Two adaptive radiation parameterisations

1. Two adaptive radiation parameterisations Annika Schomburg1) , Victor Venema1), Felix Ament2), Clemens Simmer1) 1) Department of Meteorology, University of Bonn, Germany 2) MeteoSwiss, Switzerland

2. Introduction • Today: accurate radiationschemes 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) Grid points where… Recalculate 3D-radiation fluxes with exact scheme calculate error- estimator based on a simple radiation scheme for each grid point …Δ‘large‘ …Δ ‘small‘ Apply „perturbation method“ for surface fluxes Perturbation method:

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

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 Model-domain 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 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 Median and 0.25 quantiles 1h-update 2.5 min- update Adaptive 21 June 2004 Median and 0.25 quantiles Total surface net flux: solar + IR [W/m²] Adaptive approach leads to a considerable reduction of unrealistic situations Total surface net flux: solar + IR [W/m²]

10. RMS error as function of relative number of intrinsic calculations solar infrared 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.

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/