Towards an unbiased stratospheric analysis

Abstract

The standard, strong‐constraint formulation of 4D‐Var is designed to correct for random, zero‐mean errors from the model forecast and the observations. However, significant systematic errors are generated by the forecast models used in global numerical weather prediction (NWP), and the Integrated Forecast System (IFS) model of the European Centre for Medium‐Range Weather Forecasts (ECMWF) is no exception. To deal with this type of error, a modification of the standard 4D‐Var algorithm, weak‐constraint 4D‐Var, has long been proposed and was implemented in operations at ECMWF in 2009. In the original implementation, the model error corrections were only active in the upper stratosphere, as a full application of the algorithm would lead to unacceptable degradation of forecast scores. Thus the impact of weak‐constraint 4D‐Var on ECMWF analyses and forecasts has always been small heretofore.In a companion article, it was shown through theoretical considerations and experiments with a simplified model that weak‐constraint 4D‐Var can correct accurately for model errors and initial‐state errors only when background and model errors have different spatial scales and when the observing system has a component, sufficient in number, that is unbiased and spatially homogeneous. This article presents new diagnostics based on radio occultation (RO) temperature retrievals and shows how those assumptions are verified in the IFS model. A new model‐error covariance matrix is derived and reduces the analysis and first‐guess temperature bias in the stratosphere by up to 50%. We also present how the model error tendencies diagnosed by weak‐constraint 4D‐Var can be used to reduce mean errors in medium‐range forecasts and discuss how they can also be applied in a reanalysis context to improve the fidelity and continuity of climate reconstructions.

Machine Learning for Model Error Inference and Correction

“…These results confirm that estimating model error in the IFS at the rather coarse scales we are considering here is a mildly nonlinear problem, which can partly explain the success of WC-4DVar in its current configuration (Laloyaux, Bonavita, Chrust, et al, 2020;Laloyaux, Bonavita, Dahoui, et al, 2020). In the current WC-4DVar configuration only mass and (to a lesser extent) wind model errors are estimated and corrected, which also seems a good choice based on the results in Figure 2.…”

“…This is also in view of the complex and typically nonlinear model error interactions that arise between the various components of a coupled Earth system model during extended integrations. We note, however, that recent results in both medium range NWP (Laloyaux, Bonavita, Dahoui, et al, 2020) and seasonal prediction (Ham et al, 2019) have already shown that the introduction of pure or hybrid ML/DL models can lead to significant improvements in specific aspects of forecast performance.…”

“…The work presented in this paper and recent developments in 4D-Var methodology (Laloyaux, Bonavita, Dahoui, et al, 2020;Laloyaux, Bonavita, Chrust, et al, 2020) are based on the idea that an effective strategy to deal with model error in NWP is to partition it in two components: (a) a stochastic, small-scale (temporally and spatially) component and (b) a predictable component active on larger and longer spatial/temporal scales. The random component of model error is typically represented with physically based model error simulation models (e.g., stochastically perturbed parametrization tendency [SPPT], stochastic kinetic energy backscatter [SKEB], and others; see Leutbecher et al, 2017, for a discussion) which are derived from an understanding of the approximations done in the development of the forecast model and an attempt to sample from those sources of uncertainties.…”

“…On the practical side, the coarse resolution chosen here facilitates the training phase of the ANN as it keeps its memory and 10.1029/2020MS002232 computational requirements at a manageable level (in this work we did not have access to supercomputing resources for the training of the ANN). On the science side, this choice is motivated by the findings in Laloyaux, Bonavita, Dahoui, et al (2020) and Laloyaux, Bonavita, Chrust, et al (2020) that only large-scale model errors are identifiable in a WC-4DVar framework. Additionally, there are fundamental arguments from ergodic dynamical systems theory that suggest that only large-scale features of model error can be learned statistically.…”

“…reductions of forecast bias produced by the recent version of WC-4DVar (Laloyaux, Bonavita, Dahoui, et al, 2020). Ten-day forecasts are initialized using the analysis from strong-constraint 4D-Var, WC-4DVar, NN_SC, and NN_WC between 10 and 24 August 2019.…”