Vertical Coordinate Reference Systems

1. At the OGC Tech Conference in September 2014 held in Calgary, Canada, an Ad Hoc Working Group on Vertical CRS was called. The group agreed to collect information on different examples of vertical CRSs prior to then analysing them and forming a conceptual model as a basis for extending or changing existing OGC standards.

2. Meteorology and Oceanography uses a variety of vertical coordinates. Here are some examples:
  • Altitude above Mean Seal Level or other datum
  • Elevation above the land surface (actual, or sometimes a coarse Digital Terrain Model used by a specific Numerical Weather Prediction model)
  • Pressure levels, measured in hectoPascals (which have the same numerical values as milliBars)
  • Potential Temperature levels (the potential temperature of a parcel of air is the temperature it would be if brought down to the surface or a standard pressure level, using the adiabatic gas laws)
  • Isopycnic levels below the sea surface, where the coordinate is density. This is useful because both temperature and salinity affect density.
  • Sigma levels, which are the pressure level values normalised by the surface pressure, in the range (0,1), with 1 at the surface and 0 at the top of the atmosphere.
  • Oceanographic sigma levels, which may be normalised density values.
  • Hybrid sigma levels (sometimes called eta levels), which are linear combinations of sigma and scaled altitude.
  • etc
3. The key feature of many of these CRSs is that the datum from which the coordinate is measured is itself a 2 dimensional near-horizontal field or coverage, which can also be time varying. In some domains, such as avation, these datums are tightly controlled and have to be updated very regularly every few hours and when moving to a different geographical region.

4. Extracts from the WMO Manual on Codes

4.1 Grib Edition 1 uses a single octet (0-255) to indicate a Vertical CRS type listed in Code Table 3:

01 Ground or water surface
02 Cloud base level
03 Level of cloud tops
04 Level of 0°C isotherm
05 Level of adiabatic condensation lifted from the surface
06 Maximum wind level
07 Tropopause
08 Nominal top of atmosphere
09 Sea bottom
20 Isothermal level, Temperature in 1/100 K
100 Isobaric surface, Pressure in hPa
101 Layer between two isobaric surfaces, Pressure of top in kPa, Pressure of bottom in kPa
102 Mean Sea Level
103 Specified altitude above Mean Sea Level, in metres
104 Layer between two specified altitudes above mean sea level, Altitude of top in hm, Altitude of bottom in hm
105 Specified height level above ground, in metres
106 Layer between two specified height levels above ground, Height of top in hm, Height of bottom in hm
107 Sigma level, value in 1/10 000
108 Layer between two sigma levels, Sigma value of top in 1/100, Sigma value of bottom in 1/100
109 Hybrid level, Level number
110 Layer between two hybrid levels, Level number of top, Level number of bottom
111 Depth below land surface, in centimetres
112 Layer between two depths below land, Depth of upper surface in cm, Depth of lower surface surface in cm
113 Isentropic (theta) level, Potential temperature in K
114 Layer between two isentropic levels, 475 K minus theta of top in K, 475 K minus theta of bottom in K
115 Level at specified pressure difference, Pressure difference in hPa from ground to level
116 Layer between two levels at specified pressure differences from ground to level, Pressure difference from ground to top level in hPa, Pressure difference from ground to to bottom level in hPa
117 Potential vorticity surface, in 10–9K m2 kg–1 s–1
119 ETA level, ETA value in 1/10000
120 Layer between two ETA levels, ETA value at top of layer in 1/100, ETA value at bottom of layer in 1/100
121 Layer between two isobaric surfaces (high precision), 1100 hPa minus pressure of top in hPa, 1100 hPa minus pressure of bottom in hPa

4.2 Review of above. Four types identified:
4.2.1 Single levels, though some are not easily defined
4.2.2 Multiple levels, each identified by a single coordinate value
4.2.3 Multiple layers, each identified by two coordinate values, each layer assumed to be relatively homogeneous
4.2.4 Single layer encompassing a significant depth or height

4.3 Grib Edition 2

Notes
(1) Coordinate values are intended to document the vertical discretization associated with model data on hybrid coordinate vertical levels. A number of zero in octets 6-7 indicates that no such values are present. Otherwise the number corresponds to the whole set of values.
(2) Hybrid systems, in this context, employ a means of representing vertical coordinates in terms of a mathematical combination of pressure and sigma coordinates. When used in conjunction with a surface pressure field and an appropriate mathematical expression, the vertical coordinate parameters may be used to interpret the hybrid vertical coordinate.
(3) Hybrid coordinate values, if present, should be encoded in IEEE 32-bit floating point format. They are intended to be encoded as pairs.
(4) Two distinct pressure-based hybrid coordinate formulations can be expressed in GRIB Edition 2. If the hybrid coordinate being used is based on pressure, then level type 105 (Code table 4.5) shall be used to specify the vertical level type. If the formulation is based on the natural logarithm of pressure then level type 113 (Code table 4.5) shall be used. In both cases Notes 1 to 3 (above) apply fully.
(5) In the case of a generalized vertical height coordinate (fixed surface type 150), no pairs of coordinate values follow after the template, but six sets of additional information (each 4 octets long and encoded in IEEE 32-bit floating point format) follow, starting with the number of vertical levels and the identification number of the used vertical system in the additional GRIB2 message with the 3D vertical system. This identification number together with an UUID (Universally Unique IDentifier) in four parts allows a unique identification of the grid.
[xx+1]–[xx+4] Number of vertical levels
[xx+5]–[xx+8] Identification number of 3D vertical grid GRIB2 message (defined by originating centre)
[xx+9]–[xx+12] UUID part 1 of 4
[xx+13]–[xx+16] UUID part 2 of 4
[xx+17]–[xx+20] UUID part 3 of 4
[xx+21]–[xx+24] UUID part 4 of 4

Grid definition template 3.1000 – cross-section grid with points equally spaced on the horizontal

61–62 Number of vertical points
63 Physical meaning of vertical coordinate (see Code table 3.15)
64 Vertical dimension coordinate values definition (see Code table 3.21)
65–66 NC–number of coefficients or values used to specify vertical coordinates
67–(66+NCx4) Coefficients to define vertical dimension coordinate values in functional form, or the explicit coordinate values (IEEE 32-bit floating-point values)

Grid definition template 3.1200 – time section grid

39 Physical meaning of vertical coordinate (see Code table 3.15)
40 Vertical dimension coordinate values definition (see Code table 3.21)
41–42 NC–number of coefficients or values used to specify vertical coordinates
43–(42+NCx4) Coefficients to define vertical dimension coordinate values in functional form, or the explicit coordinate values (IEEE 32-bit floating-point values)

Product definition template 4.0 – analysis or forecast at a horizontal level or in a horizontal layer at a point in time
Product definition template 4.1 – individual ensemble forecast, control and perturbed, at a horizontal level or in a horizontal layer at a point in time
Product definition template 4.2 – derived forecasts based on all ensemble members at a horizontal level or in a horizontal layer at a point in time
Product definition template 4.3 – derived forecasts based on a cluster of ensemble members over a rectangular area at a horizontal level or in a horizontal layer at a point in time
Product definition template 4.4 – derived forecasts based on a cluster of ensemble members over a circular area at a horizontal level or in a horizontal layer at a point in time
Product definition template 4.5 – probability forecasts at a horizontal level or in a horizontal layer at a point in time
Product definition template 4.6 – percentile forecasts at a horizontal level or in a horizontal layer at a point in time
Product definition template 4.7 – analysis or forecast error at a horizontal level or in a horizontal layer at a point in time
Product definition template 4.8 – average, accumulation and/or extreme values or other statistically processed values at a horizontal level or in a horizontal layer in a continuous or non-continuous time interval
Product definition template 4.9 – probability forecasts at a horizontal level or in a horizontal layer in a continuous or non-continuous time interval
Product definition template 4.10 – percentile forecasts at a horizontal level or in a horizontal layer in a continuous or non-continuous time interval
Product definition template 4.11 – individual ensemble forecast, control and perturbed, at a horizontal level or in a horizontal layer in a continuous or non-continuous time interval
Product definition template 4.12 – derived forecasts based on all ensemble members at a horizontal level or in a horizontal layer in a continuous or non-continuous time interval
Product definition template 4.13 – derived forecasts based on a cluster of ensemble members over a rectangular area at a horizontal level or in a horizontal layer in a continuous or non-continuous time interval
Product definition template 4.14 – derived forecasts based on a cluster of ensemble members over a circular area at a horizontal level or in a horizontal layer in a continuous or non-continuous time interval
Product definition template 4.15 – average, accumulation, extreme values, or other statistically processed values over a spatial area at a horizontal level or in a horizontal layer at a point in time
Product definition template 4.40 – analysis or forecast at a horizontal level or in a horizontal layer at a point in time for atmospheric chemical constituents
Product definition template 4.41 – individual ensemble forecast, control and perturbed, at a horizontal level or in a horizontal layer at a point in time for atmospheric chemical constituents
Product definition template 4.42 – average, accumulation, and/or extreme values or other statistically processed values at a horizontal level or in a horizontal layer in a continuous or non-continuous time interval for atmospheric chemical constituents
Product definition template 4.43 – individual ensemble forecast, control and perturbed, at a horizontal level or in a horizontal layer in a continuous or non-continuous time interval for atmospheric chemical constituents
Product definition template 4.44 – analysis or forecast at a horizontal level or in a horizontal layer at a point in time for aerosol
Product definition template 4.45 – individual ensemble forecast, control and perturbed, at a horizontal level or in a horizontal layer at a point in time for aerosol
Product definition template 4.46 – average, accumulation, and/or extreme values or other statistically processed values at a horizontal level or in a horizontal layer in a continuous or non-continuous time interval for aerosolProduct definition template 4.47 – individual ensemble forecast, control and perturbed, at a horizontal level or in a horizontal layer in a continuous or non-continuous time interval for aerosolProduct definition template 4.48 – analysis or forecast at a horizontal level or in a horizontal layer at a point in time for optical properties of aerosol
Product definition template 4.51 – categorical forecasts at a horizontal level or in a horizontal layer at a point in time
Product definition template 4.53 – partitioned parameters at a horizontal level or in a horizontal layer at a point in time
Product definition template 4.54 – individual ensemble forecast, control and perturbed, at a horizontal level or in a horizontal layer at a point in time for partitioned parameters
Product definition template 4.91 – categorical forecasts at a horizontal level or in a horizontal layer in a continuous or non-continuous time interval
Product definition template 4.1100 – Hovmφller-type grid with no averaging or other statistical processing
Product definition template 4.1101 – Hovmφller-type grid with averaging or other statistical processing

+1 Type of first fixed surface (see Code table 4.5)
+2 Scale factor of first fixed surface
+3-7 Scaled value of first fixed surface
+8 Type of second fixed surface (see Code table 4.5)
+9 Scale factor of second fixed surface
+10-13 Scaled value of second fixedsurface

Code table 3.15 – Physical meaning of vertical coordinate

20 Temperature K
100 Pressure Pa
101 Pressure deviation from mean sea level Pa
102 Altitude above mean sea level m
103 Height above ground (see Note 1) m
104 Sigma coordinate
105 Hybrid coordinate
106 Depth below land surface m
107 Potential temperature (theta) K
108 Pressure deviation from ground to level Pa
109 Potential vorticity K m–2 kg–1 s–1
110 Geometrical height m
111 Eta coordinate (see Note 2)
112 Geopotential height gpm
113 Logarithmic hybrid coordinate 160 Depth below sea level m
Notes:
(1) Negative values associated to this coordinate will indicate depth below ground surface. If values are all below surface, use of entry 106 is recommended, with positive coordinate values instead.
(2) The Eta vertical coordinate system involves normalizing the pressure at some point on a specific level by the mean sea level pressure at that point.

Code table 3.21 – Vertical dimension coordinate values definition
0 Explicit coordinate values set
1 Linear coordinates
f(1) = C1
f(n) = f(n–1) + C2
11 Geometric coordinates
f(1) = C1
f(n) = C2 Χ f(n–1)

Code table 4.5 – Fixed surface types and units
1 Ground or water surface –
2 Cloud base level –
3 Level of cloud tops –
4 Level of 0°C isotherm –
5 Level of adiabatic condensation lifted from the surface –
6 Maximum wind level –
7 Tropopause –
8 Nominal top of the atmosphere –
9 Sea bottom –
10 Entire atmosphere –
11 Cumulonimbus (CB) base m
12 Cumulonimbus (CB) top m
20 Isothermal level K
100 Isobaric surface Pa
101 Mean sea level
102 Specific altitude above mean sea level m
103 Specified height level above ground m
104 Sigma level “sigma” value
105 Hybrid level –
106 Depth below land surface m
107 Isentropic (theta) level K
108 Level at specified pressure difference from ground to level Pa
109 Potential vorticity surface K m2 kg–1 s–1
111 Eta level –
113 Logarithmic hybrid level
114 Snow level Numeric
117 Mixed layer depth m
118 Hybrid height level –
119 Hybrid pressure level –
150 Generalized vertical height coordinate (see Note 5)
160 Depth below sea level m
161 Depth below water surface m
162 Lake or river bottom –
163 Bottom of sediment layer –
164 Bottom of thermally active sediment layer –
165 Bottom of sediment layer penetrated by thermal wave –
166 Mixing layer –

Notes:
(1) The Eta vertical coordinate system involves normalizing the pressure at some point on a specific level by the mean sea level pressure at that point.
(2) Hybrid height level (Code figure 118) can be defined as:
z(k) = A(k) + B(k) x orog(k = 1,...,NLevels; orog = orography; z(k) = height in metres at level k)
(3) Hybrid pressure level, for which Code figure 119 shall be used instead of 105, can be defined as:
p(k) = A(k) + B(k) x sp
(k = 1,...,NLevels; sp = surface pressure; p(k) = pressure at level k)
(4) Ice internal pressure or stress (Pa m) is the integrated pressure across the vertical thickness of a layer of ice. It is produced when concentrated ice reacts to external forces such as wind and ocean currents.
(5) The definition of a generalized vertical height coordinate implies the absence of coordinate values in Section 4 but the presence of an external 3D-GRIB message that specifies the height of every model grid point in metres (see Notes to Section 4 in the section above entitled Specification of Octet Contents), i.e., this GRIB message will
contain the field with discipline = 0, category = 3, parameter = 6 (Geometric height).

Code table 4.216 – Elevation of snow-covered terrain
0–90 Elevation in increments of 100 m
254 Clouds
255 Missing

5. Datums (I know it sounds awful, but writing 'data' does not help either)

DIGEST (DIgital Geographic Exchange STandard) was a defence defined (DIGWG) set of geospatial standards.This is a list of the kinds of vertical datums allowed in DIGEST and Jason Smith believes it is set up to build tables that list all the vertical datums, their assigned codes in DIGEST, and the related ellipsoids or gravity models.

The DIGEST Datum Codes provide the extensive list of datums, both vertical and horizontal, which were supported by the Digital Geographic Information Exchange Standard (DIGEST) published by the Defense Geospatial Information Working Group (DGIWG) (formerly known as the Digital Geographic Information Working Group). Though the DIGEST standard is no longer actively supported, it is still maintained as a reference by the DGIWG, and provides a wealth of information regarding datums used within the international community. The list of datums, provided hereafter, are taken from the datum code listings provided in section 6.2 of DIGEST Part 3: Codes and Parameters, Edition 2.1 published in September 2000.

The following table provides the allowable datums and their codes as assigned under DIGEST. Details of the transformations between most of these datums and WGS84 can be found in DMA Technical Report 8350.2.

In some cases, a geodetic datum with a 3-letter code is followed by a sub-list of 4-letter codes referring to the same datum but specifying particular regions. The 4-letter codes are not different datums, but “regional” solutions to the datum. Regional solutions represent regional variations in the datum’s relationship with WGS84 (arising from regional distortions in the datum). Use of the 4-letter code was recommended by DIGEST only when there was a need to specifically identify that relationship.

Unless otherwise indicated at the end of the datum name, the Zero Meridian is always Greenwich. Datums with a zero meridian other than Greenwich have “1” as a fourth character in the data code.

To assist the process of matching ellipsoids to datums, ellipsoid names are shown in the final column of the table.

Note that DIGEST distinguished between Geodetic Datums and Sounding Datums, but both categories represent vertical datums used in the geospatial information community. Also, note that each horizontal datum in this table can also be used as a vertical datum, but only in the case where the ellipsoid is the surface from which elevation is measured.

-- ChrisLittle - 20 Nov 2014
Topic revision: r3 - 20 Nov 2014, ChrisLittle
 

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