Weak constraint 4D-Var at ECMWF How to deal with model error in data assimilation Patrick Laloyaux - Earth System Assimilation Section Acknowledgement: Massimo Bonavita, Jacky Goddard, Elias Holm, Simon Lang, Mike Fisher, Yannick Tremolet In in Sept 2011 Out in June 2013 In in Nov 2016

4D-Var formulations Bias-blind data assimilation designed to correct the background with observations when errors are random with zero means model is assumed to be perfect Biases in reality Observations (satellite miscalibrations) Observation operator (approximations in radiative transfer calculations) Model trajectory (inaccurate surface forcing, simplified representations of physics)

Biases in observations and observation operators Departure between observations and model depends on the scan position of the satellite instrument AMSUA channel 7 Obs-FG bias Limb Nadir Limb Departure between observations and model depends on the spectroscopy used in the radiative transfer model Obs-FG bias Channel number (HIRS)

4D-Var formulations Bias-aware data assimilation (VarBC) estimate simultaneously the initial condition and parameters of the observation bias model the bias model copes with instrument miscalibration or systematic errors in the observation operator the model is a strong constraint

Biases in model trajectory Estimating the systematic error in the model over a short period of time is not straightforward (disentangle model error and IC error) Timeseries of estimated temperature model error after 12 hours [fc12h – an] Pressure hPa Nov 2016 Aug 2017

4D-Var formulations Bias-aware data assimilation (VarBC + Weak constraint) Introduce additional controls to target an unbiased analysis and to move the assimilation away from a perfect-model trajectory The model error represents the systematic error which develops in the model over the assimilation window The model error covariance matrix Q constrains the model error field Size on the control vector increased by ~25%

Implemented in operations (22 Nov 2016, CY43R1) Weak constraint 4D-Var has been implemented in operations constant model forcing applied every hour  only active above 40 hPa Estimate the model error covariance matrix (Q) run the ensemble forecasting system (ENS) with SPPT (51 members with the same initial condition for 20 days)  differences after 12 hours are used to compute Q

Impact of weak constraint 4D-Var Comparison between strong and weak constraint 4D-VAR. Verification against GPS-RO (good for highlighting improvements in the stratosphere)

Impact of weak constraint 4D-Var Comparison between strong and weak constraint 4D-VAR in the stratosphere. Verification against radiosondes.

Monitoring of the weak constraint 4D-Var in operations Timeseries of estimated temperature model error after 12 hours [fc12h – an] Pressure hPa Timeseries of temperature model error estimated by the weak constraint 4D-Var Pressure hPa Nov 2016 Aug 2017 Negative (positive) model errors are corrected by positive (negative) forcings, especially in the upper stratosphere

Weak constraint 4D-Var in the troposphere Model error variability for vorticity at 850hPa (September 2016) Spurious day-to-day variability near airports T399 T64 Q T399 Q T64 Aircraft observations are fitted in the 4D-Var by changing the model error current model error covariance matrix contains small scales (T399) new model error covariance matrix contains longer scales (T64) localisation techniques and better set of ensemble forecasts to build Q

Summary and conclusions 4D-Var designed to correct the background with observations when errors are random with zero means VarBC to deal with systematic errors in observations and observation operators Weak constraint to deal with systematic errors in the model Weak constraint 4D-Var performs well in the stratosphere but more work is required to disentangle background and model errors in the troposphere Q matrix with longer correlation lengthscales and proper localisation is required Within the OOPS framework, ECMWF is interested to use the weak constraint 4D-Var parallelization (subwindows)