Federal Department of Home Affairs FDHA Federal Office of Meteorology and Climatology MeteoSwiss High-resolution data assimilation in COSMO: Status and plans Daniel Leuenberger MeteoSwiss, Zürich, Switzerland Swiss COSMO User Workshop 16 December 2010, ETH Zurich

2 COSMO Data Assimilation Daniel Leuenberger Swiss COSMO User Workshop 2010 Data Assimilation Data Assimilation = „use of all the available information to determine as accurately as possible the state of the atmospheric flow“ (Talagrand, 1997) i.e. (sparse) observations and a numerical model Analysis = „best possible atmospheric state at the model grid“ Initial condition in NWP observations analysis forecast time Model state

3 COSMO Data Assimilation Daniel Leuenberger Swiss COSMO User Workshop 2010 Challenges in Convective-scale DA Convective-scale:  x=O(1km) Limited domain of O(1000km) length Limited predictability at this scale Highly complex and non-linear model physics Observations are very sparse in space and time (e.g. radiosondes, surface observations, aircraft observations) Remote sensing observations important to constrain the model fields (e.g. Radar, GPS / Satellites, Lidar / Radiometer) Indirect and non-linear link between observations and model fields

4 COSMO Data Assimilation Daniel Leuenberger Swiss COSMO User Workshop 2010 Statistical Analysis Update (BLUE) Analysis Analysis variance InnovationKalman Gain Background

5 COSMO Data Assimilation Daniel Leuenberger Swiss COSMO User Workshop 2010 Analysis update step Forecast step Ensemble Kalman Filter Kalman Gain Analysis mean Analysis covariance (spread) Background (ensemble forecast) Background error covariance (spread)

6 COSMO Data Assimilation Daniel Leuenberger Swiss COSMO User Workshop 2010 Comparison Nudging - EnKF Nudging (today)EnKF (tomorrow) Restriction to observations of prog- nostic model variables Remote sensing observations only with error-prone retrievals (e.g. latent heat nudging) Allows direct assimilation of complex observations through observation operator Kalman gain constant, mainly diagonal and empirical Kalman gain multivariate and based on observation errors and flow dependent background errors Computationally cheap and conceptually simple Expensive (ensemble propagation) and conceptually more challenging, particularly on the convective scale No direct Gaussian assumption of errors Assumes Gaussian errors

7 COSMO Data Assimilation Daniel Leuenberger Swiss COSMO User Workshop 2010 OSSE (Observation System Simulation Experiments) Used to test data assimilation systems Model simulation regarded as „truth“. Serves as Source to generate synthetic observations Reference for verification The synthetic observations are „spoiled“ with errors and then assimilated either in The same model (perfect model assumption) Another model (lower resolution, other configuration, etc.) Powerful tool

8 COSMO Data Assimilation Daniel Leuenberger Swiss COSMO User Workshop 2010 Lorenz 96 model

9 COSMO Data Assimilation Daniel Leuenberger Swiss COSMO User Workshop 2010 First test 10 members Obs every gp Obs error = 1 RMS free5.18 RMS Nud0.63 RMS EnkF0.25 Truth Obs Free forecast Nudging analysis EnKF analysis EnKF Spread

10 COSMO Data Assimilation Daniel Leuenberger Swiss COSMO User Workshop 2010 Sparse observations 10 members Sparse obs Obs error = 1 RMS free5.18 RMS Nud4.05 RMS EnkF3.98 Truth Obs Free forecast Nudging analysis EnKF analysis EnKF Spread

11 COSMO Data Assimilation Daniel Leuenberger Swiss COSMO User Workshop 2010 Covariance inflation 10 members Sparse obs Obs error = 1 Covariance in- flation RMS free5.18 RMS Nud4.05 RMS EnkF3.56 Truth Obs Free forecast Nudging analysis EnKF analysis EnKF Spread

12 COSMO Data Assimilation Daniel Leuenberger Swiss COSMO User Workshop 2010 More ensemble members 50 members Sparse obs Obs error = 1 RMS free5.14 RMS Nud3.86 RMS EnkF1.82 Truth Obs Free forecast Nudging analysis EnKF analysis EnKF Spread

13 COSMO Data Assimilation Daniel Leuenberger Swiss COSMO User Workshop 2010 Summary Convective-scale data assimilation is a challenging task Increased focus on remote-sensing observations Nudging is simple and cheap but has some disadvantages particularly at the convective scale COSMO EnKF is being developed First results look promising but much work ahead!

14 COSMO Data Assimilation Daniel Leuenberger Swiss COSMO User Workshop 2010 Nudging: pro‘s and con‘s Advantages 4D DA, applied every time step, strong coupling to model dynamics -> more or less balanced Able to assimilate high-frequency observations at appropriate time Computationally cheap COSMO: < 10% more expensive than forecast Conceptionally simple Disadvantages No optimal combination of obs and model Can only assimilate prognostic model variables Retrieval of prognostic variables from other observations E.g. Latent Heat Nudging for Surface Rainfall Needs explicit balancing (difficult/unknown for small scales)

15 COSMO Data Assimilation Daniel Leuenberger Swiss COSMO User Workshop 2010 Statistical Analysis Update (BLUE) Optimal combination of two temperature measurements with known gaussian error statistics Bias-free known variances errors uncorrelated Analysis: Bias-free: Minimize:

16 COSMO Data Assimilation Daniel Leuenberger Swiss COSMO User Workshop 2010 probability T Statistical Analysis Update (BLUE)

17 COSMO Data Assimilation Daniel Leuenberger Swiss COSMO User Workshop 2010 The weight W k for the model grid point (x,t) depends on - temporal distance to the observation (w t ) - spatial distance to the observation (w xy, w z ) - observation errors (  k ) G  determines the characteristic time scale for the relaxation Observation Nudging

18 COSMO Data Assimilation Daniel Leuenberger Swiss COSMO User Workshop 2010 Observations Surface Stations Radiosondes Weather radar Aircraft Obs

19 COSMO Data Assimilation Daniel Leuenberger Swiss COSMO User Workshop 2010 EZMW IFS EZMW IFS (global) 16km, 91 levels 2 x 240h per day + 2 x 78h per day MeteoSwiss Model Chain COSMO-7 (regional) 6.6km, 60 levels 2 x 72h per day COSMO-7 COSMO-2 (local) 2.2km, 60 levels 8 x 24h per day COSMO-2

20 COSMO Data Assimilation Daniel Leuenberger Swiss COSMO User Workshop 2010 Ensemble Kalman Filter Background error matrix Ensemble anomaly matrix Observation error matrix Observation operator i =

21 COSMO Data Assimilation Daniel Leuenberger Swiss COSMO User Workshop 2010 LETKF Local Ensemble Transform Kalman Filter (Hunt et al., 2007) Local do separate analysis at every grid point, select only certain nearby observations analysis ensemble members are locally linear combination of first guess ensemble members Transform Do analysis in the space of the ensemble perturbations computationally ecient, but restricts corrections to subspace spanned by the ensemble

22 COSMO Data Assimilation Daniel Leuenberger Swiss COSMO User Workshop 2010 LETKF Analysis mean Analysis ensemble Transformed Analysis error matrix (ensemble space) Kalman Gain Innovation Background