PCM vertical coordinate - Revision history

Emillour at 08:50, 23 January 2026

2026-01-23T08:50:41Z

Emillour at 15:07, 21 August 2025

2025-08-21T15:07:06Z

Emillour at 14:58, 21 August 2025

2025-08-21T14:58:34Z

Emillour at 09:31, 6 March 2025

2025-03-06T09:31:19Z

Emillour at 17:12, 5 March 2025

2025-03-05T17:12:54Z

Emillour at 09:48, 5 March 2025

2025-03-05T09:48:20Z

Emillour: Created page with "== Overview == The PCM vertical coordinate, also called "model levels" is rather specific in the PCM and typically consists of hybrid "sigma-pressure" coordinates. === sigma..."

2025-03-05T09:23:09Z

Created page with "== Overview == The PCM vertical coordinate, also called "model levels" is rather specific in the PCM and typically consists of hybrid "sigma-pressure" coordinates. === sigma..."

New page

== Overview ==
The PCM vertical coordinate, also called "model levels" is rather specific in the PCM and typically consists of hybrid "sigma-pressure" coordinates.

=== sigma coordinates ===

=== hybrid sima pressure coordinates ===

== in practice ==
Information about the vertical coordinate is only partially stored in the PCM dynamics start files

[[Category:Generic-Model]]
[[Category:Mars-Model]]
[[Category:Venus-Model]]
[[Category:Titan-Model]]
[[Category:Pluto-Model]]

@@ Line 29: / Line 29: @@
   hybrid=.true.
 </pre>
-If $$hybrid$$ is set to $$.false.$$ the generated model levels will be purely sigma levels, i.e. the $$ap()$$ coefficients will be zero.
+If $$hybrid$$ is set to $$.false.$$ the generated model levels will be purely sigma levels, i.e. the $$ap()$$ coefficients will be zero. If running a simulation without any topography it is recommended to stick to purely sigma levels.
 You can check out the code where this is done, in the ''disvert_noterre'' routine: https://trac.lmd.jussieu.fr/Planeto/browser/trunk/LMDZ.COMMON/libf/dyn3d_common/disvert_noterre.F and/or its "mirror" version in the dynamico-LMDZ interface ''disvert_icosa_lmdz'' https://trac.lmd.jussieu.fr/Planeto/browser/trunk/ICOSA_LMDZ/src/disvert_icosa_lmdz.f90

@@ Line 6: / Line 6: @@
 \end{align}
 $$
-Where $$ap(k)$$ and $$bp(k)$$ are respectively hybrid pressure and hybrid sigma coefficients (note that $$ap()$$ and $$bp()$$ are time-independent) and $$Ps(t)$$ is surface pressure (and typically varies with time).
+Where $$ap(k)$$ and $$bp(k)$$ are respectively hybrid pressure and hybrid sigma coefficients. Note that $$ap()$$ and $$bp()$$ are time-independent and $$Ps(t)$$ is surface pressure (which typically varies with time).
 === sigma coordinates ===

@@ Line 9: / Line 9: @@
 === sigma coordinates ===
-If in the general equation above one sets $$ap(k)=0$$ for all $$k$$, then $$P(k,t)=bp(k).Ps(t)$$, which can be re-written as $$bp(k)=P(k,t)/Ps(t)$$, which is the expression of a "sigma" coordinate (often represented with the notation $$\Sigma=P/Ps$$). In case of a hydrostatic system, pressure monotonically decreases with altitude and thus "sigma" is indeed a coordinate, which monotonically decreases from 1 at the surface (where $$P=P_s$$) to 0 at the top of the atmosphere (where $$P=0$$). "Sigma" coordinates are also often called "terrain-following" coordinates because for given model level $$k$$ the pressure is a constant factor of the surface pressure, which to first order depends on the topography.
+If in the general equation above one sets $$ap(k)=0$$ for all $$k$$, then $$P(k,t)=bp(k).Ps(t)$$, which can be re-written as $$bp(k)=P(k,t)/Ps(t)$$, which is the expression of a "sigma" coordinate (often represented with the notation $$\sigma=P/Ps$$). In case of a hydrostatic system, pressure monotonically decreases with altitude and thus "sigma" is indeed a coordinate, which monotonically decreases from 1 at the surface (where $$P=P_s$$) to 0 at the top of the atmosphere (where $$P=0$$). "Sigma" coordinates are also often called "terrain-following" coordinates because for given model level $$k$$ the pressure is a constant factor of the surface pressure, which to first order depends on the topography.
 === pressure coordinates ===

@@ Line 20: / Line 20: @@
 == In practice ==
-Information about the vertical coordinate is only partially stored in the PCM dynamics start files (lon-lat or dynamico) which contain the number of atmospheric layer (llm), the ap() and bp() coefficients and the preff and pa values.
+Information about the vertical coordinate is only partially stored in the PCM (lon-lat) dynamics start files which contain the number of atmospheric layer (llm), the ap() and bp() coefficients (along with the the $$preff$$ and $$pa$$ parameters discussed below, which are in the "controle" array). Note that the DYNAMICO dynamics start file do not contain this information.
-In addition the input [[The z2sig.def Input File|z2sig.def file]] contains extra information to generate the model vertical coordinate at run time.
+In practice the vertical layer discretisation is generated at run time, using information from the input [[The z2sig.def Input File|z2sig.def file]] and a couple of related parameters : $$preff$$, reference surface pressure, (in Pa), and $$pa$$, a nameless parameter homogeneous to a pressure (also expressed in Pa) which roughly corresponds to a "reference transition pressure" from which hybrid-sigma coordinates become essentially pressure coordinates. Based on these parameters, and the specified atmospheric scale height and related target pseudo-altitudes of model levels from file [[The z2sig.def Input File|z2sig.def]] the model iteratively (requires solving a non-linear problem with no analytic solution) computes and builds the sought model levels.
-'''TODO: ADD MORE DETAILS HERE ABOUT HOW MODEL LEVELS ARE COMPUTED/GENERATED'''
+An additional input parameter that will impact on the generation of model levels is the $$hybrid$$ (logical) parameter set in [[The run.def Input File|run.def]], e.g.:
 [[Category:Generic-Model]]

@@ Line 1: / Line 1: @@
 == Overview ==
-The PCM vertical coordinate, also called "model levels" is rather specific in the PCM and typically consists of "sigma" or hybrid "sigma-pressure" coordinates. What one needs to keep in mind is that model levels are not at fixed altitude, nor in most cases at fixed pressure.
+The PCM vertical coordinate, also called "model levels" is rather specific in the PCM and typically consists of "sigma" or hybrid "sigma-pressure" coordinates. What one needs to keep in mind is that model levels are not at fixed altitude, nor in most cases at fixed pressure. The pressure $$P$$ of a model level $$k$$ at time $$t$$ is:
 === sigma coordinates ===
-=== hybrid sigma pressure coordinates ===
+=== pressure coordinates ===
 == In practice ==
@@ Line 10: / Line 23: @@
 In addition the input [[The z2sig.def Input File|z2sig.def file]] contains extra information to generate the model vertical coordinate at run time.
 [[Category:Generic-Model]]