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Introduce section numbering and remove table captions in Appendix J
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AndersMS committed Jul 23, 2021
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Expand Up @@ -9,9 +9,9 @@ The definitions and guidance given here allow an application to compress an exis
Futhermore, the definitions given here allow an application to uncompress coordinate and auxiliary coordinate variables that have been compressed using coordinate subsampling. The key element of this process is the reconstitution of the full resolution coordinates in the domain of the data by interpolation between the subsampled coordinates, the tie points, stored in the compressed dataset.


The appendix is organised in a sections on <<common_definitions_and_notation>>, <<common_conversions_and_formulas>>, <<interpolation_methods>> and finally two sections with step procedures <<coordinate_compression_steps>> and <<coordinate_uncompression_steps>>.
The appendix is organised in a sections on <<common-definitions-and-notation>>, <<interpolation-methods>>, <<common-conversions-and-formulas>> and finally two sections with step procedures <<coordinate-compression-steps>> and <<coordinate-uncompression-steps>>.

[[common_definitions_and_notation]]
[[common-definitions-and-notation, Section J.1, "Common Definitions and Notation"]]
=== Common Definitions and Notation

The target domain is segmented into smaller interpolation subareas as described in <<compression-by-coordinate-subsampling-tie-points-and-interpolation-subareas>>.
Expand Down Expand Up @@ -60,7 +60,7 @@ For two dimensional interpolation, `i1` and `i2` are indices in the interpolated

Note that, for simplicity of notation, the descriptions of the interpolation methods in most places leave out the indices of tie point related variables and refer to these with `a` and `b` in the one dimensional case and with `a`, `b`, `c` and `d` in the two dimensional case. In the two dimensional case, `a = tp(tpi2, tpi1)`, `b = tp(tpi2, tpi1+1)`, `c = tp(tpi2+1, tpi1)` and `d = tp(tpi2+1, tpi1+1)` would reflect the way the tie point data would be stored in the data set, see also <<interpolation>>.

[[interpolation_methods]]
[[interpolation-methods, Section J.2, "Interpolation Methods"]]
=== Interpolation Methods

==== Linear Interpolation
Expand Down Expand Up @@ -272,8 +272,8 @@ where +
image::images/ci_quadratic3.svg[,50%,pdfwidth=50vw,align="center"]


[[common_conversions_and_formulas]]
==== Common conversions and formulas
[[common-conversions-and-formulas, Section J.3, "Common Conversions and Formulas"]]
==== Common Conversions and Formulas

[cols="1, 8, 8"]
|===============
Expand Down Expand Up @@ -305,13 +305,9 @@ image::images/ci_quadratic3.svg[,50%,pdfwidth=50vw,align="center"]
|===============



[[coordinate_compression_steps]]
[[coordinate-compression-steps, Section J.4, "Coordinate Compression Steps"]]
=== Coordinate Compression Steps

[[compression-by-coordinate-subsampling-generation-of-tie-points]]
.Generation of Tie Point Variables and Interpolation Variables
[options="header",cols="1,16,6",caption="Table J.1. "]
|===============
| Step | Description | Link

Expand Down Expand Up @@ -356,9 +352,9 @@ image::images/ci_quadratic3.svg[,50%,pdfwidth=50vw,align="center"]
| <<compression-by-coordinate-subsampling-interpolation-of-cell-boundaries>>

| 10
| If required by the selected interpolation method, follow the steps defined for the method in <<interpolation_methods>> to create any required interpolation parameter variables. As relevant, create the **`interpolation_parameters`** attribute and populate it with the interpolation parameter variables.
| If required by the selected interpolation method, follow the steps defined for the method in <<interpolation-methods>> to create any required interpolation parameter variables. As relevant, create the **`interpolation_parameters`** attribute and populate it with the interpolation parameter variables.
| <<compression-by-coordinate-subsampling-interpolation-variable>> +
<<interpolation_methods>>
<<interpolation-methods>>

| 11
| Optionally, check the consistency of the original coordinates and the reconstructed coordinates and add a **`comments`** attribute to one or more of the tie point coordinate variables reporting key figures like maximum error, mean error, etc.
Expand All @@ -367,13 +363,9 @@ image::images/ci_quadratic3.svg[,50%,pdfwidth=50vw,align="center"]

|===============

[[coordinate_uncompression_steps]]
[[coordinate-uncompression-steps, Section J.5, "Coordinate Uncompression Steps"]]
=== Coordinate Uncompression Steps


[[compression-by-coordinate-subsampling-reconstitution-of-coordinates]]
.Reconstitution of Coordinate and Auxillary Coordinate Variables
[options="header",cols="1,16,6",caption="Table J.2. "]
|===============
| Step | Description | Link

Expand Down Expand Up @@ -411,9 +403,9 @@ image::images/ci_quadratic3.svg[,50%,pdfwidth=50vw,align="center"]
| <<compression-by-coordinate-subsampling-interpolation-parameters>>

| 8
| For each of the tie point coordinate and auxillary coordinate variables, create the corresponding target coordinate variable. For each interpolation subarea, apply the interpolation method, as described in <<interpolation_methods>>, to reconstitute the target domain coordinate values and store these in the target domain coordinate variables. Repeat this step for each combination of indices of the non-interpolated dimensions.
| For each of the tie point coordinate and auxillary coordinate variables, create the corresponding target coordinate variable. For each interpolation subarea, apply the interpolation method, as described in <<interpolation-methods>>, to reconstitute the target domain coordinate values and store these in the target domain coordinate variables. Repeat this step for each combination of indices of the non-interpolated dimensions.
| <<compression-by-coordinate-subsampling-tie-point-mapping-attribute>> +
<<interpolation_methods>>
<<interpolation-methods>>

| 9
| For each of the tie point coordinate and auxillary coordinate variables having a **`bounds_tie_points`** attribute, add the **`bounds`** attribute to the target coordinate variable and create the target domain bounds variable. For each interpolation subarea, apply the interpolation method to reconstitute the target domain bound values and store these in the target domain bound variables. Repeat this step for each combination of indices of the non-interpolated dimensions.
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