## 1. Introduction

The relative advantages and disadvantages of four-dimensional variational data assimilation (4D-Var), already operational in several numerical forecasting centres, and Ensemble Kalman Filter (EnKF), a newer approach that does not require the adjoint of the model, are the focus of considerable current research (e.g. Lorenc, 2003; Kalnay *et al*, 2007a,b; Gustafsson, 2007; WWRP/THORPEX Workshop, 2008).

One area where 4D-Var may have an advantage over EnKF is in the initial spin-up, since there is evidence that 4D-Var converges faster than EnKF to its asymptotic level of accuracy. For example, Caya *et al*(2005) compared 4D-Var and EnKF for a storm simulating the development in a sounding corresponding to 0000 UTC on 25 May 1999. They found that

Overall, both assimilation schemes perform well and are able to recover the supercell with comparable accuracy, given radial-velocity and reflectivity observations where rain was present. 4D-Var produces generally better analyses than EnKF given observations limited to a period of 10 min (or three volume scans), particularly for the wind components. In contrast, EnKF typically produces better analyses than 4D-Var after several assimilation cycles, especially for model variables not functionally related to the observations.

In other words, for the severe storm problem, EnKF eventually yields better results than 4D-Var, presumably because of the assumptions made in the 4D-Var background-error covariance, but during the crucial *initial time of storm development*, when radar data start to become available, EnKF provides a worse analysis. For a global shallow-water model, which is only mildly chaotic, Zupanski *et al*(2006) found that initial perturbations that had horizontally correlated errors converged faster and to a lower level of error than perturbations created with white noise. In agreement with these results, Liu (2007) found using the SPEEDY global primitive-equations model that perturbations obtained from differences between randomly chosen states (which are naturally balanced and have horizontal correlations of the order of the Rossby radius of deformation) spun up faster than white noise perturbations.

Yang *et al*(2009) compared 4D-Var and the Local Ensemble Transform Kalman Filter (LETKF; Hunt *et al*, 2007) within a quasi-geostrophic (QG) channel model (Rotunno and Bao, 1996). They found that, if the LETKF is initialized from randomly chosen fields with uniform distribution perturbations, it takes more than 100 days before it converges to the optimal level of error. If, on the other hand, the ensemble mean is initialized from an existing 3D-Var analysis, which is already close to the true state, using the same random perturbations, the LETKF converges to its optimal level very quickly, within about 3 to 5 days. However, with a well-tuned background-error covariance, 3D-Var and 4D-Var converge fast without needing a good initial guess. This has also been observed for severe storm simulations (Caya *et al*, 2005), especially when using real radar observations (Jidong Gao, 2008, personal communication). It is not surprising that EnKF spins up more slowly than 3D-Var or 4D-Var because, in order to be optimal, the ensemble has to satisfy two independent requirements, namely that the mean be close to the true state of the system, and that the ensemble perturbations represent the characteristics of the ‘errors of the day’ in order to estimate the evolving background-error covariance **B**. In both 3D-Var and 4D-Var, by contrast, **B** is tuned *a priori* and assumed to be constant.

Within a global operational system it is feasible to initialize the EnKF from a state close enough to the optimal analysis, such as an existent 3D-Var analysis, with balanced perturbations drawn from a 3D-Var error covariance, so that spin-up may not be a serious problem. However, there are other situations, such as the storm development discussed above, where radar information is not available before the storm starts, so that no information is available to guide the EnKF in the spin-up towards the optimal analysis. The system may start from an unperturbed state without precipitation, and if a severe storm develops within a few minutes and the EnKF takes considerable real time to spin up from the observations, it will not give reliable forecasts until later in the storm evolution, and thus give results that are less useful for severe storm forecasting than 4D-Var or even 3D-Var. Similarly, a regional model initialized from a global analysis at lower resolution may take too long to spin up when confronted with mesoscale observations.

In this note we propose a new method to accelerate the spin-up of the EnKF by ‘running in place’ (RIP) during the spin-up phase and using the observations more than once in order to extract maximum initial information. We find that it is possible to accelerate the convergence of the EnKF so that (in real time) it spins up even faster than 3D-Var or 4D-Var without losing accuracy after spin-up and without requiring prior information such as a ‘well tuned’ initial background-error covariance. After spinning up, RIP is automatically turned off and the system returns to the standard EnKF formulation. Section 2 contains a brief theoretical motivation and discussion of the method, results are presented in section 3 and a discussion is given in section 4.