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Kinematic datum shifting utilizing a deformation model

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New in version 5.0.0.

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Perform datum shifts means of a deformation/velocity model.

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Alias

deformation

Input type

Cartesian coordinates (spatial), decimalyears (temporal).

Output type

Cartesian coordinates (spatial), decimalyears (temporal).

Domain

4D

Input type

Geodetic coordinates

Output type

Geodetic coordinates

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The deformation operation is used to adjust coordinates for intraplate deformations. +Usually the transformation parameters for regional plate-fixed reference frames such as +the ETRS89 does not take intraplate deformation into account. It is assumed that +tectonic plate of the region is rigid. Often times this is true, but near the plate +boundary and in areas with post-glacial uplift the assumption breaks. Intraplate +deformations can be modelled and then applied to the coordinates so that +they represent the physical world better. In PROJ this is done with the deformation +operation.

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The horizontal grid is stored in CTable2 format and the vertical grid is stored in the +GTX format. Both grids are expected to contain grid-values in units of +mm/year. GDAL both reads and writes both file formats. Using GDAL for +construction of new grids is recommended.

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Starting with PROJ 7.0, use of a GeoTIFF format is recommended to store both +the horizontal and vertical velocities.

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More complex deformations can be done with the Multi-component time-based deformation model transformation.

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Example

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In [Hakli2016] coordinate transformation including a deformation model is described. +The paper describes how coordinates from the global ITRFxx frames are transformed to the +local Nordic realisations of ETRS89. Scandinavia is an area with significant post-glacial +rebound. The deformations from the post-glacial uplift is not accounted for in the +official ETRS89 transformations so in order to get accurate transformations in the Nordic +countries it is necessary to apply the deformation model. The transformation from ITRF2008 +to the Danish realisation of ETRS89 is in PROJ described as:

+
proj =  pipeline ellps = GRS80
+        # ITRF2008@t_obs -> ITRF2000@t_obs
+step    init = ITRF2008:ITRF2000
+        # ITRF2000@t_obs -> ETRF2000@t_obs
+step    proj=helmert t_epoch = 2000.0 convention=position_vector
+        x =  0.054  rx =  0.000891 drx =  8.1e-05
+        y =  0.051  ry =  0.00539  dry =  0.00049
+        z = -0.048  rz = -0.008712 drz = -0.000792
+        # ETRF2000@t_obs -> NKG_ETRF00@2000.0
+step    proj = deformation t_epoch = 2000.0
+        grids = ./eur_nkg_nkgrf03vel_realigned.tif
+        inv
+        # NKG_ETRF@2000.0 -> ETRF92@2000.0
+step    proj=helmert convention=position_vector s = -0.009420e
+        x = 0.03863 rx = 0.00617753
+        y = 0.147   ry = 5.064e-05
+        z = 0.02776 rz = 4.729e-05
+        # ETRF92@2000.0 -> ETRF92@1994.704
+step    proj = deformation dt = -5.296
+        grids = ./eur_nkg_nkgrf03vel_realigned.tif
+
+
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From this we can see that the transformation from ITRF2008 to the Danish realisation of +ETRS89 is a combination of Helmert transformations and adjustments with a deformation +model. The first use of the deformation operation is:

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proj = deformation t_epoch = 2000.0 grids = ./eur_nkg_nkgrf03vel_realigned.tif
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Here we set the central epoch of the transformation, 2000.0. The observation epoch +is expected as part of the input coordinate tuple. The deformation model is +described by two grids, specified with +xy_grids and +z_grids. +The first is the horizontal part of the model and the second is the vertical +component.

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Parameters

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++xy_grids=<list>
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Comma-separated list of grids to load. If a grid is prefixed by an @ the +grid is considered optional and PROJ will the not complain if the grid is +not available.

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Grids for the horizontal component of a deformation model is expected to be +in CTable2 format.

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Note

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+xy_grids is mutually exclusive with +grids

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++z_grids=<list>
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Comma-separated list of grids to load. If a grid is prefixed by an @ the +grid is considered optional and PROJ will the not complain if the grid is +not available.

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Grids for the vertical component of a deformation model is expected to be +in either GTX format.

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Note

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+z_grids is mutually exclusive with +grids

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+ +
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++grids=<list>
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New in version 7.0.0.

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Comma-separated list of grids to load. If a grid is prefixed by an @ the +grid is considered optional and PROJ will the not complain if the grid is +not available.

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Grids should be in GeoTIFF format with the first 3 components being +respectively the easting, northing and up velocities in mm/year. +Setting the Description and Unit Type GDAL band metadata items is strongly +recommended, so that gdalinfo reports:

+
Band 1 Block=... Type=Float32, ColorInterp=Gray
+    Description = east_velocity
+    Unit Type: mm/year
+Band 2 Block=... Type=Float32, ColorInterp=Undefined
+    Description = north_velocity
+    Unit Type: mm/year
+Band 3 Block=... Type=Float32, ColorInterp=Undefined
+    Description = up_velocity
+    Unit Type: mm/year
+
+
+
+

Note

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+grids is mutually exclusive with +xy_grids +and +z_grids

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++t_epoch=<value>
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Central epoch of transformation given in decimalyears. Will be used in +conjunction with the observation time from the input coordinate to +determine \(dt\) as used in eq. (1) below.

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Note

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+t_epoch is mutually exclusive with +dt

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++dt=<value>
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New in version 6.0.0.

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\(dt\) as used in eq. (1) below. Is useful when +no observation time is available in the input coordinate or when +a deformation for a specific timespan needs to be applied in a +transformation. \(dt\) is given in units of decimalyears.

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Note

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+dt is mutually exclusive with +t_epoch

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Mathematical description

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Mathematically speaking, application of a deformation model is simple. The deformation model is +represented as a grid of velocities in three dimensions. Coordinate corrections are +applied in cartesian space. For a given coordinate, \((X, Y, Z)\), velocities +\((V_X, V_Y, V_Z)\) can be interpolated from the gridded model. The time span +between \(t_{obs}\) and \(t_c\) determine the magnitude of the coordinate +correction as seen in eq. (1) below.

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+(1)\[\begin{split}\begin{align} + \begin{pmatrix} + X \\ + Y \\ + Z \\ + \end{pmatrix}_B = + \begin{pmatrix} + X \\ + Y \\ + Z \\ + \end{pmatrix}_A + + (t_{obs} - t_c) + \begin{pmatrix} + V_X \\ + V_Y \\ + V_Z \\ + \end{pmatrix} +\end{align}\end{split}\]
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Corrections are done in cartesian space.

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Coordinates of the gridded model are in ENU (east, north, up) space because it +would otherwise require an enormous 3 dimensional grid to handle the corrections +in cartesian space. Keeping the correction in lat/long space reduces the +complexity of the grid significantly. Consequently though, the input coordinates +needs to be converted to lat/long space when searching for corrections in the +grid. This is done with the cart operation. The converted grid +corrections can then be applied to the input coordinates in cartesian space. The +conversion from ENU space to cartesian space is done in the following way:

+
+(2)\[\begin{split}\begin{align} + \begin{pmatrix} + X \\ + Y \\ + Z \\ + \end{pmatrix} = + \begin{pmatrix} + -\sin\phi \cos\lambda N - \sin\lambda E + \cos\phi \cos\lambda U \\ + -\sin\phi \sin\lambda N + \sin\lambda E + \cos\phi \sin\lambda U \\ + \cos\phi N + \sin\phi U \\ + \end{pmatrix} +\end{align}\end{split}\]
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where \(\phi\) and \(\lambda\) are the latitude and longitude of the coordinate +that is searched for in the grid. \((E, N, U)\) are the grid values in ENU-space and +\((X, Y, Z)\) are the corrections converted to cartesian space.

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See also

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  1. Behavioural changes from version 5 to 6

    2. +
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