Difference between revisions of "GEOS-Chem vertical grids"
(Created page with "Image: Page is under construction.jpg") |
|||
Line 1: | Line 1: | ||
[[Image: Page is under construction.jpg]] | [[Image: Page is under construction.jpg]] | ||
+ | |||
+ | == Hybrid grid definition == | ||
+ | |||
+ | Earlier versions of the GMAO met data products used a pure-sigma grid definition. The problem with a sigma-grid is that you still see the signature of the mountains at the very top of the atmosphere. This was the case in GEOS-3 and this caused a lot of noise in the stratospheric winds, which led to poor STE. | ||
+ | |||
+ | The improvement on the sigma grid is the hybrid (or η) grid. This grid is defined with A and B coefficients, which are specified by the makers of the met data products (e.g. GMAO). | ||
+ | |||
+ | The following met data products use the hybrid grid formulation: | ||
+ | |||
+ | #[[GMAO GEOS-4]] | ||
+ | #[[GEOS-5|GMAO GEOS-5]] | ||
+ | #[[MERRA|GMAO MERRA]] | ||
+ | #[[MERRA-2|GMAO MERRA-2]] | ||
+ | #[[GEOS-FP|GMAO GEOS-FP]] | ||
+ | |||
+ | === Definition === | ||
+ | |||
+ | The pressure at the bottom edge of grid box <tt>(I,J,L)</tt> is defined as follows: | ||
+ | |||
+ | P<sub>edge</sub>(I,J,L) = A<sub>p</sub>(L) + [ B<sub>p</sub>(L) * P<sub>surface</sub>(I,J) ] | ||
+ | |||
+ | P<sub>center</sub>(I,J,L) = [ P<sub>edge</sub>(I,J,L) + P<sub>edge</sub>(I,J,L) ] / 2 | ||
+ | where | ||
+ | |||
+ | I,J,L are the lon, lat, level indices of the grid box | ||
+ | P<sub>surface</sub>(I,J) is the "true" surface pressure at lon,lat (I,J) | ||
+ | A<sub>p</sub>(L) has the same units as surface pressure [hPa] | ||
+ | B<sub>p</sub>(L) is a unitless constant given at level edges | ||
+ | |||
+ | The <tt>A<sub>p</sub>(L)</tt> and <tt>B<sub>p</sub>(L)</tt> for each met field type are listed in the GEOS-Chem source code file <tt>pressure_mod.f</tt>. | ||
+ | |||
+ | === The hybrid grid formula in more depth === | ||
+ | |||
+ | '''''[mailto:rb864@uowmail.edu.au Rebecca Buchholz] wrote:''''' | ||
+ | |||
+ | :I'm having trouble conceptualising exactly how GEOS-Chem deals with the vertical grid. I'm using the [[GEOS-5]] reduced vertical resolution of 47 eta levels. I've seen the [http://amsglossary.allenpress.com/glossary/search?id=eta-vertical-coordinate1 AMS definition of eta]. | ||
+ | |||
+ | :I can see the first fraction is the sigma definition (which follows terrain). Is the second fraction essentially a scaling by the pressure at altitude relative to pressure at sea surface? I'm not sure how it fits in with the GEOS-Chem definition, i.e. when rearranging the equation, what becomes A_p and B_p. | ||
+ | |||
+ | :The manual and wiki pages indicate GEOS-5 is a hybrid pressure-sigma grid. Are the first 31 levels pure sigma levels in both the reduced vertical 47 and native 72 level GEOS-5 fields? Does this mean GEOS-5 doesn't use the above eta definition of the levels - only sigma definition? Does GEOS-Chem then change the sigma levels to eta levels? | ||
+ | |||
+ | '''''[mailto:yantosca@seas.harvard.edu Bob Yantosca] replied:''''' | ||
+ | |||
+ | :Maybe we have used “eta” as a synonym for “hybrid” grid. Basically it refers to a grid that transitions smoothly from a sigma terrain-following coordinate near the surface to fixed pressure levels in the upper atmosphere. | ||
+ | |||
+ | :Older met fields (e.g. GEOS-3) came on pure-sigma grids. However, the problem is that with a pure-sigma grid, you still see some signal of the mountains even at the top of the atmosphere. This makes the upper-atmosphere winds very noisy and it messes up the strat-trop exchange. (Or so GMAO tells us.) | ||
+ | |||
+ | :The way I like to think of it is we specify the pressure at the bottom edge of grid box <tt>(I,J,L)</tt> with this formula: | ||
+ | |||
+ | Pedge(I,J,L) = Ap(L) + [ Bp(L) * Psurface(I,J) ] | ||
+ | |||
+ | :where <tt>Ap(L)</tt> and <tt>Bp(L)</tt> are specified by GMAO. Then you specify the pressures at the center of grid box <tt>(I,J,L)</tt> with this formula: | ||
+ | |||
+ | Pcenter(I,J,L) = [ Pedge(I,J,L) + Pedge(I,J,L+1) ] / 2 | ||
+ | |||
+ | :i.e. it’s an average of the pressure at both edges. | ||
+ | |||
+ | :Note that the <tt>Pedge(I,J,L)</tt> and <tt>Pcenter(I,J,L)</tt> vary w/ the topography up until about 170 hPa. That is where the first fixed-pressure levels occur. Skyward of that, then <tt>Pedge(I,J,L)</tt> and <tt>Pcenter(I,J,L)</tt> will be constant for all longitudes and latitudes <tt>(I,J)</tt>. | ||
+ | |||
+ | :Once you have computed <tt>Pedge(I,J,L)</tt> and <tt>Pcenter(I,J,L)</tt>, you can construct an ETA coordinate such as: | ||
+ | |||
+ | ETAedge(I,J,L) = [ Pedge(I,J,L) – Ptop ] / [ Psurface – Ptop ] | ||
+ | |||
+ | ETAcenter(I,J,L) = [ Pcenter(I,J,L) – Ptop ] / [ Psurface – Ptop ] | ||
+ | |||
+ | :but for the purposes of GEOS-Chem, we don’t really use the ETA values. We use the pressures computed from the <tt>Ap(L)</tt> and <tt>Bp(L)</tt> values. | ||
+ | |||
+ | :The most important thing to note is that the thicknesses of the grid boxes near the surface vary with the surface pressure. When you come to a mountain, the levels all kind of bunch together and get small. When you are over flat land or ocean, the levels widen out. | ||
+ | |||
+ | :Also note that a pure-sigma grid (like GEOS-3) can also be expressed using the same type of hybrid formulation: | ||
+ | |||
+ | Pedge(I,J,L) = Ap(L) + [ Bp(L) * ( Psurface(I,J) – PTOP ) ] | ||
+ | |||
+ | where | ||
+ | |||
+ | Ap(L) = PTOP (for all L) | ||
+ | Bp(L) = Sigma_Edge(L) = the bottom sigma edge for level L | ||
+ | |||
+ | :In <tt>GeosUtil/pressure_mod.f</tt> we use the same hybrid formula but we use the <tt>Ap(L)</tt> and <tt>Bp(L)</tt> that pertain to each grid (GEOS-3, GEOS-4, GEOS-5, GCAP, etc). That simplifies the coding. | ||
+ | |||
+ | --[[User:Bmy|Bob Y.]] 15:58, 6 April 2011 (EDT) | ||
+ | |||
+ | |||
+ | == GEOS-5, GEOS-FP, MERRA, MERRA-2 vertical grid == | ||
+ | |||
+ | == GEOS-4 vertical grid == |
Revision as of 18:12, 14 November 2016
File:Page is under construction.jpg
Contents
Hybrid grid definition
Earlier versions of the GMAO met data products used a pure-sigma grid definition. The problem with a sigma-grid is that you still see the signature of the mountains at the very top of the atmosphere. This was the case in GEOS-3 and this caused a lot of noise in the stratospheric winds, which led to poor STE.
The improvement on the sigma grid is the hybrid (or η) grid. This grid is defined with A and B coefficients, which are specified by the makers of the met data products (e.g. GMAO).
The following met data products use the hybrid grid formulation:
Definition
The pressure at the bottom edge of grid box (I,J,L) is defined as follows:
Pedge(I,J,L) = Ap(L) + [ Bp(L) * Psurface(I,J) ] Pcenter(I,J,L) = [ Pedge(I,J,L) + Pedge(I,J,L) ] / 2
where
I,J,L are the lon, lat, level indices of the grid box Psurface(I,J) is the "true" surface pressure at lon,lat (I,J) Ap(L) has the same units as surface pressure [hPa] Bp(L) is a unitless constant given at level edges
The Ap(L) and Bp(L) for each met field type are listed in the GEOS-Chem source code file pressure_mod.f.
The hybrid grid formula in more depth
Rebecca Buchholz wrote:
- I'm having trouble conceptualising exactly how GEOS-Chem deals with the vertical grid. I'm using the GEOS-5 reduced vertical resolution of 47 eta levels. I've seen the AMS definition of eta.
- I can see the first fraction is the sigma definition (which follows terrain). Is the second fraction essentially a scaling by the pressure at altitude relative to pressure at sea surface? I'm not sure how it fits in with the GEOS-Chem definition, i.e. when rearranging the equation, what becomes A_p and B_p.
- The manual and wiki pages indicate GEOS-5 is a hybrid pressure-sigma grid. Are the first 31 levels pure sigma levels in both the reduced vertical 47 and native 72 level GEOS-5 fields? Does this mean GEOS-5 doesn't use the above eta definition of the levels - only sigma definition? Does GEOS-Chem then change the sigma levels to eta levels?
Bob Yantosca replied:
- Maybe we have used “eta” as a synonym for “hybrid” grid. Basically it refers to a grid that transitions smoothly from a sigma terrain-following coordinate near the surface to fixed pressure levels in the upper atmosphere.
- Older met fields (e.g. GEOS-3) came on pure-sigma grids. However, the problem is that with a pure-sigma grid, you still see some signal of the mountains even at the top of the atmosphere. This makes the upper-atmosphere winds very noisy and it messes up the strat-trop exchange. (Or so GMAO tells us.)
- The way I like to think of it is we specify the pressure at the bottom edge of grid box (I,J,L) with this formula:
Pedge(I,J,L) = Ap(L) + [ Bp(L) * Psurface(I,J) ]
- where Ap(L) and Bp(L) are specified by GMAO. Then you specify the pressures at the center of grid box (I,J,L) with this formula:
Pcenter(I,J,L) = [ Pedge(I,J,L) + Pedge(I,J,L+1) ] / 2
- i.e. it’s an average of the pressure at both edges.
- Note that the Pedge(I,J,L) and Pcenter(I,J,L) vary w/ the topography up until about 170 hPa. That is where the first fixed-pressure levels occur. Skyward of that, then Pedge(I,J,L) and Pcenter(I,J,L) will be constant for all longitudes and latitudes (I,J).
- Once you have computed Pedge(I,J,L) and Pcenter(I,J,L), you can construct an ETA coordinate such as:
ETAedge(I,J,L) = [ Pedge(I,J,L) – Ptop ] / [ Psurface – Ptop ] ETAcenter(I,J,L) = [ Pcenter(I,J,L) – Ptop ] / [ Psurface – Ptop ]
- but for the purposes of GEOS-Chem, we don’t really use the ETA values. We use the pressures computed from the Ap(L) and Bp(L) values.
- The most important thing to note is that the thicknesses of the grid boxes near the surface vary with the surface pressure. When you come to a mountain, the levels all kind of bunch together and get small. When you are over flat land or ocean, the levels widen out.
- Also note that a pure-sigma grid (like GEOS-3) can also be expressed using the same type of hybrid formulation:
Pedge(I,J,L) = Ap(L) + [ Bp(L) * ( Psurface(I,J) – PTOP ) ]
where
Ap(L) = PTOP (for all L) Bp(L) = Sigma_Edge(L) = the bottom sigma edge for level L
- In GeosUtil/pressure_mod.f we use the same hybrid formula but we use the Ap(L) and Bp(L) that pertain to each grid (GEOS-3, GEOS-4, GEOS-5, GCAP, etc). That simplifies the coding.
--Bob Y. 15:58, 6 April 2011 (EDT)