The ECMWF operational implementation of four‐dimensional variational assimilation. I: Experimental results with simplified physics

Abstract

This paper presents results of a comparison between four‐dimensional variational assimilation (4D‐Var). using a 6‐hour assimilation window and simplified physics during the minimization, and three‐dimensional variational assimilation (3D‐Var). Results have been obtained at ‘operational’ resolution T213L31/T63L31. (T defines the spectral triangular truncation and L the number of levels in the vertical, with the first parameters defining the resolution of the model trajectory, and the second the resolution of the inner‐loop.) The sensitivity of the 4D‐Var performance to different set‐ups is investigated. In particular, the performance of 4D‐Var in the Tropics revealed some sensitivity to the way the adiabatic nonlinear normal‐mode initialization of the increments was performed. Going from four outer‐loops to only one (as in 3D‐Var), together with a change to the 1997 formulation of the background constraint and an initialization of only the small scales, helped to improve the 4D‐Var performance. Tropical scores then became only marginally worse for 4D‐Var than for 3D‐Var. Twelve weeks of experimentation with the one outer‐loop 4D‐Var and the 1997 background formulation have been studied. The averaged scores show a small but consistent improvement in both hemispheres at all ranges. In the short range, each two‐ to three‐week period has been found to be slightly positive throughout the troposphere. The better short‐range performance of the 4D‐Var system is also shown by the fits of the background fields to the data. More results are presented for the Atlantic Ocean area during FASTEX (the Fronts and Atlantic Storm‐Track Experiment), during which 4D‐Var is found to perform better. In individual synoptic cases corresponding to interesting Intensive Observing Periods, 4D‐Var has a clear advantage over 3D‐Var during rapid cyclogeneses. The very short‐range forecasts used as backgrounds are much closer to the data over the Atlantic for 4D‐Var than for 3D‐Var. The 4D‐Var analyses also display more day‐to‐day variability. Some structure functions are illustrated in the 4D‐Var case for a height observation inserted at the beginning, in the middle or at the end of the assimilation window. The dynamical processes seem to be relevant, even with a short 6‐hour assimilation period, which explains the better overall performance of the 4D‐Var system.

Flow-Dependent Reliability: A Path to More Skillful Ensemble Forecasts

“…1a , blue curves), the rapid rise in spread to day 2 reflected the inclusion of fast-growing "singular vector" (SV) perturbations to the initial conditions (Molteni and Pa lmer 1993), which helped the spread keep pace with error growth over the first 2 days, but it can be seen that this was not sustained beyond 2 days. Since 1996, four-dimensional variational data assimilation (Rabier et al 2000) was developed and subsequently incorporated into an ensemble of data assimilations (EDA; Isaksen et al 2010) to produce a set of equally likely initial conditions that take into account observation and model uncertainty and the growth of uncertainty from the previous set of initial conditions. These developments, together with many other incremental improvements (e.g., English I n the landfalling hurricane example, suppose that the overall forecast probability for landfall is p and that this probability is reliable (so that landfall does occur in a fraction p of these cases).…”

A GSI-Based Coupled EnSRF–En3DVar Hybrid Data Assimilation System for the Operational Rapid Refresh Model: Tests at a Reduced Resolution

“…Three-dimensional variational (3DVar; Lorenc 1986) and four-dimensional variational (4DVar; Le Dimet and Talagrand 1986;Talagrand and Courtier 1987) data assimilation (DA) methods have been used successfully at operational numerical weather prediction (NWP) centers for more than two decades (e.g., Parrish and Derber 1992;Courtier et al 1998;Rabier et al 2000). Typically, static, flow-independent background error covariance (BEC) is used in the background term of the variational cost function.…”

Testing variational estimation of process parameters and initial conditions of an earth system model

“…Rabier et al, 2000). We also refrained from using a prior (or background) term in the cost function (eq.…”

“…To the atmospheric component, the adjoint approach is being routinely applied at operational centres for numerical weather prediction (NWP) for forecast initialisation (see e.g. Rabier et al, 2000). Adjoint-based calibration has been demonstrated (e.g.…”

“…In NWP, it is common to run the assimilation with 'simplified physics', that is, to remove a set of particularly non-linear processes or replace them by less complex and smoother formulations (Rabier et al, 2000). What is feasible for the short assimilation windows typical for NWP can be problematic on longer time scales, where it may result in considerable biases in the simulated state of the system.…”