Post on 20-Dec-2015
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/