan = 6201

Datum_Australian_Geodetic_Datum_1966 = 6202

Datum_Australian_Geodetic_Datum_1984 = 6203

Datum_Ain_el_Abd_1970 = 6204

Datum_Afgooye = 6205

Datum_Agadez = 6206

Datum_Lisbon = 6207

Datum_Aratu = 6208

Datum_Arc_1950 = 6209

Datum_Arc_1960 = 6210

Datum_Batavia = 6211

Datum_Barbados = 6212

Datum_Beduaram = 6213

Datum_Beijing_1954 = 6214

Datum_Reseau_National_Belge_1950 = 6215

Datum_Bermuda_1957 = 6216

Datum_Bern_1898 = 6217

Datum_Bogota = 6218

Datum_Bukit_Rimpah = 6219

Datum_Camacupa = 6220

Datum_Campo_Inchauspe = 6221

Datum_Cape = 6222

Datum_Carthage = 6223

Datum_Chua = 6224

Datum_Corrego_Alegre = 6225

Datum_Cote_d_Ivoire = 6226

Datum_Deir_ez_Zor = 6227

Datum_Douala = 6228

Datum_Egypt_1907 = 6229

Datum_European_Datum_1950 = 6230

Datum_European_Datum_1987 = 6231

Datum_Fahud = 6232

Datum_Gandajika_1970 = 6233

Datum_Garoua = 6234

Datum_Guyane_Francaise = 6235

Datum_Hu_Tzu_Shan = 6236

Datum_Hungarian_Datum_1972 = 6237

Datum_Indonesian_Datum_1974 = 6238

Datum_Indian_1954 = 6239

Datum_Indian_1975 = 6240

Datum_Jamaica_1875 = 6241

Datum_Jamaica_1969 = 6242

Datum_Kalianpur = 6243

Datum_Kandawala = 6244

Datum_Kertau = 6245

Datum_Kuwait_Oil_Company = 6246

Datum_La_Canoa = 6247

Datum_Provisional_S_American_Datum_1956 = 6248

Datum_Lake = 6249

Datum_Leigon = 6250

Datum_Liberia_1964 = 6251

Datum_Lome = 6252

Datum_Luzon_1911 = 6253

Datum_Hito_XVIII_1963 = 6254

Datum_Herat_North = 6255

Datum_Mahe_1971 = 6256

Datum_Makassar = 6257

Datum_European_Reference_System_1989 = 6258

Datum_Malongo_1987 = 6259

Datum_Manoca = 6260

Datum_Merchich = 6261

Datum_Massawa = 6262

Datum_Minna = 6263

Datum_Mhast = 6264

Datum_Monte_Mario = 6265

Datum_M_poraloko = 6266

Datum_North_American_Datum_1927 = 6267

Datum_NAD_Michigan = 6268

Datum_North_American_Datum_1983 = 6269

Datum_Nahrwan_1967 = 6270

Datum_Naparima_1972 = 6271

Datum_New_Zealand_Geodetic_Datum_1949 = 6272

Datum_NGO_1948 = 6273

Datum_Datum_73 = 6274

Datum_Nouvelle_Triangulation_Francaise = 6275

Datum_NSWC_9Z_2 = 6276

Datum_OSGB_1936 = 6277

Datum_OSGB_1970_SN = 6278

Datum_OS_SN_1980 = 6279

Datum_Padang_1884 = 6280

Datum_Palestine_1923 = 6281

Datum_Pointe_Noire = 6282

Datum_Geocentric_Datum_of_Australia_1994 = 6283

Datum_Pulkovo_1942 = 6284

Datum_Qatar = 6285

Datum_Qatar_1948 = 6286

Datum_Qornoq = 6287

Datum_Loma_Quintana = 6288

Datum_Amersfoort = 6289

Datum_RT38 = 6290

Datum_South_American_Datum_1969 = 6291

Datum_Sapper_Hill_1943 = 6292

Datum_Schwarzeck = 6293

Datum_Segora = 6294

Datum_Serindung = 6295

Datum_Sudan = 6296

Datum_Tananarive_1925 = 6297

Datum_Timbalai_1948 = 6298

Datum_TM65 = 6299

Datum_TM75 = 6300

Datum_Tokyo = 6301

Datum_Trinidad_1903 = 6302

Datum_Trucial_Coast_1948 = 6303

Datum_Voirol_1875 = 6304

Datum_Voirol_Unifie_1960 = 6305

Datum_Bern_1938 = 6306

Datum_Nord_Sahara_1959 = 6307

Datum_Stockholm_1938 = 6308

Datum_Yacare = 6309

Datum_Yoff = 6310

Datum_Zanderij = 6311

Datum_Militar_Geographische_Institut = 6312

Datum_Reseau_National_Belge_1972 = 6313

Datum_Deutsche_Hauptdreiecksnetz = 6314

Datum_Conakry_1905 = 6315

Datum_WGS72 = 6322

Datum_WGS72_Transit_Broadcast_Ephemeris = 6324

Datum_WGS84 = 6326

Datum_Ancienne_Triangulation_Francaise = 6901

Datum_Nord_de_Guerre = 6902

Ellipsoid-Only Datum:

Note: the numeric code is equal to the corresponding ellipsoid

code, minus 1000.

DatumE_Airy1830 = 6001

DatumE_AiryModified1849 = 6002

DatumE_AustralianNationalSpheroid = 6003

DatumE_Bessel1841 = 6004

DatumE_BesselModified = 6005

DatumE_BesselNamibia = 6006

DatumE_Clarke1858 = 6007

DatumE_Clarke1866 = 6008

DatumE_Clarke1866Michigan = 6009

DatumE_Clarke1880_Benoit = 6010

DatumE_Clarke1880_IGN = 6011

DatumE_Clarke1880_RGS = 6012

DatumE_Clarke1880_Arc = 6013

DatumE_Clarke1880_SGA1922 = 6014

DatumE_Everest1830_1937Adjustment = 6015

DatumE_Everest1830_1967Definition = 6016

DatumE_Everest1830_1975Definition = 6017

DatumE_Everest1830Modified = 6018

DatumE_GRS1980 = 6019

DatumE_Helmert1906 = 6020

DatumE_IndonesianNationalSpheroid = 6021

DatumE_International1924 = 6022

DatumE_International1967 = 6023

DatumE_Krassowsky1960 = 6024

DatumE_NWL9D = 6025

DatumE_NWL10D = 6026

DatumE_Plessis1817 = 6027

DatumE_Struve1860 = 6028

DatumE_WarOffice = 6029

DatumE_WGS84 = 6030

DatumE_GEM10C = 6031

DatumE_OSU86F = 6032

DatumE_OSU91A = 6033

DatumE_Clarke1880 = 6034

DatumE_Sphere = 6035

6.3.2.3 Ellipsoid Codes

Ranges:

0 = undefined

[ 1, 1000] = Obsolete EPSG/POSC Ellipsoid codes

[1001, 6999] = Reserved by GeoTIFF

[7000, 7999] = EPSG Ellipsoid codes

[8000, 32766] = Reserved by GeoTIFF

32767 = user-defined

[32768, 65535] = Private User Implementations

Values:

Ellipse_Airy_1830 = 7001

Ellipse_Airy_Modified_1849 = 7002

Ellipse_Australian_National_Spheroid = 7003

Ellipse_Bessel_1841 = 7004

Ellipse_Bessel_Modified = 7005

Ellipse_Bessel_Namibia = 7006

Ellipse_Clarke_1858 = 7007

Ellipse_Clarke_1866 = 7008

Ellipse_Clarke_1866_Michigan = 7009

Ellipse_Clarke_1880_Benoit = 7010

Ellipse_Clarke_1880_IGN = 7011

Ellipse_Clarke_1880_RGS = 7012

Ellipse_Clarke_1880_Arc = 7013

Ellipse_Clarke_1880_SGA_1922 = 7014

Ellipse_Everest_1830_1937_Adjustment = 7015

Ellipse_Everest_1830_1967_Definition = 7016

Ellipse_Everest_1830_1975_Definition = 7017

Ellipse_Everest_1830_Modified = 7018

Ellipse_GRS_1980 = 7019

Ellipse_Helmert_1906 = 7020

Ellipse_Indonesian_National_Spheroid = 7021

Ellipse_International_1924 = 7022

Ellipse_International_1967 = 7023

Ellipse_Krassowsky_1940 = 7024

Ellipse_NWL_9D = 7025

Ellipse_NWL_10D = 7026

Ellipse_Plessis_1817 = 7027

Ellipse_Struve_1860 = 7028

Ellipse_War_Office = 7029

Ellipse_WGS_84 = 7030

Ellipse_GEM_10C = 7031

Ellipse_OSU86F = 7032

Ellipse_OSU91A = 7033

Ellipse_Clarke_1880 = 7034

Ellipse_Sphere = 7035

6.3.2.4 Prime Meridian Codes

Ranges:

0 = undefined

[ 1, 100] = Obsolete EPSG/POSC Prime Meridian codes

[ 101, 7999] = Reserved by GeoTIFF

[ 8000, 8999] = EPSG Prime Meridian Codes

[ 9000, 32766] = Reserved by GeoTIFF

32767 = user-defined

[32768, 65535] = Private User Implementations

Values:

PM_Greenwich = 8901

PM_Lisbon = 8902

PM_Paris = 8903

PM_Bogota = 8904

PM_Madrid = 8905

PM_Rome = 8906

PM_Bern = 8907

PM_Jakarta = 8908

PM_Ferro = 8909

PM_Brussels = 8910

PM_Stockholm = 8911

6.3.3 Projected CS Codes

6.3.3.1 Projected CS Type Codes

Ranges:

[ 1, 1000] = Obsolete EPSG/POSC Projection System Codes

[20000, 32760] = EPSG Projection System codes

32767 = user-defined

[32768, 65535] = Private User Implementations

Special Ranges:

1. For PCS utilising GeogCS with code in range 4201 through 4321 (i.e. geodetic datum code 6201 through 6319): As far as is possible the PCS code will be of theformat gggzz where ggg is (geodetic datum code -2000) and zz is zone.

2. For PCS utilising GeogCS with code out of range 4201 through 4321 (i.e.geodetic datum code 6201 through 6319). PCS code 20xxx where xxx is a sequential number.

3. Other:

WGS72 / UTM northern hemisphere: 322zz where zz is UTM zone number

WGS72 / UTM southern hemisphere: 323zz where zz is UTM zone number

WGS72BE / UTM northern hemisphere: 324zz where zz is UTM zone number

WGS72BE / UTM southern hemisphere: 325zz where zz is UTM zone number

WGS84 / UTM northern hemisphere: 326zz where zz is UTM zone number

WGS84 / UTM southern hemisphere: 327zz where zz is UTM zone number

US State Plane (NAD27): 267xx/320xx

US State Plane (NAD83): 269xx/321xx

Values:

PCS_Adindan_UTM_zone_37N = 20137

PCS_Adindan_UTM_zone_38N = 20138

PCS_AGD66_AMG_zone_48 = 20248

PCS_AGD66_AMG_zone_49 = 20249

PCS_AGD66_AMG_zone_50 = 20250

PCS_AGD66_AMG_zone_51 = 20251

PCS_AGD66_AMG_zone_52 = 20252

PCS_AGD66_AMG_zone_53 = 20253

PCS_AGD66_AMG_zone_54 = 20254

PCS_AGD66_AMG_zone_55 = 20255

PCS_AGD66_AMG_zone_56 = 20256

PCS_AGD66_AMG_zone_57 = 20257

PCS_AGD66_AMG_zone_58 = 20258

PCS_AGD84_AMG_zone_48 = 20348

PCS_AGD84_AMG_zone_49 = 20349

PCS_AGD84_AMG_zone_50 = 20350

PCS_AGD84_AMG_zone_51 = 20351

PCS_AGD84_AMG_zone_52 = 20352

PCS_AGD84_AMG_zone_53 = 20353

PCS_WGS84_UTM_zone_43S = 32743

PCS_WGS84_UTM_zone_44S = 32744

PCS_WGS84_UTM_zone_45S = 32745

PCS_WGS84_UTM_zone_46S = 32746

PCS_WGS84_UTM_zone_47S = 32747

PCS_WGS84_UTM_zone_48S = 32748

PCS_WGS84_UTM_zone_49S = 32749

PCS_WGS84_UTM_zone_50S = 32750

PCS_WGS84_UTM_zone_51S = 32751

PCS_WGS84_UTM_zone_52S = 32752

PCS_WGS84_UTM_zone_53S = 32753

PCS_WGS84_UTM_zone_54S = 32754

PCS_WGS84_UTM_zone_55S = 32755

PCS_WGS84_UTM_zone_56S = 32756

PCS_WGS84_UTM_zone_57S = 32757

PCS_WGS84_UTM_zone_58S = 32758

PCS_WGS84_UTM_zone_59S = 32759

PCS_WGS84_UTM_zone_60S = 32760

6.3.3.2 Projection Codes

Note: Projections do not include GCS/datum definitions. If possible, use the PCS code for standard projected coordinate systems, and use this code only if nonstandard datums are required.

Ranges:

0 = undefined

[ 1, 9999] = Obsolete EPSG/POSC Projection codes

[10000, 19999] = EPSG/POSC Projection codes

32767 = user-defined

[32768, 65535] = Private User Implementations

Special Ranges:

US State Plane Format: 1sszz

where ss is USC&GS State code

zz is USC&GS zone code for NAD27 zones

zz is (USC&GS zone code + 30) for NAD83 zones

Larger zoned systems (16000-17999)

UTM (North) Format: 160zz

UTM (South) Format: 161zz

zoned Universal Gauss-Kruger Format: 162zz

Universal Gauss-Kruger (unzoned) Format: 163zz

Australian Map Grid Format: 174zz

Southern African STM Format: 175zz

Smaller zoned systems: Format: 18ssz

where ss is sequential system number

z is zone code

Single zone projections Format: 199ss

where ss is sequential system number

Values:

Proj_Alabama_CS27_East = 10101

Proj_Alabama_CS27_West = 10102

Proj_Alabama_CS83_East = 10131

Proj_Alabama_CS83_West = 10132

Proj_Arizona_Coordinate_System_east = 10201

Proj_Arizona_Coordinate_System_Central = 10202

Proj_Arizona_Coordinate_System_west = 10203

Proj_Arizona_CS83_east = 10231

Proj_Arizona_CS83_Central = 10232

Proj_Arizona_CS83_west = 10233

Proj_Arkansas_CS27_North = 10301

Proj_Arkansas_CS27_South = 10302

Proj_Arkansas_CS83_North = 10331

Proj_Map_Grid_of_Australia_57 = 17357

Proj_Map_Grid_of_Australia_58 = 17358

Proj_Australian_Map_Grid_48 = 17448

Proj_Australian_Map_Grid_49 = 17449

Proj_Australian_Map_Grid_50 = 17450

Proj_Australian_Map_Grid_51 = 17451

Proj_Australian_Map_Grid_52 = 17452

Proj_Australian_Map_Grid_53 = 17453

Proj_Australian_Map_Grid_54 = 17454

Proj_Australian_Map_Grid_55 = 17455

Proj_Australian_Map_Grid_56 = 17456

Proj_Australian_Map_Grid_57 = 17457

Proj_Australian_Map_Grid_58 = 17458

Proj_Argentina_1 = 18031

Proj_Argentina_2 = 18032

Proj_Argentina_3 = 18033

Proj_Argentina_4 = 18034

Proj_Argentina_5 = 18035

Proj_Argentina_6 = 18036

Proj_Argentina_7 = 18037

Proj_Colombia_3W = 18051

Proj_Colombia_Bogota = 18052

Proj_Colombia_3E = 18053

Proj_Colombia_6E = 18054

Proj_Egypt_Red_Belt = 18072

Proj_Egypt_Purple_Belt = 18073

Proj_Extended_Purple_Belt = 18074

Proj_New_Zealand_North_Island_Nat_Grid = 18141

Proj_New_Zealand_South_Island_Nat_Grid = 18142

Proj_Bahrain_Grid = 19900

Proj_Netherlands_E_Indies_Equatorial = 19905

Proj_RSO_Borneo = 19912

6.3.3.3 Coordinate Transformation Codes

Ranges:

0 = undefined

[ 1, 16383] = GeoTIFF Coordinate Transformation codes

[16384, 32766] = Reserved by GeoTIFF

32767 = user-defined

[32768, 65535] = Private User Implementations

Values:

CT_TransverseMercator = 1

CT_TransvMercator_Modified_Alaska = 2

CT_ObliqueMercator = 3

CT_ObliqueMercator_Laborde = 4

CT_ObliqueMercator_Rosenmund = 5

CT_ObliqueMercator_Spherical = 6

CT_Mercator = 7

CT_LambertConfConic = 8

CT_LambertConfConic_Helmert = 9

CT_LambertAzimEqualArea = 10

CT_AlbersEqualArea = 11

CT_AzimuthalEquidistant = 12

CT_EquidistantConic = 13

CT_Stereographic = 14

CT_PolarStereographic = 15

CT_ObliqueStereographic = 16

CT_Equirectangular = 17

CT_CassiniSoldner = 18

CT_Gnomonic = 19

CT_MillerCylindrical = 20

CT_Orthographic = 21

CT_Polyconic = 22

CT_Robinson = 23

CT_Sinusoidal = 24

CT_VanDerGrinten = 25

CT_NewZealandMapGrid = 26

CT_SouthOrientedGaussConformal = 27

Aliases:

CT_AlaskaConformal = CT_TransvMercator_Modified_Alaska

CT_TransvEquidistCylindrical = CT_CassiniSoldner

CT_ObliqueMercator_Hotine = CT_ObliqueMercator

CT_SwissObliqueCylindrical = CT_ObliqueMercator_Rosenmund

CT_GaussBoaga = CT_TransverseMercator

CT_GaussKruger = CT_TransverseMercator

6.3.4 Vertical CS Codes

6.3.4.1 Vertical CS Type Codes

Ranges:

0 = undefined

[ 1, 4999] = Reserved

[ 5000, 5099] = EPSG Ellipsoid Vertical CS Codes

[ 5100, 5199] = EPSG Orthometric Vertical CS Codes

[ 5200, 5999] = Reserved EPSG

[ 6000, 32766] = Reserved

32767 = user-defined

[32768, 65535] = Private User Implementations

Values:

VertCS_Airy_1830_ellipsoid = 5001

VertCS_Airy_Modified_1849_ellipsoid = 5002

VertCS_ANS_ellipsoid = 5003

VertCS_Bessel_1841_ellipsoid = 5004

VertCS_Bessel_Modified_ellipsoid = 5005

VertCS_Bessel_Namibia_ellipsoid = 5006

VertCS_Clarke_1858_ellipsoid = 5007

VertCS_Clarke_1866_ellipsoid = 5008

VertCS_Clarke_1880_Benoit_ellipsoid = 5010

VertCS_Clarke_1880_IGN_ellipsoid = 5011

VertCS_Clarke_1880_RGS_ellipsoid = 5012

VertCS_Clarke_1880_Arc_ellipsoid = 5013

VertCS_Clarke_1880_SGA_1922_ellipsoid = 5014

VertCS_Everest_1830_1937_Adjustment_ellipsoid = 5015

VertCS_Everest_1830_1967_Definition_ellipsoid = 5016

VertCS_Everest_1830_1975_Definition_ellipsoid = 5017

VertCS_Everest_1830_Modified_ellipsoid = 5018

VertCS_GRS_1980_ellipsoid = 5019

VertCS_Helmert_1906_ellipsoid = 5020

VertCS_INS_ellipsoid = 5021

VertCS_International_1924_ellipsoid = 5022

VertCS_International_1967_ellipsoid = 5023

VertCS_Krassowsky_1940_ellipsoid = 5024

VertCS_NWL_9D_ellipsoid = 5025

VertCS_NWL_10D_ellipsoid = 5026

VertCS_Plessis_1817_ellipsoid = 5027

VertCS_Struve_1860_ellipsoid = 5028

VertCS_War_Office_ellipsoid = 5029

VertCS_WGS_84_ellipsoid = 5030

VertCS_GEM_10C_ellipsoid = 5031

VertCS_OSU86F_ellipsoid = 5032

VertCS_OSU91A_ellipsoid = 5033

Orthometric Vertical CS;

VertCS_Newlyn = 5101

VertCS_North_American_Vertical_Datum_1929 = 5102

VertCS_North_American_Vertical_Datum_1988 = 5103

VertCS_Yellow_Sea_1956 = 5104

VertCS_Baltic_Sea = 5105

VertCS_Caspian_Sea = 5106

6.3.4.2 Vertical CS Datum Codes

Ranges:

0 = undefined

[ 1, 16383] = Vertical Datum Codes

[16384, 32766] = Reserved

32767 = user-defined

[32768, 65535] = Private User Implementations

No vertical datum codes are currently defined, other than those implied bythe corrsponding Vertical CS code.

7. Glossary

ASCII - [American Standard Code for Information Interchange] The predominant character set encoding of present-day computers.

Cell - A rectangular area in Raster space, in which a single pixel value is filled.

Code - In GeoTIFF, a code is a value assigned to a GeoKey, and has one of 65536 possible values.

Coordinate System - A systematic way of assigning real (x,y,z..) coordinates to a surface or volume. In Geodetics the surface is an ellipsoid used to model the earth.

Datum - A mathematical approximation to all or part of the earth's surface. Defining a datum requires the definition of an ellipsoid, its location and orientation, as well as the area for which the datum is valid.

Device Space - A coordinate space referencing scanner, printers and display devices.

DOUBLE - 8-bit IEEE double precision floating point.

Ellipsoid: A mathematically defined quadratic surface used to model the earth.

Flattening - For an ellipsoid with major and minor axis lengths (a,b), the flattening is defined by:

f = (a - b)/a

For the earth, the value of f is approximately

1/298.3

Geocoding - An image is geocoded if a precise algorithm for determining the earth-location of each point in the image is defined.

Geographic Coordinate System - A Geographic CS consists of a well-defined ellipsoidal datum, a Prime Meridian, and an angular unit, allowing the assignment of a Latitude-Longitude (and optionally, geodetic height) vector to a location on earth.

GeoKey - In GeoTIFF, a GeoKey is equivalent in function to a TIFF tag, but uses a different storage mechanism.

Georeferencing - An image is georeferenced if the location of its pixels in some model space is defined, but the transformation tying model space to the earth is not known.

GeoTIFF - A standard for storing georeference and geocoding information in a TIFF 6.0 compliant raster file.

Grid - A coordinate mesh upon which pixels are placedIEEE Institute of Electrical and Electronics Engineers, Inc.

IFD - In TIFF format, an Image File Directory, containing all the TIFF tags for one image in the file (there may be more than one).

Meridian - Arc of constant longitude, passing through the poles.

Model Space - A flat geometrical space used to model a portion of the earth.

Parallel - Lines of constant latitude, parallel to the equator.

Pixel - A dimensionless point-measurement, stored in a raster file.

Prime Meridian - An arbitrarily chosen meridian, used as reference for all others, and defined as 0 degrees longitude.

Projection - A projection in GeoTIFF consists of a linear (X,Y) coordinate system, and a coordinate transformation method (such as Transverse Mercator) to tie this system to an unspecified Geographic CS..

Projected Coordinate System - A PCS consists of a Geographic (Lat-Long) coordinate system, and a Projection to tie this system to a linear (X,Y) space.

Raster Space - A continuous planar space in which pixel values are visually realized.

RATIONAL - In TIFF format, a RATIONAL value is a fractional value represented by the ratio of two unsigned 4-byte integers.

SDTS - The USGS Spatial Data Transmission Standard.

Tag - In TIFF format, a tag is packet of numerical or ASCII values, which have a numerical "Tag" ID indicating their information content.

TIFF - Acronym for Tagged Image File Format; a platform-independent, extensive specification for storing raster data and ancillary information in a single file.

USGS - U.S. Geological Survey

END OF SPECIFICATION

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Last modified: Friday, 15-Aug-97 07:47:12 CDT

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