Why does 4D‐Var beat 3D‐Var?

Abstract

SUMMARYA set of four experiments is described which measure the expected beneficial aspects of incremental fourdimensional variational (4D-Var) compared to 3D-Var data assimilation systems: allowing for the time of each observation in the full and increment fields with which it is compared, and using time-evolved covariances. Judging each scheme by the overall accuracy of resulting numerical weather prediction forecasts compared to observations, each aspect is shown to provide benefit.On other measures of analysis quality, such as the fit of short-period forecasts and analyses to observations, the benefits of 4D-Var are less clear; it is sometimes worse. Perhaps 4D-Var is improving the analysis of growing modes, which are more important for forecasts, without improving all aspects of the analysis.Our basic 4D-Var was not provided with many observations distributed in time, and had very simple parametrizations. There is an expectation of enhanced benefits as these aspects are developed.

A review of forecast error covariance statistics in atmospheric variational data assimilation. I: Characteristics and measurements of forecast error covariances

“…All occurrences of B in (15) appear as MBM T , which is identified as the propagation of B (which is itself valid at t 0 ) to time t by the linearized forecast model. This property, which is implicit in 4d-VAR, is one reason why 4d-VAR is superior to 3d-VAR (Lorenc and Rawlins, 2005), as it allows maximum gain from the manifestations of the B-matrix (sections 3.1-3.4) as the B-matrix will be more appropriate at each subsequent time than if the Bmatrix was not propagated. This is especially beneficial in cases where the evolving B-matrix becomes significantly different to the static B-matrix (e.g.…”

Mathematical foundations of hybrid data assimilation from a synchronization perspective

“…Thus, for simplicity, we chose 3DVar as the variation method. If observations are taken over an interval between analysis times, the higher-dimensional extension 4DVar has generally been shown to be more accurate (Lorenc and Rawlins, 2005 and Yang et al, 2009). Bonavita et al (2015) showed performance gains with the Hybrid-Gain method combining 4DVar and LETKF compared to using either alone when applied to the operational forecast system of the European Centre for Medium-Range Weather Forecasts (ECMWF).…”

Improving Flood Prediction Assimilating Uncertain Crowdsourced Data into Hydrological and Hydraulic Models

“…In contrast to the previous sequential methods, variational assimilation methods have been widely used in weather forecasting and costal engineering applications (Li and Navon, 2001;Seo et al, 2003;Valstar et al, 2004;Fischer et al, 2005;Lorenc and Rawlins, 2005;Seo et al, 2009;Lee et al, 2011aLee et al, , 2012Liu et al, 2012). In these methods, the cost function that measures the difference between the error in the initial conditions and the error between model predictions and observations over time is minimised to identify the best estimate of the initial state condition (Seo et al, 2009;Lee et al, 2011a).…”