1. Challenges in data assimilation for ‘high resolution’ numerical weather prediction (NWP) Today’s observations + uncertainty information Today’s forecast (a-priori) + uncertainty information DATA ASSIMILATION Model’s prediction of future Today’s analysis Thanks to: Stefano Migliorini (NCEO), Mark Dixon (MetO), Mike Cullen (MetO), Alison Fowler (Reading), Ruth Petrie (Reading) Ross Bannister

2. Small-scale vs large-scale weather Jul 7 2007 Oct 29 2008 ‘Convective’ precip ‘Large scale’ precip “Small-scale” “Convective-scale” “High-resolution”

3. What is required of high-resolution NWP? Forecasting of ‘extreme events’ a few hours ahead. Weather warnings and coverage of special events. Probabilistic forecasting. Data assimilation is critical to its success. MSG visible Radar Probability of rain (MOGREPS) Courtesy Met Office (c) Crown copyright Friday 26 th June 2009, 09 Z

4. What does data assimilation do? ‘Forward’ model:Known ‘state vector’, xPredicted observations, y p ‘Inverse’ model:Yet unknown state vector, x a New actual observations, y + a-priori information in the form of a forecast

5. How is the data assimilation problem tackled for operational forecasting? t = -T t = 0 ← past future → 1. Four-dimensional variational data assimilation 2. Ensemble Kalman filtering All sources of error should be accounted for: a-priori error observational error model errors unknown parameters positional errors now

6. What issues are especially important for high-resolution data assimilation?

7. / 1.5km Resolution of atmospheric models convective scale 1-10 km meso-scale 100 km synoptic scale 1000 km (c) MeteoFrance Met Office

8. Balance Geostrophic balance Hydrostatic balance H L L ρ δz g p(z+δz) p(z)

9. What is different about processes and NWP at convective scales? Global/synoptic/mesoscaleConvective scale Error growth timescale~ 3 daysFew hours FeaturesCyclones, frontsConvective storms Diagnostic relationships Hydrostatic balance, near geostrophic balance (except in tropics) Near hydrostatic balance for non- convecting regions Important quantitiesVorticity, pressure, divergence, humidity + vertical velocity, temperature, cloud water and ice, surface quantities... ObservationsAircraft, sonde, buoys, IR sounders, scatterometer, etc. + radar Other Complications Simultaneous ‘large’ and ‘small’ scale features Limited area model Lateral boundary conditions Inadequate representation of large- scale More scope to forecast features in the wrong locations (phase errors)

10. Forecast error covariances are important in data assimilation Forecast error covariances/correlations quantify the following information: the uncertainty of the forecast how information from observations is spread locally how different quantities should be adjusted together Pressure with pressure E-ward wind with pressure N-ward wind with pressure Measured correlations Correlations derived from geostrophic balance Red: positive correlation Blue: negative correlation

11. Misspecification of forecast error covariance statistics Data assimilation is suboptimal if the error covariances (uncertainty quantification) are misspecified. E.g. If Forecast or observation error uncertainties are misspecified Correlation lengthscales are wrong Balance relationships are applied inappropriately Errors are present but not accounted for in the data assimilation (e.g. model error, phase errors)

12. Phase error considerations E.g. Positional error in the height of a temperature inversion (Alison Fowler) I. Considering amplitude errors only II. Amplitude and phase errors

13. Accurate high-resolution forecasts (for a-priori) Large-scale analyses (e.g. for lateral boundary conditions) An affordable way of achieving these requirements: No. of ensembles? Higher resolution? Larger domain? Quantification of errors of all uncertain /unknown quantities in the data assimilation problem: observation error, a-priori error, model error, other errors Frequent high-resolution observations with information of relevant quantities and accurate observation operators Less balance (etc) at convective scales:  non-geostrophic,  non-hydrostatic,  non-separable,  anisotropic … More balance at convective scales (to minimize spin-up problems):  moisture balances?  anelastic balance? Ensemble of forecasts (for a-priori error characterization in ensemble Kalman filter schemes) Choice of control variables in variational schemes  appropriate degree of balance,  Include lateral boundary conditions,  new small-scale variables. How to incorporate large- scale information