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

2. 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

3. 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 exact scheme Perturbation method:

4. Simple radiation scheme: → Multivariate linear regression Predictands: – longwave: – shortwave: transmissivity: Distinction of 4 categories, with different sets of predictors: solar cloud free infrared cloud free solar cloudy infrared cloudy Scheme I (Temporal scheme)

5. 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:

6. 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

7. RMSE for 12:30: Solar

8. RMSE for 12:30: Infrared

9. Results: Improvements of model consistency 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

10. 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. solarinfrared

11. 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

12. 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

13. Thank you for your attention! For further information see also: www.meteo.uni-bonn.de/venema/themes/adaptive_parameterisations/