A method for merging flow-dependent forecast error statistics from an ensemble with static statistics for use in high resolution variational data assimilation

The background error covariance matrix, B, is often used in variational data assimilation for numerical weather prediction as a static and hence poor approximation to the fully dynamic forecast error covariance matrix, Pf. In this paper the concept of an Ensemble Reduced Rank Kalman Filter (EnRRKF) is outlined. In the EnRRKF the forecast error statistics in a subspace defined by an ensemble of states forecast by the dynamic model are found. These statistics are merged in a formal way with the static statistics, which apply in the remainder of the space. The combined statistics may then be used in a variational data assimilation setting. It is hoped that the nonlinear error growth of small-scale weather systems will be accurately captured by the EnRRKF, to produce accurate analyses and ultimately improved forecasts of extreme events.

Correlations of control variables in variational data assimilation

Variational data assimilation systems for numerical weather prediction rely on a transformation of model variables to a set of control variables that are assumed to be uncorrelated. Most implementations of this transformation are based on the assumption that the balanced part of the flow can be represented by the vorticity. However, this assumption is likely to break down in dynamical regimes characterized by low Burger number. It has recently been proposed that a variable transformation based on potential vorticity should lead to control variables that are uncorrelated over a wider range of regimes. In this paper we test the assumption that a transform based on vorticity and one based on potential vorticity produce an uncorrelated set of control variables. Using a shallow-water model we calculate the correlations between the transformed variables in the different methods. We show that the control variables resulting from a vorticity-based transformation may retain large correlations in some dynamical regimes, whereas a potential vorticity based transformation successfully produces a set of uncorrelated control variables. Calculations of spatial correlations show that the benefit of the potential vorticity transformation is linked to its ability to capture more accurately the balanced component of the flow.

Aidos

Aidos, an abstraction whose meaning ranges from shame to modesty, is personified in literature (Hani 1980) but not art (Cairns 1996). Homer contrasts aidos, personal shame, with Nemesis, public indignation (Scott 1980).

Aletheia

The abstract concept Aletheia, Truth, is personified in literature as a daughter of Zeus (Pind. Ol. 10.3–4 and fr. 205) and nurse of Apollo (Plut. Symp. 657e).

Ananke

Ananke, Homeric “compulsion,” becomes an important philosophical term among the pre-Socratics. To Thales it is the natural necessity that powers all phenomena and compels divinities to epiphany (71 A12 DK).

Eros/Cupid

Eros, sexual love, is personified as an adolescent boy, as are his Latin equivalents, Amor and Cupido.

Graces

The Graces, known by their Greek name Charites (sing. Charis) are young and benevolent models of feminine grace. Homer does not specify their number and ages, but Hesiod explains that they are three daughters of Zeus and Eurynome (a daughter of Okeanos), named Aglaia, Euphrosyne, and Thaleia (Theog. 907–9); they live with Himeros (Desire) on Olympos, beside the Muses (Theog. 64); and they assisted with the birth of Pandora (Op. 73).

Homonoia

Homonoia, “oneness of mind,” brings together unrelated groups, including poleis. This political ideal was contrasted with stasis, civil strife, in the fifth century bce (Funke 1980; Rosler 2005: 210–14).

Muses

The Muses are goddesses and teachers of divine wisdom evoked in dance, music, and poetry. Late sources suggest that they invented the alphabet (Diod. Sic. 7.74.1) and the arts and sciences (Anth. Lat. 1.1.88; 1.2.664).