ERA-Interim is the latest global atmospheric reanalysis produced by the European Centre for Medium-Range Weather Forecasts (ECMWF). The ERA-Interim project was conducted in part to prepare for a new atmospheric reanalysis to replace ERA-40, which will extend back to the early part of the twentieth century. This article describes the forecast model, data assimilation method, and input datasets used to produce ERA-Interim, and discusses the performance of the system. Special emphasis is placed on various difficulties encountered in the production of ERA-40, including the representation of the hydrological cycle, the quality of the stratospheric circulation, and the consistency in time of the reanalysed fields. We provide evidence for substantial improvements in each of these aspects. We also identify areas where further work is needed and describe opportunities and objectives for future reanalysis projects at ECMWF. Copyright © 2011 Royal Meteorological Society

The ERA-Interim reanalysis: configuration and performance of the data assimilation system

The ERA5 global reanalysis

Matrix Differential Calculus with Applications in Statistics and Econometrics

The potential for sea ice-albedo feedback to give rise to nonlinear climate change in the Arctic Ocean – defined as a nonlinear relationship between polar and global temperature change or, equivalently, a time-varying polar amplification – is explored in IPCC AR4 climate models. Five models supplying SRES A1B ensembles for the 21 st century are examined and very linear relationships are found between polar and global temperatures (indicating linear Arctic Ocean climate change), and between polar temperature and albedo (the potential source of nonlinearity). Two of the climate models have Arctic Ocean simulations that become annually sea ice-free under the stronger CO 2 increase to quadrupling forcing. Both of these runs show increases in polar amplification at polar temperatures above-5 o C and one exhibits heat budget changes that are consistent with the small ice cap instability of simple energy balance models. Both models show linear warming up to a polar temperature of-5 o C, well above the disappearance of their September ice covers at about-9 o C. Below-5 o C, surface albedo decreases smoothly as reductions move, progressively, to earlier parts of the sunlit period. Atmospheric heat transport exerts a strong cooling effect during the transition to annually ice-free conditions. Specialized experiments with atmosphere and coupled models show that the main damping mechanism for sea ice region surface temperature is reduced upward heat flux through the adjacent ice-free oceans resulting in reduced atmospheric heat transport into the region.

Geophysical fluid dynamics.

An overview of the Community Earth System Model Version 2 (CESM2) is provided, including a discussion of the challenges encountered during its development and how they were addressed. In addition, an evaluation of a pair of CESM2 long preindustrial control and historical ensemble simulations is presented. These simulations were performed using the nominal 1° horizontal resolution configuration of the coupled model with both the “low-top” (40 km, with limited chemistry) and “high-top” (130 km, with comprehensive chemistry) versions of the atmospheric component. CESM2 contains many substantial science and infrastructure improvements and new capabilities since its previous major release, CESM1, resulting in improved historical simulations in comparison to CESM1 and available observations. These include major reductions in low-latitude precipitation and shortwave cloud forcing biases; better representation of the Madden-Julian Oscillation; better El Nino-Southern Oscillation-related teleconnections; and a global land carbon accumulation trend that agrees well with observationally based estimates. Most tropospheric and surface features of the low- and high-top simulations are very similar to each other, so these improvements are present in both configurations. CESM2 has an equilibrium climate sensitivity of 5.1–5.3 °C, larger than in CESM1, primarily due to a combination of relatively small changes to cloud microphysics and boundary layer parameters. In contrast, CESM2's transient climate response of 1.9–2.0 °C is comparable to that of CESM1. The model outputs from these and many other simulations are available to the research community, and they represent CESM2's contributions to the Coupled Model Intercomparison Project Phase 6.

The Community Earth System Model Version 2 (CESM2)

The ECMWF twentieth century reanalysis (ERA-20C; 1900–2010) assimilates surface pressure and marine wind observations. The reanalysis is single-member, and the background errors are spatiotemporally varying, derived from an ensemble. The atmospheric general circulation model uses the same configuration as the control member of the ERA-20CM ensemble, forced by observationally based analyses of sea surface temperature, sea ice cover, atmospheric composition changes, and solar forcing. The resulting climate trend estimations resemble ERA-20CM for temperature and the water cycle. The ERA-20C water cycle features stable precipitation minus evaporation global averages and no spurious jumps or trends. The assimilation of observations adds realism on synoptic time scales as compared to ERA-20CM in regions that are sufficiently well observed. Comparing to nighttime ship observations, ERA-20C air temperatures are 1 K colder. Generally, the synoptic quality of the product and the agreement in terms of climat...

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ERA-20C: An Atmospheric Reanalysis of the Twentieth Century

In most operational implementations of four-dimensional variational data assimilation (4D-Var), it is assumed that the model used in the data assimilation process is perfect or, at least, that errors in the model can be neglected when compared to other errors in the system. In this paper, we study how model error could be accounted for in 4D-Var.

We present three approaches for the formulation of weak-constraint 4D-Var: estimating explicitly a model-error forcing term, estimating a representation of model bias or, estimating a four-dimensional model state as the control variable. The consequences of these approaches with respect to the implementation and the properties of 4D-Var are discussed.

We show that 4D-Var with an additional model-error representation as part of the control variable is essentially an initial-value problem and that its characteristics are very similar to that of strong constraint 4D-Var. Taking the four-dimensional state as the control variable, however, leads to very different properties. In that case, weak-constraint 4D-Var can be interpreted as a coupling between successive strong-constraint assimilation cycles. A possible extension towards long-window 4D-Var and possibilities for evolutions of the data assimilation system are presented. Copyright © 2006 Royal Meteorological Society

https://www.emc.ncep.noaa.gov/seminars/old/presentations/2006/Tremolet.ModErrTalk.pdf

Accounting for an imperfect model in 4D‐Var

Current operational implementations of 4D-Var rely on the assumption that the numerical model representing the evolution of the atmospheric flow is perfect, or at least that model errors are small enough (relative to other errors in the system) to be neglected. This paper describes a formulation of weak-constraint 4D-Var that removes that assumption by explicitly representing model error as part of the 4D-Var control variable.



The consequences of this choice of control variable for the implementation of incremental 4D-Var are discussed. It is shown that the background-error covariance matrix cannot be used as an approximate model-error covariance matrix. Another model-error covariance matrix, based on statistics of model tendencies, is proposed.



Experimental results are presented. They show that this approach to accounting for and estimating model error captures some known model errors and improves the fit to observations, both in the analysis and in the background, but that it also captures part of the observation bias. We show that the model error estimated in this approach varies rapidly, and cannot be used to correct medium- or long-range forecasts. We also show that, because it relies on the tangent linear assumption for the entire assimilation window, the incremental formulation of weak-constraint 4D-Var is not the most suitable formulation for long assimilation windows. Copyright © 2007 Royal Meteorological Society

Model‐error estimation in 4D‐Var

Variational data assimilation is used at major weather prediction centers to produce the initial conditions for 7- to 10-day weather forecasts. This technique requires the solution of a very large data-fitting problem in which the major element is a set of partial differential equations that models the evolution of the atmosphere over a time window for which observational data has been gathered. Real-time solution of this difficult computational problem requires sophisticated models of atmospheric physics and dynamics, effective use of supercomputers, and specialized algorithms for optimization and linear algebra. The optimization algorithm can be accelerated by using a spectral preconditioner based on the Lanczos method. This paper shows how practical demands of the application dictate the various algorithmic choices that are made in the nonlinear optimization solver, with particular reference to the system in operation at the European Centre for Medium-Range Weather Forecasts.

/pdf/data-assimilation-in-weather-forecasting-a-case-study-in-pde-2onolesdg5.pdf

Data assimilation in weather forecasting: a case study in PDE-constrained optimization

Since its operational implementation at European Centre for Medium-Range Weather Forecasts, the incremental fourdimensional variational data assimilation system (4D-Var) has run with two outer loop iterations. It has been shown in the past that more outer loop iterations were leading to the divergence of the algorithm. We re-evaluate here the convergence of 4D-Var at outer loop level with the current system. Experimental results show that 4D-Var in its current implementation does diverge after four outer loop iterations. Various configurations are tested and show that convergence can be obtained when inner and outer loops are run at the same resolution, or at least with the same time-step. This is explained by the presence of gravity waves which propagate at different speeds in the linear and non-linear models. It is shown that these gravity waves are related to the shape of the leading eigenvector of the Hessian of the 4D-Var cost function which is determined by surface pressure observation and which controls the behaviour of the minimization algorithm. The influence of the choice of the inner loop minimization algorithm and preconditioner is also presented. Finally, some directions for possible future configurations of incremental 4D-Var are given.

Yannick Trémolet

Papers

ERA-20C: An Atmospheric Reanalysis of the Twentieth Century

Accounting for an imperfect model in 4D‐Var

Model‐error estimation in 4D‐Var

Data assimilation in weather forecasting: a case study in PDE-constrained optimization

Incremental 4D‐Var convergence study