# Presentation: 762452

## The Eta Model: Design, History, Performance, What Lessons have we Learned?

- <date/time>

-    Fedor Mesinger
- NCEP/EMC, and UCAR, Camp Springs, MD;
- fedor.mesinger@noaa.gov
- 15 June 2004

## Early history:

- <date/time>

- Design of the Eta ancestor code started in Belgrade, first code written beginning of 1973
-        (Notes on my code worksheets:
- 	                          started January 24, done March 2.
- In the same time period, on 7 February 1973, for the first time fcst BCs incorporated in the NMC’s first operational PE LAM, the LFM)

- Aim:  use the Arakawa approach
- •  Maintenance of chosen integral properties;
- •  Avoidance of computational modes;
- •  . . .
-                        The very first code: some of each

## Original

- flow-chart:

## Some of the features of this very first code that survive 

- 	in today’s Eta
- •  Choice of the E horizontal grid;
- •  Lateral BC scheme
- 	BCs prescribed (or, extrapolated from the inside) along a single outer line of grid points (consistent with the mathematical nature of our initial-boundary value problem)

## Some of the features of this very first code that survive 

- 	in today’s Eta
- •  Choice of the E horizontal grid;
- •  Lateral BC scheme
- 	BCs prescribed (or, extrapolated from the inside) along a single outer line of grid points (consistent with the mathematical nature of our initial-boundary value problem)

- Many milestones (see the pdf !)  A few:
- •  gravity-wave coupling scheme (Mesinger 1973,1974)
- •  E-grid enstrophy, energy conservation, “”,(Janjic 1977)
- •  Janjic (1984) Arakawa C-grid enstrophy ... conserving scheme;
- •  eta coordinate (Mesinger 1984);

- Eta dynamical core code:  Belgrade (Dushka Zupanski), GFDL,
-  NMC (1984), ....

## Why eta?

- I convinced myself (Mesinger 1982) the sigma system problem
- •  seems to have no acceptable solution;
- •  should become more serious as we increase resolution;
- Quasi-horizontal coordinates are needed !

## Operational implementation: 12z 8 June 1993,

- Back to NMC:  more milestones:
- •  physics package (Janjic, Black; acknowledgements:
- Betts-Miller, Mellor-Yamada, Harshvardhan);
- •  testing, removal of physics problems identified;
- •  analysis system (Rogers, ...)
- •  ...

- Operational implementation: 12z 8 June 1993,
- as a replacement of the LFM

## Challenges, and an inadvertent experiment:

- •  Comparisons against the NGM and the RSM;
- •  The “Early” vs the “Meso” Eta;
- •  Eta vs the Avn/GFS

## Eta vs the NGM, 1st 24 months of the Eta, NGM and Avn precip scores:

- (Both Eta and NGM ~80 km resolution, physics packages of similar/
- not too different complexity)   “All Periods”:  00-24, 12-36, 24-48 h forecasts

- Recall: NGM 4th order formal accuracy, Eta never more than 2nd

## Eta vs the RSM, 

- 2 years of scores, 1996-1997, at ~50 km resolution:

- Note:  Eta is using 12 h “old” Avn LBCs, RSM is using current Avn LBCs

## The “Early” vs the “Meso” Eta

- “Early”: 48 km, 12 h old Avn LBCs,
- “Meso”: 29 km, current Avn LBCs;

- Domains:

## 2 years of scores:

- Scores of the the “Early” and the “Meso” Eta about the same!
- The benefit of the large domain compensates the combined
- benefit of more accurate LBCs and higher resolution

## Eta vs the Avn/GFS

- 2nd 24 months of the Eta, NGM and Avn scores:

- Eta is using 12 h old LBCs; can one detect the impact of the advection of the error?

## Not at that time.  But what about today?  

- Both models have increased resolution;
- Eta has been extended to 84 h as of April 2001;
- Can one now detect the the impact of the advection of the LB error?
- (Eta is now driven by the GFS forecast of 6 h ago.  At 00 and 12z, in view
-     of the “off” times, this is considered equivalent to about an 8 h error)

- For an answer, I have looked into, Eta vs the Avn/GFS:
- •  precip scores, 24 accumulations, 00-48 h vs 36 to 84 h,
- 	 May 2001-April 2002;
- •  rms fist to raobs as a function of time;
- •  position forecast errors of “major lows” at 60 h,
- 	December 2000-February 2001

## 00-24, 12-36, 24-48 h

- Eta

- Avn

## 36-60, 48-72, 60-84 h

## “Warm Season”

- “Warm Season”

## “Cold Season”

- “Cold Season”

## In cold season, 250 mb winds, for a 6 months sample, the Eta is

- •  ~10-11 h behind the GFS at 60 h;
- •  ~9 h behind the GFS at 84 h

## Position forecast errors: winter 2000-2001, rules, 31 cases;

- •  ~10-11 h behind the GFS at 60 h;
- •  ~9 h behind the GFS at 84 h

- Position forecast errors: winter 2000-2001, rules, 31 cases;
- (see the pdf for #s)  the Eta was significantly more accurate !
- E.g.:  Average errors:  Eta 244 km, Avn 324 km
- # of wins:  Eta 20, Avn 10

## Position forecast errors: winter 2000-2001, rules, 31 cases;

- •  ~10-11 h behind the GFS at 60 h;
- •  ~9 h behind the GFS at 84 h

- Position forecast errors: winter 2000-2001, rules, 31 cases;
- (see the pdf for #s)  the Eta was significantly more accurate !
- E.g.:  Average errors:  Eta 244 km, Avn 324 km
- # of wins:  Eta 20, Avn 10

- In relative terms, the Eta is doing best in winter, and,
- if anything, it improves with time !
- Ingredient(s)/ component(s) must exist in the Eta
- that compensate for the inflow of the LB error !

##                for this role is the eta coordinate

-                for this role is the eta coordinate
- Some of the arguments:
- •  One eta/ sigma experiment;
- •  Precip scores for the 1st 12 months of the availability
- 	of three model scores on NMM domains
- 	(ConUS “East”, ..., “West”, ...)

## The experiment: Eta (left), 22 km, switched to use sigma (center),  48 h position error of a major low increased from 215 to 315 km:

## Three-model precipitation scores, 

- Three-model precipitation scores,
- on NMM ConUS domains ("East" ,..., "West"),
- available since Sep. 2002

- • Operational Eta: 12 km, driven by 6 h old GFS forecasts;
- • NMM: “Nonhydrostatic Mesoscale Model” nonhydrostatic, 8 km, most other features same or similar to Eta, but switched back to sigma, driven by the Eta;
- • GFS (Global Forecasting System) as of the end of Oct. 2002 T254 (55 km) resolution

## Slide 25

## GFS

- Eta

- NMM

- Bias normalized eq. threats

## Eta

- NMM

- GFS

- (Five very heavy el Niño precip events)

## Eta vs NMM:

- East, no major topography:  12-km Eta about the same as the 8-km NMM, even a tiny bit better;
- West, complex topography:  12-km Eta much better than the 8-km (sigma system) NMM !!
- GFS vs Eta:
- East:  GFS (when corrected for bias) uniformly better;
- West:  Eta *much* better (overcoming handicaps of  the 6 h lateral boundary error, and less successful data assimilation) !

## However: what about a lot of bad press the eta had 

- 	lately:

- Schär et al., *Mon. Wea. Rev.,* 2002;
- Janjic, *Meteor. Atmos. Phys.,* 2003;
- Steppeler et al., *Meteor. Atmos. Phys*., 2003;
- Mass et al., *Bull. Amer. Meteor. Soc*., 2003;
- Zängl, *Mon. Wea. Rev.,* 2003;
- the eta coordinate system is
- "ill suited for high resolution prediction models” ?

## The Eta Problem

- Flow separation on the lee side (à la Gallus and Klemp 2000)

## Suggested explanation

- Flow from left:  from the box 1 the flow enters box 2 to the right of it.  When conditioned to move downward, it will move downward via the interface between boxes 2 and 5.  Some of the air that entered box 2 will continue to move horizontally into box 3.
- Missing:  the flow directly from box 1 into 5 !
- (It would have existed had the discretization accounted for the terrain slope !)  As a result:  some of the air which should have moved slantwise from box 1 directly into 5 gets deflected horizontally into box 3.

## Refined (sloping steps) eta discretization

- Discretization accounting for slopes.  Continuity equation (    at      points not zero):
- 								(3)
- Effort in progress:
- Define slopes at **v** points, based on four surrounding *h* points.  Slopes discrete, valid on halves of the sides of *h* points, and halves of the eta layers. Slantwise transports calculated within the 1st term on the right of (3), and in other equations as appropriate.
- Other possibilities available.  However: keep the eta feature of having cells in horizontal of about equal volume (difference compared to shaved cells) !   This makes Arakawa-type conservation schemes, used in the Eta, approximately finite-volume schemes.  Also, robust in the CFL sense.

## The sloping steps, vertical grid

- The central **v** box exchanges momentum, on its right side, with **v** boxes of two layers:

## Horizontal treatment, 3D

- Example #1:  topography of box 1 is higher than those of 2, 3, and 4;
- “Slope 1”

- Inside the central **v** box, topography descends from the center of T1 box
- down by one layer thickness, linearly, to the centers of T2, T3 and T4

## Slantwise advection of mass, momentum, and temperature, 

- and “”:

- Velocity at the ground immediately behind the mountain increased from between
- 1 and 2, to between 7 and 8 m/s.
-  Zig-zag features in isentropes at the upslope side removed.

## Thus,

- 12-km Eta: excellent QPF performance over complex topography !  Better than the sigma system 8-km NMM, and better than the GFS;
- The Eta downslope windstorm problem: correctible, while keeping favorable Eta features:
- •  quasi horizontal coordinates (PGF !);
- •  approximately finite-volume (because of the quasi-	horizontal coordinate and flux-type schemes);
- •  robustness in the CFL sense

## “The Future of NWP”:

- Yes.  How can we tell?

- “The Future of NWP”:

## “The Future of NWP”:

- Yes.  How can we tell?
- Eta view of things:
- •  The Eta skill at NCEP – throughout its extended forecast range – is comparable to that of GFS, in spite of its handicaps of
- 1)  absorbing a 6 (or, 8) h error advected at the lateral boundaries;
- 2)  using a considerably less successful data assimilation system

- “The Future of NWP”:

## “The Future of NWP”:

- Yes.  How can we tell?
- Eta view of things:
- •  The Eta skill at NCEP – throughout its extended forecast range – is comparable to that of GFS, in spite of its handicaps of
- 1)  absorbing a 6 (or, 8) h error advected at the lateral boundaries;
- 2)  using a considerably less successful data assimilation system

- “The Future of NWP”:

- The LB error, 1), is removed by
- 	•  having a global Eta-like model, or
- 	•  running a global model and the Eta simultaneously

## At 250-300 mb, error reduced more than 10%  

- Eta rms wind fits to raobs vs same except in. cnd. interpolated from GFS

- October 2002-May 2003, 48 h fcsts:

- At 250-300 mb, error reduced more than 10%

##      Each on the order of 10% error at 48 h;  

-                             both can be removed/ improved upon !
- •  Numerous options to improve the Eta further.  Dynamical core:
- -   Sloping steps;
- -   Advection of scalars: piecewise linear, or biparabolic (Rancic);
- -   Gravity wave coupling: do momentum equation forward;
- -   Lateral boundaries: avoid space interpolation
- -    ...
- -    ...

- The two operational Eta handicaps:

- And:  discretizations still more consistent with “physics”;
-  and/or, physics that moves away from forcing at
-  individual grid points