New Directions in 4D-Var: the ECMWF Perspective Massimo Bonavita and many colleagues ECMWF Special Acknow.: Peter Lean and Elias Holm EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS October 29, 2014 1
Introduction • Since its operational implementation (November 1997) incremental 4D-Var has been the cornerstone of the ECMWF atmospheric DA system • Over the past ~10 years the main development in the ECMWF DA has been the introduction of an error cycling component (EDA, Bonavita et al, 2012, 2016) • Over this period the ECMWF 4D-Var setup has been essentially remained the same, except for resolution upgrades (both outer and inner loops) • However, this is about to change… EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS October 29, 2014 2
Introduction • In the next few years a number of 4D-Var developments will significantly change the way Data Assimilation is performed at ECMWF: 1) Outer Loop Atmosphere-Ocean Coupling (Laloyaux et al, 2016, 2018) 2) Bias-aware 4D-Var (a.k.a., weak constraint 4D-Var) 3) Parallel-in-time minimisation (no, not the Saddle Point algorithm) 4) 4D-Var analysis of surface variables Model parameters’ estimation in 4D-Var 5) 6) Cheaper, more effective EDA (Lang et al, 2018) 7) Continuous Data Assimilation (Lean et al, 2018) EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS October 29, 2014 3
Observations ERA5 Reanalysis 10 millions 1 million 0.1 million Courtesy of Gionata Biavati October 29, 2014 4
Observations: timeliness Timeline of number of obs received by the ECMWF acquisition and pre-proc. system (SAPP), 15/10/2018 Radiosonde obs. GEOS rad. Aircraft obs. October 29, 2014 5
Observations: nonlinearity Forecast sensitivity (FSO) of major observing systems in ECMWF DA --- ALL-SKY obs --- Clear SKY MW from Alan Geer October 29, 2014 6
Observation: nonlinearities • For linear observation operators in an ensemble DA: 𝑑𝑢𝑠𝑚 = 𝐼 𝑁 𝑗 𝑗 𝐼 𝐲 𝑐 𝐲 𝑏 ≈ 𝐼 𝐲 𝑐 𝑗 = 1, … , 𝑂 𝑓𝑜𝑡 Radiosonde temperatures ATMS ch. 20 AMSR-2 ch. 6 Point temperature measurement Tropospheric humidity Cloud liquid water 𝑑𝑢𝑠𝑚 𝐼 𝐲 𝑐 𝑗 𝐼 𝐲 𝑐 EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS October 29, 2014 7
Model • Increased resolution, fidelity From Sylvie Malardel EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS October 29, 2014 8
Model nonlinearities • Model nonlinearity: how much initial increments evolved by the linearised model and the nonlinear model differ? 𝑡𝑢𝑒𝑓𝑤 𝑁 𝐲 𝑢 + 𝜀𝐲 0 − 𝑁 𝐲 𝑢 + 𝐍 𝜀𝐲 0 Vorticity 500 hPa (units: 10 -5 s -1 ) T+9h T+3h EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS October 29, 2014 9
Model nonlinearities 𝑇𝑢𝐸𝑓𝑤 𝑁 𝐲 𝑢 + 𝜀𝐲 0 − 𝑁 𝐲 𝑢 + 𝐍 𝜀𝐲 0 Vorticity • Larger nonlinearities than in the past, due to: 1. Increased resolution (40 km -> 9 km) 2. Increase mismatch of outer- inner loop resol. ( from 3 -> 5) 3. Less diffusive model EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS October 29, 2014 10
Nonlinear effects: the incremental approach • Incremental 4D-Var deals with nonlinearities by a succession of quadratic optimizations around progressively more accurate first guess trajectories => progressively smaller increments => more accurate local linearisation! Taylor diagram for differences in obs-dep for StDev of vorticity analysis incr . nonlinear and linearised trajectories in successive minimizations EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS October 29, 2014 11
Observation and Model trends 1. Ever increasing number of observations 2. Nearly continuous flow of available observations 3. Increasing number and influence of nonlinear observations 4. Increase of model resolution and fidelity => Increasing nonlinearity of error evolution in 4D-Var assimilation window 5. Need to do more re-linearisations, decrease mismatch between inner/outer loops configurations, etc. => spend more time in DA computations EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS October 29, 2014 12
Current operational 4D-Var at ECMWF (Haseler, 2004) 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 12h 12h FG/BG FG/BG 4DVar 4DVar 21-09Z 09-21Z 00UTC 10-day FCST 12UTC 10-day FCST 6h 6h 4DVar 4DVar 09-15Z 21-03Z 1. Analysis work is concentrated in two windows during the day (2-5 UTC and 14-17 UTC) 2. Operational time constraints impose simplifications on the 6h 4D-Vars (Early Delivery Analyses) used to provide initial conditions for the deterministic 10-day forecasts (and centre analysis for the ENS forecasts) EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS October 29, 2014 13
Current Early Delivery system: Trade-off Users expect all products cut-off time are available ? Allow more time for computations Collect more observations 04z 06:55z (earlier cut-off) (later cut-off) 14 EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS October 29, 2014
Continuous data assimilation cutoff 1 2 3 Current cutoff Effective cut-off time Extra obs 1 2 3 is 30 minutes later n-3 n-2 n Extra obs, start earlier n-1 • Key point: Start running data assimilation before all of the observations have arrived • ~ 70% of 4D-Var is removed from the time critical path • Configurations which were previously unaffordable can now be considered • Opens the possibility of a fully continuous assimilation system. 15 EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS October 29, 2014
Continuous data assimilation: Trade-off Users expect all cut-off products are time available ? Collect more observations Allow more time for computations 04z (later cut-off) (earlier cut-off) 06:55z Continuous DA configuration allows both : • Later cut-off to collect more observations • A longer assimilation window • More time to perform DA computations 16 EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS October 29, 2014
Extra observations assimilated in Continuous DA configuration Number of obs 21z 03z 05z Timeslot 17 EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS October 29, 2014
Continuous DA • Of this new-found freedom to explore and use more complex 4D-Var configurations, only the increase in # of outer loops has been exploited so far (IFS CY46R1 – Q1 2019) • This leads to 2-3% forecast skill improvement Vector wind RMS error (bad) Impact of additional observations in Cont. DA Additional observations + 4 outer loops (good) EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS October 29, 2014 18
Continuous Long Window DA • Continuous DA offers significant advantages over current Early Delivery setup, but does not solve all the problems • In particular, issues about homogeneous exploitation of 4D-Var convergence, time- homogeneous exploitation of available computer resources, resilience of the assimilation cycle, etc. • We think a fully continuous DA configuration will help in these respects • We call this future setup Continuous Long Window DA EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS October 29, 2014 19
Continuous Long Window DA 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 00 BG/FG 6h 6h FG FG BG/FG 4DVar 4DVar 21-03Z 09-15Z 00UTC 10-day FCST 12UTC 10-day FCST 8h 8h 4DVar 4DVar BG 21-05Z BG 09-17Z FG FG 10h 10h 4DVar 4DVar BG BG FG FG 21-07Z 09-19Z 12h 12h 4DVar 4DVar 21-09Z 09-21Z BG BG 1. Single DA cycle 2. Vastly improved resilience and product timeliness 3. Time-uniform exploitation of computing resources 4. Possibility of more complex/costly 4D-Var configurations within operational time constraints EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS October 29, 2014 20
Thanks for your attention! Bonavita, M., P. Lean and E. Hólm, 2018: Nonlinear effects in 4D-Var. Nonlin. Proc. Geo ., https://doi.org/10.5194/npg-2018-20 Bonavita, M. and co-Authors, 2018: Non-linearity and non-Gaussianity in 4D-Var (and beyond). ECMWF Annual Seminar 2018. Available at https://www.ecmwf.int/en/learning/workshops/annual-seminar-2018 Lean, P., E. Hólm and M. Bonavita, 2018: Continuous Data Assimilation, in preparation. EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS October 29, 2014 21
Additional Slides EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS October 29, 2014 22
Continuous DA • Many other aspects of 4D-Var algorithm can be improved within the Continuous DA setup: Consistency between outer/inner loop models’ timesteps; 1. Increased consistency between outer/inner loop models’ resolutions; 2. 3. Stricter convergence criteria in the minimisation of the linearised cost function; Difference between analysis increments computed by nonlinear and linearised model t+9h in the assimilation window ( temperature at ~ 5 hPa ) Nonlin. Model tstep=450s; Linearised Model tstep=900s Nonlin. Model tstep=450s; Linearised Model tstep=450s EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS October 29, 2014 23
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