ECMWF Training Course 2005 slide 1 Forecast sensitivity to Observation Carla Cardinali

ECMWF Training Course 2005 slide 2 Outline Part 2: Forecast Sensitivity Forecast Sensitivity to Observation Sensitivity gradient A-TReC campaigns Comparing Observation Analysis Influence and Observation Forecast Impact Results and Conclusion

ECMWF Training Course 2005 slide 3 Forecast Sensitivity to Observation J is measures the forecast error: its gradient respect the observation vector y gives the forecast error sensitivity respect observations used in the initial condition for model forecast the sensitivity respect the initial condition x a Analysis sensitivity with respect the observation

ECMWF Training Course 2005 slide 4 Define Forecast Sensitivity

ECMWF Training Course 2005 slide 5 Change of Variable

ECMWF Training Course 2005 slide 6 Computation z Linear system to solve zaza

ECMWF Training Course 2005 slide 7 Forecast Sensitivity to Observations Tangent Linear Model ResolutionT95 L60

ECMWF Training Course 2005 slide 8 Sensitivity Gradients Sensitive area Verification area T1T1 100* TE at t=0 100* KE at t=0 TE at t=T 1 KE at t=T hPa Temperature Sensitivity Gradients

ECMWF Training Course 2005 slide 9 Fc Sensitivity to Aircraft Temperature 500 hPa

ECMWF Training Course 2005 slide 10 Fc Sensitivity to Surface Pressure

ECMWF Training Course 2005 slide 11 Observation Campaign 5 Dec 18 UTC---Verification 7 Dec 12 UTC AtreC 13% MSLP Relative Fc Improvement 9% Total Energy Targeting = Verification Region Lat(30,50)-Lon(-85,-60) 42 h TargetIN/NOTargetIN % AMDAR 2.5 SONDE 5.5 An 5 Dec 18 UTC

ECMWF Training Course 2005 slide 12 Observations Contribution to Forecast Total Contribution Mean Contribution

ECMWF Training Course 2005 slide 13 Forecast and Analysis Sensitivity to Targeted Observations

ECMWF Training Course 2005 slide hPa Targeted Aircraft Temperature Forecast Error

ECMWF Training Course 2005 slide 15 Aircraft Observation U-Comp hPa Forecast Impact Observation Influence in Analysis Background Influence = 1-Observation Influence

ECMWF Training Course 2005 slide 16 TEMP Observation Temperature hPa Forecast Impact Observation Influence in Analysis Background Influence = 1-Observation Influence

ECMWF Training Course 2005 slide 17 Total Forecast Error 5 Dec 2003 TargetIN/NOTargetIN 8%

ECMWF Training Course 2005 slide 18 Observation Campaign 8 Dec 18 UTC---Verification 11 Dec 00 UTC TargetIN/NOTargetIN % AMDAR 2.6 SONDE 0.9 AtreC -71% MSLP Relative Fc Degradation -7% Total Energy Targeting Lat(30,60)-Lon(-70,-15) Verification Lat(45,65)-Lon(-15,+10) 54 h

ECMWF Training Course 2005 slide hPa Targeted Aircraft U Forecast Error

ECMWF Training Course 2005 slide 20 Total Forecast Error 8 Dec 2003 TargetIN/NOTargetIN 3.5%

ECMWF Training Course 2005 slide 21 Conclusions Forecast sensitivity to observations has been computed for the campaigns showing an impact (ATreC-Cntr)/Cntr ≥ ± 10%  13 cases out of 38: 9 positive and 4 negative Two campaigns have been shown  5 Dec at 18 UTC - Targeted observations improved the forecast of a cyclone moving along the east coast of North America for which severe weather impact was forecast  8 Dec at 18 UTC – Targeted observations deployed to clarify the models uncertainties for the remnants of the east cost storm, degraded the forecast over Northern Europe – UK

ECMWF Training Course 2005 slide 22

ECMWF Training Course 2005 slide 23 References Forecast sensitivity to observations Baker and Daley, Observation and background adjoint sensitivity in the adaptive observation-targeting problem. QJRMS 126, Langland and Baker, Estimation of observation impact using the NRL atmospheric variational data assimilation adjoint system. Tellus, 56A, Gelaro, Buizza, Palmer and Klinker, Sensitivity analysis of forecast errors and the construction of optimal perturbations using singular vectors. JAS 55, Influence Matrix Cardinali, Pezzulli and Andersson, Influence-matrix diagnostic of data assimilation system. QJRMS 130, Pre-processing Järvinen. Observations and diagnostic tools for data assimilation. ECMWF lecture note

ECMWF Training Course 2005 slide 24 Singular vectors brief definition Singular vectors was one of technique used in AtreC-TOST campaign to find sensitivity areas where releasing additional observations Singular vectors (SVs) define perturbations with fastest growth during a finite time interval (optimization time interval). They are defined by:  The model characteristics: T L 95L60, dry, with simplified physics  The norm used to measure growth: localized total energy  The optimization time interval: hours Diagnostic Singular vectors have been computed to investigate the observation impact in the forecast time Sensitive area Verification area

ECMWF Training Course 2005 slide 25 Linear combination of 10 Diagnostic SVs valid at observation time AtreC observation time forecast step T 1 localized total energy maximum in verification area eigenvalues decomposition forecast error step T 1 proj. fc error onto SVs Back to the observation time Sensitive area Verification area T1T1