Updating prediction models by dynamical relaxation: an examination of the technique

Abstract

SUMMARYA study is undertaken of a particular method of updating numerical prediction models. The method constrains the time development of a subset of the model fields toward a prescribed space-time estimate of those fields, while the other model variables are allowed to evolve in an explicitly unconstrained fashion. It represents an attempt to update the model by a form of dynamical relaxation.An analysis of the method is carried out in the context of the primitive equations linearized about an isothermal basic state of no motion. It is shown that, for a particular form of the scheme and the availability of :he time history of the mass field (or the wind field) on an f-plane, all the time-and space-scale error fields in the initial specification suffer an amplitude reduction of a t least the order on the timescale of one day. On an equatorial p-plane it is shown that the same rate of amplitude reduction can be achieved if an accurate time history is known for both the mass field and the zonal-wind field. Numerical experiments performed with the nonlinear shallow-water equations for a mid-latitude ,&plane geometry support these results and demonstrate that the technique compares favourably with the conventional direct insertion update method. Consideration is also given to the possible effects of errors in the prescribed fields and it is shown that !he relaxation scheme can to some extent be tuned to offset the effect of this particular source of error.This study of the relaxation update scheme, although not comprehensive, is nevertheless sufficient to indicate its potential. However, it is stressed that a trenchant assessment of the scheme's usefulness should be based at least in part upon its performance under more testing and realistic conditions.

Investigation of indiscriminate nudging and predictability in a nested quasi‐geostrophic model

“…In order to prevent this drift, we use the nudging technique (or Newtonian relaxation) developed for assimilation purposes (Davies and Turner, 1977;Schraff, 1997;Yong et al, 1998;Vidard et al, 2003) and commonly available for dynamical downscaling purposes. The nudging technique consists of relaxing the model state towards the analyses by adding a non-physical term to the model equation.…”

“…Williams, 1992a, 1992b;Miguez-Macho et al, 1992;von Storch et al, 2000;Biner et al, 2002;Genthon et al, 2002;Lo et al, 2008;Salameh et al, 2010). Indiscriminate nudging was originally developed for assimilation issues (Davies and Turner, 1977;Schraff, 1997;Li et al, 1998;Vidard et al, 2003) but has become increasingly popular to drive Regional Climate Models (RCMs). The term 'indiscrimnate nudging' is thus not as commonly used as 'spectral nudging'.…”

“…The term 'indiscrimnate nudging' is thus not as commonly used as 'spectral nudging'. Salameh et al(2010) use the term 'indiscriminate nudging', Anthes (1974), Hoke and Anthes (1976) and Stauffer and Seaman (1990) refer to 'data assimilation', and other synonymous terminologies exist such as 'dynamical relaxation' (Davies and Turner, 1977) or 'grid' or 'analysis nudging'. In the following we will use 'indiscriminate nudging'.…”

The effect of indiscriminate nudging time on large and small scales in regional climate modelling: Application to the Mediterranean basin

“…All these studies have shown that RCM internal variability may be very complex and that its impact on regional climate predictions is far from negligible. One way to overcome this problem is to consider the effects on internal variability of large-scale nudging, which is a technique originally developed for assimilation issues (Davies and Turner, 1977;Schraff, 1997;Li et al, 1998;Vidar et al, 2003) but increasingly popular to drive RCMs. This technique consists of partially imposing the large scale of the driving fields on the RCM simulation with the aim of disallowing large and unrealistic departures between driving and driven fields.…”

Spectral nudging in regional climate modelling: how strongly should we nudge?

“…Kida et al, 1991;Waldron et al, 1996;von Storch et al, 2000;Raluca Rad et al, 2008) and the indiscriminate nudging which consists in driving the RCM indiscriminately at all scales. Indiscriminate nudging is also referred to as data assimilation, dynamical relaxation, grid-point nudging or analysis nudging (Anthes, 1974;Hoke and Anthes, 1976;Davies and Turner, 1977;Stauffer et al, 1990;Lo et al, 2008;Salameh et al, 2010;Omrani et al, 2012). For indiscriminate nudging, Omrani et al (2012) showed that there exists an optimal nudging value τ closely related to the predictability time τ p τ ∼ 0.4τ p which minimizes the error both on the large and small scales.…”