Abstract
Singular vectors (SVs) have long been employed in the initialization of ensemble numerical weather prediction (NWP) in order to capture the structural organization and growth rates of those perturbations or "errors" associated with initial condition errors and instability processes of the large scale flow. Due to their (super) exponential growth rates and spatial scales, initial SVs are typically combined empirically with evolved SVs in order to generate forecast perturbations whose structures and growth rates are tuned for specified lead-times. Here, we present a systematic approach to generating finite time or "mixed" SVs (MSVs) based on a method for the calculation of covariant Lyapunov vectors and appropriate choices of the matrix cocycle. We first derive a data-driven reduced-order model to characterize persistent geopotential height anomalies over Europe and Western Asia (Eurasia) over the period 1979-present from the National Centers for Environmental Prediction v1 reanalysis. We then characterize and compare the MSVs and SVs of each persistent state over Eurasia for particular lead-times from a day to over a week. Finally, we compare the spatiotemporal properties of SVs and MSVs in an examination of the dynamics of the 2010 Russian heatwave. We show that MSVs provide a systematic approach to generate initial forecast perturbations projected onto relevant expanding directions in phase space for typical NWP forecast lead-times.
Highlights
When it comes to predicting atmospheric conditions, it has been long known that the prediction of the distant future is practically impossible
In relation to medium-range weather forecasting, the mixed singular vectors (MSVs) provide the basis of initial conditions isolating large-scale features and their subsequent evolution and, may be optimal to use over singular vectors (SVs) in this context
We propose in this study that MSVs, which are dynamical objects that incorporate the mixing of initial and evolved singular vectors within their calculation, can provide a theoretical basis on which to project initial perturbations for medium-range weather forecasting given their ability to identify and track the evolution of large-scale disturbances and their connection to both the instantaneous and asymptotic dynamics
Summary
When it comes to predicting atmospheric conditions, it has been long known that the prediction of the distant future is practically impossible. While each regime was found individually to be asymptotically stable, the MSVs showed positive growth rates over short time periods (3 days) associated with structures of a large spatial extent The characteristics of these MSVs are potentially useful in forecasting in terms of defining the directions in phase space associated with the evolution of large-scale persistent structures of the NAO. The respective differences in the spatial scales, growth, and convergence rates of SVs, MSVs, and CLVs associated with Northern Hemisphere anticyclogenesis over Eurasia are examined in this study through a reduced-order linear delay model shown to capture the largescale switching between various identifiable metastable atmospheric states. We compute SVs and MSVs associated with each persistent state and compare their relative growth rates and spatial structures when optimized over various time windows This is put into the context of extreme event forecasting through a case study of the 2010 Russian heat wave. We discuss the potential utility of such MSVs in application to the initialization of numerical weather prediction (NWP) ensembles for medium-range forecasts
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