Adaptive parameterisation scheme

An adaptive paramterisation consists of two

parts (visualised in the plate below):

Called in fraction of the time steps, grid boxes

More complex and physical

Can be called by the adaptive generalisation

Generalises the results to the full domain and

time steps

Utilises nearby intrinsic calculations

Uses temporal and spatial correlations

Intrinsic calculation of sub scale processes

Simple (statistical) adaptive generalisation

�

�

�

�

�

�

C o n c l u s i o n s & O u t l o o k

�

�

�

�

�

�

�

The poster illustrates two adaptive schemes

Adaptive spatial method

Adaptive temporal algorithm

The schemes can be over a factor two more

accurate or three times more efficient relative to

the common persistence assumption

We expect that the general idea is useful for other

parameterisations

The two schemes may be combined

More info and an article can be found on:

http://www.meteo.uni-bonn.de/

venema/themes/adaptive_parameterisations/

I n t r o d u c t i o n

Almost any geophysical dynamical model will

need parameterisations for of sub-scale pro-

cesses that take place on scales below the model

resolution. We introduce the term

for a scheme, which uses spatial and temporal

correlations in the resolved geophysical fields to

make the parameterisation computationally more

efficient.

This poster presents two adaptive radiative trans-

fer (RT) parameterisation schemes for the

COSMO numerical weather prediction (NWP)

model.

“adaptive parameterisation scheme”

Te m p o r a l a d a p t i v e s c h e m e

�

�

A simple regression scheme is used to cal-

culate the changes

If the changes become too large, a new

intrinsic calculation is performed

)()()(

)()(

tFttFttF

FtFttF

simplesimplesimple

simpleexact

���

���

�������

�����

Perturbation method:

calculate error-Estimator (� ) based on

a very simpleradiation scheme for

each grid point

apply `perturbationmethod‘ for surface-

fluxes

update 2-streamradiation-scheme

�…‘large‘

… ‘moderate‘�

Spatial local search method

�

�

�

�

�

The spatial adaptive scheme computes theradiation at the other 15 columns bysearching for similar column in the vicinity

Search region 5x5 pixels

Search algorithm minimises a similarityindex:

with, w weights, CCL: cloud cover (low

clouds), CCT: cloud cover (all clouds),

LWP: total column cloud water, : surfacealbedo, t: time

The weights were found by optimisation

The result is not sensitive to the weights

i:

�

|||||||||| 43321 twwLWPwCCTwCCLw ���������� ��

15

16

1

2

3

4

5

6

7

8

910

11

12

13

14

15

16

1

2

3

4

5

6

7

8

910

11

12

13

14

15

16

1

2

3

4

5

6

7

8

910

11

12

13

14

15

16

1

2

3

4

5

6

7

8

910

11

12

13

14

15

16

1

2

3

4

5

6

7

8

910

11

12

13

14

15

16

1

2

3

4

5

6

7

8

910

11

12

13

14

15

16

1

2

3

4

5

6

7

8

910

11

12

13

14

15

16

1

2

3

4

5

6

7

8

910

11

12

13

14

15

16

1

2

3

4

5

6

7

8

910

11

12

13

14

S p a t i a l a d a p t i v e s c h e m e

This scheme uses spatial correlations

(mainly in the cloud field)

In every 4x4 intrinsic region, one intrinsic

(2-stream RT calculation) is performed

every 5 minutes

In which column the

intrinsic calculation

is called depends

on the regular pattern

to the right

�

�

�

The two schemesThe two schemes

COSMO ModelCOSMO Model

Efficient and accurate parameterisations for radiative

transfer that utilise spatial and temporal correlations( )Effizientere und genauere Parametrisierungen für den Strahlungstransport durch Verwendung räumlicher und zeitlicher Korrelationen

Victor Venema, Annika Schomburg, Felix Ament, and Clemens SimmerVictor.Venema@uni-bonn.de -- http://www.meteo.uni-bonn.de/venema

Universität

MeteorologischesInstitut

Bonn

Adaptive parameterisation scheme

Past

Future

Medium complexparameterisation

Adaptive parameterisationscheme

Intrinsiccalculation

Adaptivegeneralisation

Request intrinsic calculation

Results intrinsic calculation

Introduction

Rad ia t i ve t r ans fe r scheme

�

�

�

�

COSMO model uses the delta 2-stream radi-

ative transfer approximation

One hour calls lead to

Physical inconsistencies (plate to the right)

Other weather prediction

The standard scheme can be called "too com-

plex", as it should be executed more often

Adaptive scheme allows the utilisation of the

2-stream method at high temporal resolution

�

�

�

�

�

Liquid and ice cloud water, cloud cover profile, gas

absorption, aerosols, ground albedo

Called once an hour

Costs 5-7 % of calculation time

COSMO-LM weather prediction model

�

�

�

�

�

�

Formerly called the Lokal Modell (LM)

Nonhydrostatic dynamical equations for:

Discretisation: horizontal resolution 2.8 km;

50 vertical layers.

Boundary conditions

from coarse resolution

global model (GME)

Case study:

19th September 2001;

12:30 h UTC

the wind vector, pressure perturbation, air temperature,

specific humidity of water vapour, cloud liquid water and

ice, and precipitation in the form of rain, snow and graupel

P h y s i c a l i n c o n s i s t e n c i e s

�

�

�

Comparison of LM runs with 2-stream

parameterisation with T = 2.5 and 60 minutes

T = 60 minutes (blue curve) leads to too much

cases with high insolation and rain at the same

time compared to the 2.5 min run (red curve)

The horizontal lines

indicate the range

from the 25 to the 75

percentile showing

that also the strength

of the relation

between rain rate and

insolation differs

��

Efficiency adaptive schemes

�

�

The RMS error of the schemes for the solar flux

(a) and the infra-red surface net flux (b) as a

function of the number of intrinsic calculations

Even with a strong reduction in the number of

intrinsic calculations, the adaptive schemes

are still quite accurate

ResultsR e c o n s t r u c t e d s o l a r f l u x

Error of the persistence assumption (g) (i.e. the solar

net flux field of 12 h) and the two adaptive schemes (h)

(i) relative to the "truth" (a), a 2-stream calculation on

the full field at 12:30 h. For comparison the liquid water

path (b) and the surface albedo (c) are shown.

Logarithcloud water

Surfacealbedo

Truesolar flux

Errorpersistence

Errortemporal

Errorspatial

Cor re l a t i ons o f t he e r ro r s

�

�

The two adaptive schemes have a shorter cor-

relation length; (a) autocorrelation function for

solar net flux, (b) idem infra-red

Work on stochastic parameterisations shows

that an error field with a weaker correlations

has less influence on the model dynamics

Adaptive temporal:RMSE:Bias: 6

43 W/mW/m

2

2

Adaptive spatial:RMSE:Bias:

31 W/m2 W/m

2

2

Persistence:RMSE: 77 W/mBias: 5 W/m

2

2

Simple RT parameter isat ion

A multiple regression algorithm is used to cal-

culate the changes in:

infra-red flux at the ground (y) and

solar transmittance (y)

�

�

���� �

N

i

ii xbay1

Main predictors solar (x)i

Cloud free Cloudy

Liquid water path

Cloud cover (low clouds)

Cloud cover (total)

Geometric thickness

Surface albedo * Aerosol

Multiple scattering * Aer.

Surface pressure

Surface albedo