SSS06, Sestroretsk, June 12 - 17, 2006

Test cases for NH effects

Rein RoomTartu University, Estonia

Rein.Room@ut.ee

1

1 Presentation Subject

NH effects in dynamics

Test sites

Testing principles

Orographic test cases

Convection test examples

1

2 NH effects in dynamics

NH effects are distinguished by the ampli-tude of vertical accelerationWhen horizontal resolution becomes large enough:

∆x, ∆y < 10 km

then vertical acceleration should not be omit-ted:

1 +1

gρ

∂p

∂z= 0 ⇒ 1 +

1

gρ

∂p

∂z= −

dw/dt

g= −ε.

2

How large can become the smallquantity

ε =dw/dt

g?

How large it must be for NHquality emerging?Can ε be treated as the char-acteristic of NH nature of dy-namics at all?

3

In the atmosphere of Earth, twophenomena are recognized as gen-erators of NH behaviour:

Convection (thermally forced)

Orographic flow

4

Local convection at very short scales ∆x,∆y

∼ 100 m (< 1 km)

1

g

dw

dt∼ 0.001−0.1

dw

dt∼ w

∂w

∂z∼

(∆w)2

∆z

∆w ∼ 1 − 10 m/s ,

∆z ∼ 100m

∆ Z

∆ Z

5

Orographic flow at short scales

∆x,∆y ∼ 3 km (< 10 km)

1

g

dw

dt∼ (<) 0.01

dw

dt∼ U

∆w

∆x, ∆w ∼

U∆z

∆x

⇒dw

dt∼

U2∆z

∆x2

U ∼ 10 m/s ,

∆x = ∆z = 1 km

XZ

U

∆∆

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Thus,

(1) In convective events, NH effects become

actual at horizontal resolutions ∆x ∼ 100 m

(at resolutions which do resolve vertical con-

vection )

(2) In orographic flow case, departure from

HS state (in vertical momentum equation) is

very small yet it does causes NH quality of

flow from resolutions ∆x < 5 - 10 km

7

The NH effect manifests itself in differentbehaviour of buoyancy waves in comparisonwith HS case.

Vertical acceleration finiteness causes signif-icant changes in group speed direction andmagnitude of waves.

The wave amplitude changes,the wave pattern becomes rather different,the wave drag modifies essentially.

All this happens at ε ∼ 10−3already.

8

NH effect in orographic flow

HS NH0

200

400

600

800

1000-30 -20 -10 0 10 20 30

Pre

ssure

(hP

a)

X (km)

0

200

400

600

800

1000-30 -20 -10 0 10 20 30

Pre

ssure

(hP

a)

X (km)

Vertical velocity isolines (∆w = 10 cm/s) for stationary flow over an

isolated 1D hill (ridge) with ax = 2.5 km and h = 250 m.

T = const., U = 15 m/s (ε = 10−3)

9

3 SRNWP Test Site

http://www.mmm.ucar.edu/projects/srnwp tests/

This test site was proposed at the SRNWP (Short Range Nu-

merical Weather Prediction) workshop in Bad Orb, Germany,

27-29 October 2003, and it was then developed by:

W. Skamarock (NCAR), B. Doyle (ONR) , P. Clark and N.

Wood (MetOffice).

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4 Main principles

Main principles as formulated at SRNWP site:

(1) Tests should be easy to configure

(2) Tests should be easy to evaluate

(3) Tests should require only minimal physics(dissipation, very simple moist physics)

(4) Tests should test something in the solver

(5) Test set should be a minimal set

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The SRNWP test-site includes:

(1) Inertia gravity waves in a periodic channel

(2) Density Current

(3) Resting atmosphere

(4) Potential flow over a mountain

(5) 2-D mountain waves (hydrostatic and nonhydrostatic, lin-ear and nonlinear)

(6) 3-D mountain waves

(7) Schar test case

(8) Squall lines and/or supercells?

================Legend: Red: Existing NH testsBlue: Other existing tests Black: Wanted tests

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5 Terrain Forced Flow Test-caseThe differences in buoyancy wave properties is themost outstanding feature which makes NH dynam-ics different from HS primitive equation model dy-namics, For NH testing, orographic flows are mostsalient at 1 - 10 km resolutions

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The buoyancy wave properties of the model are not easy to observe andmeasure in real conditions.

Examples of observed NH wave fields

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Vorticity street behind Guadeloupe is-land

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The main idea of (NH) model testing based onterrain forced flow modelling

For given orography, wind and temperature distri-bution,

in linear flow regime, the numerical model is rununtil (quasi) stationary state is achieved.

16

Results are compared to exact linear stationary so-lution with the same orography, wind and temper-ature.

Coincidence is looked for macro-parameters of thewave pattern like the amplitude, phase, wave-length.

No line-to-line coincidence is looked for. (WHY?)

The linear stationary reference model must be aNH scheme of guaranteed (high) quality (exact so-lution)

17

Fortes/Strong points:

Overall debugging facilityIn addition to the main purpose (NHquality testing):– Check and testing of specific details of numeri-cal scheme (spectral smoothing, decentering, time-(Asselin-)averaging, boundary relaxation scheme )

– Testing of spatial discretization and time step sizeeffects onto model accuracy)

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Weaknesses:

– Transient flow regimes are not acces-sible

– Nonlinear effects are not accessible(Not as serious deficiency, however, as it may be expected ten-

tatively ...)

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6 Test Experiment Componets

1. Orography

2. Reference atmosphere - wind V(z) and temper-ature T (z)

3. Exact linear reference solution

4. Non-linear numerical research model (testing sub-ject)

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Orography 1. Witch of Agnesi

-0.05

0

0.05

0.1

0.15

0.2

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

h, k

m

x, km

1D Witch of Agnesi

a= 0.5 km, h= 100 m

a = 1a = 1.5

h(x, y) =h0

[1 + (x/ax)2 + (y/ay)2]α, α =

{

1.5 (1D),1.0 (2D)

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1D Witch of Agnesi

ax= 0.5 km, h= 100 m

-3-2

-1 0

1 2

3x, km

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

y, km

0

0.1

0.2

h, km

2D Witch of Agnesi

ax= 0.5 km, ay=0.5 km h= 200 m

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2x, km

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

y, km

-0.05 0

0.05 0.1

0.15 0.2

h, km

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Schar orography

h(x) = h0 exp[−(x/ax)2]cos2(πx/λ)

-0.05 0

0.05 0.1

0.15 0.2

0.25 0.3

-10 -5 0 5 10

h, k

m

x, km

1D Schaer profile

a= 5 km, h= 250 mλ = 4 km

1D Schaer profile

-10 -5 0 5 10x, km -10 -5 0 5 10y, km

0 0.1 0.2 0.3h, km

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Linear ”exact”test solutionsInitially (including the SRNWP test-site), the analytical so-lution of NH buoyancy-wave equation with constant T and Uwas applied.

For recent tests of NH HIRLAM, a special numerical solutionalgorithm of the linear semi-implicit semi-Lagrangian (option-ally Eulerian) stationary equations with arbitrary numericalresolution has been developed (Zirk and Room).

24

0

200

400

600

800

1000 100 200 300

Pre

ssur

e (h

Pa)

T (K)

T1

T2 T3

T4

(a) T

0.005 0.015 0.025

N, 1/s

T1

T2 T3 T4

(b) N

0 10 20 30 40

U, m/s

U1 U2 U3

(c) U

Reference profiles of height(pressure)-dependent tem-perature T (p) , Brunt-Vaisala frequency N(p) andwind U(p), used in model experiments.

T4 and U3 are proposed by Bouttier and were first used in

NH ALADIN - HIRLAM comparisons

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Example of an exact linear solution:vertical velocity waves in stratified atmosphere withwind shear

260220

T

4020

U

Reference temperature and windZ, km 25

0

5

10

15

20

γ=8.0

γ=4.5

T, K U, m/s

K/km

K/km

0

5

10

15

20

25

30

0 100 200 300 400 500 600 700

Z, km

X , km

w: D=0.05m/s; h=100 m,ax= 3 km,dx=.55km, M=400,dz=100m

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7 Examples of orographic test-ing

NH SISL ALADIN - NH SI Eulerian HIRLAM comparison

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

heig

ht (

km)

vertical wind (m/s) Aladin-NH dx=500m T=6h - expI

-4.75

-4.25

-3.75

-3.25

-2.75

-2.25

-1.75

-1.25

-0.75

-0.25

0.25

0.75

1.25

1.75

2.25

2.75

3.25

3.75

4.25

4.75

5.25

5.75

6.25

6.75

6.932

20 40 60 80 100 120

x-position (km)

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

heig

ht (

km)

vertical wind (m/s) Hirlam-NH dx=550m dt=7s width=3km - expD

-4.75

-4.25

-3.75

-3.25

-2.75

-2.25

-1.75

-1.25

-0.75

-0.25

0.25

0.75

1.25

1.75

2.25

2.75

3.25

3.75

4.25

4.75

5.044

20 40 60 80 100 120

x-position (km)

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Example of 2-D NH mountain wave modelling from SRNWP test-site

WRF - Weather Research and Forecasting Model (NCAR+NCEP)

ARW - Advanced Research WRF

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Testing NH HIRLAM: SISL

260220

T

600

0

1000

800

400

200

4020

U

U, m/sT, Kp,hPa

Reference temperature and wind

K/km

K/km

γ=4.5

γ=8.0

0

200

400

600

800

10000 20 40 60 80 100 120 140

p, h

Pa

X, km

HIRLAM, Vz: D(Vz)=0.05m/s,ax=3km, h=100m, MLEV=100,dx=.55km,dt=30s,600 steps

The linear reference solution

260220

T

600

0

1000

800

400

200

4020

U

U, m/sT, Kp,hPa

Reference temperature and wind

K/km

K/km

γ=4.5

γ=8.0

0

200

400

600

800

10000 20 40 60 80 100 120 140

p, h

Pa

X, km

Vz: D(Vz)=0.05m/s; U,T-HIRLAM,h=100m,ax= 3km,dx=.55km,MLEV=200,dz=100m

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Testing NH HIRLAM: ε = 0

260220

T

600

0

1000

800

400

200

4020

U

U, m/sT, Kp,hPa

Reference temperature and wind

K/km

K/km

γ=4.5

γ=8.0

0

200

400

600

800

10000 20 40 60 80 100 120 140

p, h

Pa

X, km

HIRLAM, Vz: D(Vz)=0.05m/s,ax=3km, h=100m, MLEV=100,dx=.55km,dt=30s,600 steps

Testing NH HIRLAM: ε = 0.05

260220

T

600

0

1000

800

400

200

4020

U

U, m/sT, Kp,hPa

Reference temperature and wind

K/km

K/km

γ=4.5

γ=8.0

0

200

400

600

800

10000 20 40 60 80 100 120 140

Pre

ssur

e (

hPa)

X (km)

30

NH SISL HIRLAM

15

10

5

0

-5

-10

-15

302520151050-5

Y (k

m)

X (km)

HS SISL HIRLAM

15

10

5

0

-5

-10

-15

302520151050-5

Y (k

m)

X (km)

LINEAR MODEL

-15

-10

-5

0

5

10

15

-5 0 5 10 15 20 25 30

Y (k

m)

X (km)

Vertical velocity waves at Z =

500 hPa. Mountain: h0 = 250 m,

ax = ay = 2.5 km. Increasing with

height N , constant U = 25 m/s . Con-

tour intervals: ∆w = 0.1 m/s. Grid

276× 100× 62, ∆x = ∆y = 550 m

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Example from SRNWP test-site with Schar profile

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NH SISL HIRLAM0

200

400

600

800

1000100806040200

Pres

sure

(hPa

)

X (km)

LINEAR MODEL0

200

400

600

800

10000 20 40 60 80 100

Pres

sure

(hPa

)

X (km)

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Conclusions to orographic test-ing1. The orographic (terrain forced) flow in linearregime is the best test case of NH effect at reso-lutions 1 - 10 km

2. Semi-elastic SISL HIRLAM resolves NH dynam-ics properly.

3. In general, numerical NH models have still enoughdevelopment space in fine detail capturing

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8 Convection tests

Modeling of cold bubble sinking was carried out byJan Masek, Slovak Hydrometeorological Institute,using 2D NH and HS models (both derived fromNH ALADIN)Though this experiment is not a full-scale test case(due to lack of ’exact’ reference solution), it presentsa good example of differenct NH/HS convection han-dling and can be used for model intercomparisons.

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Initial state

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1. Shallow convection, ∆x = 1 km

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1. Deep convection, ∆x = 1 km

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1. Shallow convection, ∆x = 0.1 km

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Conclusions to convection tests1. At shorter scales, ∆x < 1 km, convection mod-elling becomes more appropriate for NH effect study.

2.The NH effect in dynamics is really strong at hor-izontal resolutions ∼ 100 m.

3. High-presision reference solutions are still wantedin convection modeling experiments.

4. In general, numerical NH models have still enoughdevelopment space in fine detail presentation.

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THE END

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