Two adaptive radiation parameterisations Annika Schomburg 1), Victor Venema 1), Felix Ament 2), Clemens Simmer 1) 1) Department of Meteorology, University.

Two adaptive radiation parameterisations

Annika Schomburg1) , Victor Venema1), Felix Ament2), Clemens Simmer1)

1) Department of Meteorology, University of Bonn, Germany

2) MeteoSwiss, Switzerland

Introduction

• Today: accurate radiation schemes used in weather-prediction models -> computationally expensive

• Problem: radiative fluxes can not be updated at each time-step, are kept constant in between

• Well justified practice for large-scale models, where no large cloud cover changes on timescale of update interval

• Assumption of persistence is not suitable for models with a horizontal grid spacing of few kilometres

Adaptive parameterisation: Scheme I (Temporal scheme)

calculate error-estimator based on

a simple radiation scheme for

each grid point

Grid points where…

…Δ ‘large‘

…Δ ‘small‘

Apply „perturbation method“

for surface fluxes

Recalculate 3D-radiation

fluxes with exactscheme

Perturbation method:

)()(

)()(

tFttFF

FtFttFsimplesimplesimple

simple

• Simple radiation scheme:

→ Multivariate linear regression

• Predictands:

– longwave:

– shortwave: transmissivity:

• Distinction of 4 categories,

with different sets of predictors:

surL

ec

solarcloud free

infraredcloud free

solarcloudy

infraredcloudy

Scheme I (Temporal scheme)

Adaptive RT parameterisation II: Spatial Scheme

• uses spatial correlations• update every 5 minutes one

out of 4x4 columns• for other 15 columns: search

for similar column in the vicinity (search region 7x7 pixels)

• similarity index to be minimised:

twwLWPwCCTwCCLw 43321

The Model: Cosmo-LM

• Non hydrostatic• Horizontal resolution:

– Operational: 7km– Here: 2.8km

• Updating of radiation scheme once per forecast-hour

Radiation Scheme of the LM (Ritter and Geyleyn 1992)

• Delta-Two-Stream Approximation• Three intervals in the solar part of

the spectrum and five intervals in the thermal part

Model-domain

Case study: 19th September 2001,

a day characterised by much convection

"True" solar heating rate

(a)

Persistence scheme

(b)Bias: 5 W m-2RMS: 77 W m-2

Temporal perturbation scheme

(c)Bias: 6 W m-2RMS: 43 W m-2

Spatial local-search scheme

(d)Bias: 2 W m-2RMS: 31 W m-2

0

100

200

300

400

500

600

-500

0

500

-500

0

500

-500

0

500

RMSE for 12:30:

Solar

"True" infrared heating rate

(a)

Persistence scheme

(b)Bias: -1.0 W m-2RMS: 15.0 W m-2

Temporal perturbation scheme

(c)Bias: -0.3 W m-2RMS: 9.1 W m-2

Spatial local-search scheme

(d)Bias: -0.4 W m-2RMS: 6.3 W m-2

-150

-100

-50

0

-50

0

50

-50

0

50

-50

0

50

RMSE for 12:30:

Infrared

Results: Improvements of model consistency

Total surface net flux: solar + IR [W/m²]

Total surface net flux: solar + IR [W/m²]

21 June 2004

Adaptive approach leads to a considerable reduction of unrealistic situations

1h-update

2.5 min- update

Adaptive

Median and 0.25 quantiles

Median and 0.25 quantiles

RMS error as function of relative number of intrinsic calculations

The number of calls to the δ-two-stream scheme is normalised by the number of calculations for the full field once per hour. The blue dotted line denotes the spatial scheme with the weights of the standard scheme. The red line designates the spatial scheme where the weights are optimised for each number of function calls.

0.4 0.6 0.8 1 1.2

40

60

80

100

Rel. no. intrinsic calculations

RM

S e

rro

r [W

m-2

]

(a)

3x34x45x56x6

0.4 0.6 0.8 1 1.2

10

15

20

Rel. no. intrinsic calculations

RM

S e

rro

r [W

m-2

]

(b)

PersistenceTemporalSpatial - optimalSpatial - fixed

solar infrared

Conclusions

• Adaptive Schemes significantly reduce RMSE: – SW: 44% for temporal scheme, 60% for spatial

scheme – LW: 39% for temporal scheme, 58% for spatial

scheme

• Smaller correlation length of error fields• Significant reductions of exact calculations

leads only to small increases of errors– This increase in computational efficiency can be

utilised to employ more complex parameterisation schemes

Outlook

• Implement both schemes in model itself• Perform full day case studies• Other simple radiation scheme instead of

regression :– very simple physical scheme– neural network– or online learning regression

• Application to whole vertical column, not only to surface fluxes

• Combine both schemes

• Application to other parts of model physics

Thank you for your attention!

For further information see also:

www.meteo.uni-bonn.de/venema/themes/adaptive_parameterisations/

Cloud cover low clouds

(a)

Total cloud cover

(b)

Liquid water path

(c)

Surface albedo

(d)

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