An Overview of the NCEP Eta Model

28 March 2000

COMET/UCAR SOO Symposium on NWP

EDAS slides by Eric Rogers

Presented by Thomas Black

EMC/Mesoscale Modeling Branch

Outline

• Brief model description

• Eta Data Assimilation System

• Physics

• Examples of products/statistics

• Future

Domain

• Semi-staggered Arakawa E grid

• 32km horizontal resolution

• 45 vertical eta layers

• Silhouette step topography

Eta Domains Past & Present

32km DomainTopography w/ Water Points

Topography w/ Water Points32km CONUS

Sigma and Eta Coordinates

MSL

zgpPGF

sfcp

p

P

ground 1

1

At point P:p

0 z

P

1

1

0ref

sfcref

p

zp

At point P:0 p

zis small

is small

ground

Eta Coordinate

Mean Sea LevelP=PMSL

Reference heights and temperatures taken from the standard atmosphere

Z= ZREF

LM=1

LM-1

LM-2

at P = LM-2 PSMSL

Z=0

LM-3

P= LM-2 PMSL

P= LM-3 PMSL

P= LM-1 PMSL

at P = LM-1 PSMSL

Z= ZREF

Eta Model 45-Layer Distribution

1000 hPa

850 hPa

700 hPa

500 hPa

250 hPa

25 hPa27 hPa29

29

2726262423242630

31

32

32

32

33

33

33

33

33

32

31

29

2723211918181716141313

13131212121211 86

5 2

The Semi-Staggered E Grid

H

V

H

V

H

V

H

V

H

V

H

V

H

V

H

V

H

V

H

V

H

V

H

V

H

d

H mass point

V velocity point

d

constanttransformed

latitude

constanttransformed

longitude

GOAL : Produce best possible initial conditions for the Eta Model forecast*

• KEY COMPONENTS

- State of the art analysis (variational)

- Consistency between assimilating and forecast model (resolution, physics, dynamics)

- Intelligent selection and use of observations

* NOT necessarily the same as fitting all the observations exactly

Eta Data Assimilation System

What is 3D-VAR?

• An analysis technique that attempts to minimize analysis error

• Takes background (forecast) and observation error into account

• Variational method allows use of “non-traditional” data sources, such as GOES precipitable water

ETA 3DVAR ANALYSIS

• Loosely patterned after NCEP global SSI analysis

• Analysis variables:

- Stream function- Potential function

- Temperature- Specific humidity

- Surface pressure - Geopotential height

• More adaptable than OI for using new data types (e.g., NEXRAD radial velocities used in Eta-10 runs during 1996 Olympics)

(Parrish et al. 1996 NWP Preprint Volume)

3D-VAR vs. OI

EDAS Original Configuration Eta-48 fcst 00Z/12Z Eta-29 fcst 03Z/15Z

WHY DO CYCLING?

• Initial conditions more consistent with

• Less spinup of divergence, cloud,

• More accurate representation of soil

forecast model

precipitation, and TKE

moisture

Observations Used By ETA 3DVAR • Upper air data- Rawinsonde height/temperature/wind/moisture- Dropwindsondes- Wind Profilers- NESDIS thickness retrievals from polar orbiting satellites (oceans only)- VAD winds from NEXRAD- Aircraft (conventional and ACARS) winds/temps- Satellite cloud drift winds- SSM/I and GOES precipitable water retrievals- Synthetic tropical cyclone data

• Surface data- Surface land wind/temperature/moisture- Ships and buoys- SSM/I oceanic surface winds

DATA QUALITY CONTROL• CQC: Complex QC of raob height/temps (baseline, hydrostatic, lapse rate, radiation correction, etc.)• ACQC : Quality control of conventional aircraft data (remove duplicates, track checks, create “superobs”)

• 3DVAR : Analysis performs gross check vs. first guess:

- Temperature : +/- 15oC- Wind :+/- 25 ms-1

- RH : +/- 90%- Precipitable water : +/- 12 g/kg- Height : +/- 100 m

• SDMEDIT : NCEP Senior Duty Meteorologist can flag all or parts of suspect raobs

Use of Surface Data: Eta OI vs. Eta 3DVAR

Eta OI Analysis

Eta 3DVAR Analysis

• New 3DVAR tested in July 1998 and showed improved fit to surface and raobs (especially moisture)

• Re-tuned 3DVAR implemented on 3 November 1998

• We thought everything was OK…..

BUT……..BUT……..

Solid = Eta Short Dash = NGM Long Dash = AVN/MRF

24-H ACCUMULATED PRECIPITATION EQUITABLE THREAT SCORES: ALL FCSTS

12/1/97 - 2/28/98 12/1/98 - 2/28/99

10-15% drop in Eta skill between 1997-98 and 1998-99

Persistent synoptic error in Eta-32 during winter of 98-99: weaker and faster Eastern Pacific troughs/cyclones than observed

Example : 48-h Forecasts valid 1200 UTC 17 March 1999

PROBLEM 1: November 98 change degraded mass/wind balance in 3DVAR

• If mass / wind balance well-behaved, positive height correction is coincident with center of anticyclonic wind correction 850 mb ANL-GUESS height/wind

80KM EDAS valid 00Z 3/15/99• Note 10 degree longitude displacement between centers of wind and height correction

• Problem is most severe in regions and at analysis times without widespread raob data but with large amounts of wind or mass only data (e.g., satellite winds)

SOLUTION : Improve geostrophic coupling of mass/wind analysis corrections in 3DVAR (5/99)

Original 3DVAR analysis Improved 3DVAR analysis

Note: Improved height/wind coupling near Aleutians

PROBLEM 2: Horizontal/vertical correlations too narrow : observation had VERY limited impact on analysis away from its level

• One observation test : Insert one height observation 10 m greater than first guess at 200, 500, 900 mb and measure impact in horizontal/vertical

SOLUTION: Expand the influence of the observations (5/99)

Original 32-km 3DVAR Improved 32-km 3DVAR

200 mb

900mb

Performance of new 3DVAR : 3 December 1998 to 16 January 1999 test at 80 km resolution

24-h accumulated precipitation threat scores: All forecasts Dashed = Modified 3DVAR Solid = Operational 3DVAR

Equ

itabl

e T

hrea

t Sco

re

Threshold (in)

Split Explicit Integration: Dynamics

• Fundamental prognostic variables– T, u, v, q, Psfc, TKE, cloud water/ice

• Inertial gravity wave adjustment– forward-backward scheme (t=90s)

• Vertical advection– Euler-backward scheme– centered in space– piecewise linear for q

The Forecast Model

Split Explicit Integration: Dynamics

• Horizontal advection– modified Euler-backward scheme– Janjic advection in space– conservative, (nearly) shape-preserving

scheme for H20

– upstream advection near boundaries

Split Explicit Integration: Physics

• Betts-Miller-Janjic convection

• Mellor-Yamada level 2.5 turbulent exchange

• GFDL radiation

• explicit cloud water/ice prediction

• 4-layer NOAH land surface package

• 2 horizontal diffusion

One-way Boundary Conditions

• 3-hour tendencies

• 6 hour old AVN forecast used

Runstream Schematic of Eta Model Integration

gridscale cloudgridscale precipconvectionturbulence

horizontaladvection

verticaladvection

inertialgrv wave

adjustment

13 14 1511 1210987654321 16

timestep

t = 90 s

Radiative temperature tendency updates

Shortwave: 40 timesteps (1 hour)Longwave: 80 timesteps (2 hours)

The Betts-Miller-Janji Convection Schemein the Eta Model

References: Betts, 1986 (QJRMS) Betts and Miller, 1986 (QJRMS) Janji, 1994 (MWR)

Deep (precipitating) convection

Temperature reference profile

Moisture reference profile

Convective adjustment

Modification for “precipitation efficiency”

Shallow (non-precipitating) convectionTemperature reference profile

Moisture reference profile

Find the Deep Convective Clouds

1. For all ‘parcels’ within 0.2xPsfc mb of the ground find Psat andES

2. At each point, select parcel with the maximum ES

3. Given Psat, choose cloud base as the model level just below it

4. Adjust cloud base if needed:(a) at least 25 mb above middle of lowest layer(b) at least one model layer above lowest layer

5. Compute Tmad above cloud base using ES and P in lookup tables

6. Set cloud top at highest level where Tmad<T-T (currently T=0)

7. Gather all clouds at least 0.2xPsfc mb deep

Betts-Miller Reference Temperature Profile

Construction of 1st Guess Humidity Reference Profile

2. Linearly interpolate DSP’s for values between these 3 levels

3. Define the reference humidity profile as qsat in each layer

For Deep Convection

1. Define ‘deficit from saturation pressure’ (DSP) for cloud bottom,freezing level, and cloud top (larger DSPdrier state)

The Enthalpy Correction

Modify the profiles to ensure enthalpy in the cloud columnis conserved during adjustment

0 dpHH

top

bot

p

pmodref

)2(

)1(2(

)2(

)

ref

refref

Tq

vLpcHTT

from but before as computed ref

Tsatq

Corrections:

Initially:

Currently the above procedure is repeated two times

Final Deep Convective Adjustment

2. Convective rainfall amount is

3. At any point, deep adjustment is ignored and

1. Relax model profiles of T and q toward the reference profileswhere relaxation time equals 2400 s

oldrefcnv

oldnew TTTTt

oldrefcnv

oldnew qqt

qq

ltop

lbotloldlref

cnv pqqt

gwP

,,

a “swap” to shallow convection occurs if:

(a) S < 0(b) precipitation is negative

Deep Convective Adjustment of Temperature

cloud top

REFERENCE TEMPERATURE

Upward Transport of HeatUpward Transport of Heat

cloud base

AMBIENT TEMPERATURE

Modification for ‘Precipitation Efficiency’

So define precipitation efficiencyprecipitation efficiency as the ratio:

Numerator: Q arising from entropy change

Examination of Eta integrations shows:

As convective precipitation increases, entropy changes decrease.

pTc

STC

p

E 1

Denominator: Q arising from precipitation (H=0)

USE E TO MODERATE HEAVY RAIN

larger E less mature systemThus,

(A) Modify the humidity reference profile

smaller E more mature system

IN LONG-LIVED MATURE SYSTEMS

(B) Modify the relaxation time

Humidity Reference Profile Limits

cloud top

HUMIDITY HUMIDITY REFERENCE REFERENCE

PROFILEPROFILE

DSP’s vary between DRY (fast) and MOIST (slow) limits

cloud base

DRY PROFILE

LIMIT

MOIST PROFILE

LIMIT

E=0.2E=1

q

p

Values of DSP Limits

Dry limits

Top -1875 Pa

Freezing -5875 Pa

Bottom -3875 Pa

MOIST DSP limits equal 0.85 times DRY limits.

At t=0, DSP’s are set to the DRY limits.

Modification of Relaxation Time

OR

For simplicity assume F is linear. Then empirically:

Multiply the standard change due to adjustment by some quantity Fwhich is a function of the precipitation efficiency

oldrefcnv

oldnew TTTTt

'

)(EFqqt

qq oldrefcnv

oldnew

0.7 < F < 1.0 for 0.2 < E < 1.0

)(EFt

oldrefcnv

oldnew TTTT

oldrefcnv

oldnew qqqq t

'

where)(

'EF

Find the Shallow Convective Clouds

2. Gather all clouds that are:

(a) greater than 10 mb deep

(b) less than 0.2xPsfc mb deep

1. Find the tops of the “swapped” clouds

(a) set a preliminary top at pbot - 0.2xPsfc mb (pbot > 450 mb)

(b) reset top to level where maximum (RH)/p occurs

(c) at least two model layers deep

Construction of Temperature Reference ProfileFor Shallow Convection

cloud top

REFERENCE TEMPERATURE

cloud base

Mixing Line

bottop

bottop

pp

Correct Tref assuming (cpT p) = 0

Shallow Convection

• Moisture profile calculation

• Forces a net positive entropy change

Turbulent Exchange

References: Mellor and Yamada, 1974 (J. Atmos. Sci.) Mellor and Yamada, 1982 (Rev. Geo. Space Sci.)

Janji, 1994 (Mon. Wea. Rev.)

Vertical advection occurs through transport

Turbulent vertical diffusion of variable A is given by:

Fundamental task is to determine exchange coefficient KFundamental task is to determine exchange coefficient KAA

by resolvable vertical motion

Turbulent diffusionTurbulent diffusion occurs through transport by subgrid scale turbulent eddies

z

AK

zt

AA

Modes of Turbulent Exchange

SURFACE

free atmosphere free atmosphere

surface layersurface layer

ALM -1

ALM

Az0

LM-1

LM

z0

Exchange in the Free Atmosphere

Use second order closure scheme of Mellor-Yamada Level 2.5

Exchange coefficients for heat and momentum given by:

HH SQlK MM SQlK

l is the mixing length

Q2/2 is the turbulent kinetic energy (TKE)

SH , SM are quantities determined from MY level 2.5

TKETKE is a fully prognostic variable needed to compute exchange coefficients in the free atmosphere

The predictive relationship for TKE is:

A variety of approaches have been used to solve the production/dissipation tendency, generally with imposed limits on Q

22

22 Q

zSQl

z

Q

dt

dq Ps + Pb -

prod/dissp

Eta Model technique: Cast in terms of (l / Q)

124

24

1

1B

Q

l

Q

l

Q

l

Q

l

Q

l

t

Write in finite difference form and solve for (l / Q)

Place physical constraints on l and not on Q

Use new Q to compute new KH and KM

Exchange in the Surface Layer

Use similarity theory between the surface and the middle of the lowest layer

Vertical change of variable A is described by:

)(*

Fzk

S

z

A

S* = F/u* where F is flux, u* is friction velocity

F is a prescribed function (empirical)

= z/L where L is Monin-Obukov length

For neutral static stability or small z, 1 integration of A / z yields log profile

k is the von Karman constant (~ 0.4)

Note: L is a function of heat and momentum fluxes and thus of the exchange coefficients

Take u* and L from the previous timestep then iterate:

Replace F with the standard relationship:

12

12

zz

AAKF A

Integrate A / z for the general case between two levels:

Fku

FAA

* 12

where F is an integral function of F

Solve for KA:

L

zkuzz

K

F

A

*12

KA L KA L KA new surface exchange coefficients

Considerable application of theory and computation is needed to determine values at the lower boundary

Cloud Top Pressure

Cloud Top Temperature

Cloud Base Height

850mb Cloud Water (kg/kg)

850mb Cloud Ice (kg/kg)

Winter Precipitation Type

Area Tw > -4 C< 3000 deg m?

Coldest T in a saturated layer < 269K?

Area sfc basedTw < 0 C

< -3000 deg m?OR

Net area with respectto 0 C < -3000 deg m

and sfc based Tw > 0 C< 50 deg m?

Lowest levelT > 0 C ?

snow

freezing rain

ice pellets

rain

Y

N

Y

N

Y

N

N

Y

Example of precip type

Eta/AVN/NGM Equitable Threat Scores1 Jan - 31 Oct 1999

Impact of Fall 1999 Eta Degradation

Impact of Fall 1999 Eta Degradation

Impact of Fall 1999 Eta Degradation

Output Grid Resolution

• Be aware of the resolution of the grid being viewed

AVN Vorticity Output

24-h Eta-32 Vorticity Output : Coarse

24-h Eta-32 Vorticity Output: Fine

00-h Eta-32 Vorticity Output: Fine

Subsets (“tiles”) of 32km grid

Future Directions of Eta Effort with the Class VIII Computer

• 72-84 hours for on-time runs

• 10km/60lyr resolution

• Expanded domain

• Cloud and precipitation assimilation

• Microphysics

• 4D-VAR

• Short range ensembles

• Nonhydrostatic model

Rainfall Data Assimilation

• During the 12h pre-forecast assimilation period at each timestep compare the model predicted rainfall to observed

• Adjust the model’s latent heating profile accordingly (Carr and Baldwin, 1991)

Cloud Data Assimilation(Zhao et al, 1998, 12th NWP, Phoenix, AZ)

• Data sources– real-time Neph Analyses (USAFGWC)– hourly radar/gauge observations

Cloud Data Assimilation

• c

22km Domain / Topography

22km CONUSTopography w/ Water Points

30-h Eta-10 Rainfall Forecast

Eta Workstation Version

• Pontiac, MI running 10km– including lake temps from GLERL– other changes to the model

• NSSL/SPC running Kain-Fritsch version• Code available from NCEP: contact Matt

Pyle (mpyle@ncep.noaa.gov)• Code available from COMET: contact

Bob Rozumalski (roz@comet.ucar.edu)