Metastable Decomposition of High-Dimensional Meteorological Data with Gaps

This paper presents an extension of the recently developed method for simultaneous dimension reduction and metastability analysis of high-dimensional time series. The modified approach is based on a combination of ensembles of hidden Markov models (HMMs) with state-specific principal component analysis (PCA) in extended space (guaranteeing that the overall dynamics will be Markovian). The main advantage of the modified method is its ability to deal with the gaps in the high-dimensional observation data. The proposed method allows for (i) the separation of the data according to the metastable states, (ii) a hierarchical decomposition of these sets into metastable substates, and (iii) calculation of the state-specific extended empirical orthogonal functions simultaneously with identification of the underlying Markovian dynamics switching between those metastable substates. The authors discuss the introduced model assumptions, explain how the quality of the resulting reduced representation can be assessed, and show what kind of additional insight into the underlying dynamics such a reduced Markovian representation can give (e.g., in the form of transition probabilities, statistical weights, mean first exit times, and mean first passage times). The performance of the new method analyzing 500-hPa geopotential height fields [daily mean values from the 40-yr ECMWF Re-Analysis (ERA-40) dataset for a period of 44 winters] is demonstrated and the results are compared with information gained from a numerically expensive but assumption-free method (Wavelets–PCA), and the identified metastable states are interpreted w.r.t. the blocking events in the atmosphere

Asymptotic models for planetary scale atmospheric motions

Observations indicate the existence of a large number of low-frequency (periods longer than 10 days) atmospheric regimes with planetary spatial scales (of the order of the earth's radius, ca. 6300 km) that have an important influence on the variability of the atmosphere. Further studies show that the interactions between such planetary scale flows and the synoptic eddies (characteristic length and time scales : 1000 km and 2-6 days) play a crucial role for the atmospheric dynamics. In this theses we derive reduced model equations for three planetary regimes by applying a multiple scales asymptotic method. This method allows us to take into account in a systematic way the interactions with the synoptic scales. The numerical experiments with a primitive equations model showed that two of the asymptotic regimes reproduce basic properties of the planetary scale dynamics. The Planetary Regime (PR) is characterized by isotropic planetary horizontal scales and by a corresponding advective time scale of about one week. The variations of the background potential temperature in this regime are comparable in magnitude with those adopted in the classical quasi-geostrophic (QG) theory, larger variations are assumed in the Planetary Regime with Background Flow (PRBF). In the PR we obtain as leading order model the planetary geostrophic equations (PGEs). We derive in a systematic way from the asymptotic analysis a closure for the PGEs in the form of an evolution equation for the vertically averaged (barotropic) component of the pressure. Relative to the prognostic closures adopted in existing reduced-complexity planetary models, this new dynamical closure may provide for a more realistic large scale and long term variability in future implementations. Using a two scale asymptotic ansatz, we extended the region of validity of the PR to the synoptic spatial and temporal scales. We derive modified QG equations for the dynamics on the synoptic scale as well as terms describing new interactions between the synoptic and planetary scales. In the Anisotropic Planetary Regime (APR) we investigate motions with planetary modulation in zonal direction but with a meridional extent confined to the synoptic scale, the same assumption for the background temperature as in the PR is made. As leading order model we obtain the QG model, describing the synoptic evolution of the leading order synoptic potential vorticity (PV). The second order asymptotic model describes a coupling between the planetary evolution of this leading order synoptic PV, the synoptic evolution of the planetary scale vorticity field and the synoptic dynamics of higher order PV corrections. By applying a primitive equations model, we studied the balances in the vorticity transport on the planetary and synoptic scale. The numerical experiments showed that only the PR and the APR are relevant for the earth's atmosphere. These two models helped us to understand different aspects of the dynamics on the planetary scale and they can be further employed for the construction of intermediate complexity models for long term climate simulations

Planetary geostrophic equations for the atmosphere with evolution of the barotropic flow

Atmospheric phenomena such as the quasi-stationary Rossby waves, teleconnection patterns, ultralong persistent blockings and the polar/subtropical jet are characterized by planetary spatial scales, i.e. scales of the order of the earth’s radius. This motivates our interest in the relevant physical processes acting on the planetary scales. Using an asymptotic approach, we systematically derive reduced model equations valid for atmospheric motions with planetary spatial scales and a temporal scale of the order of about 1 week. We assume variations of the background potential temperature comparable in magnitude with those adopted in the classical quasi-geostrophic theory. At leading order, the resulting equations include the planetary geostrophic balance. In order to apply these equations to the atmosphere, one has to prescribe a closure for the vertically averaged pressure. We present an evolution equation for this component of the pressure which was derived in a systematic way from the asymptotic analysis. Relative to the prognostic closures adopted in existing reduced-complexity planetary models, this new dynamical closure may provide for more realistic increased large-scale, long-time variability in future implementations

Planetary geostrophic Boussinesq dynamics: Barotropic flow, baroclinic instability and forced stationary waves

Motions on planetary spatial scales in the atmosphere are governed by the planetary geostrophic equations. However, little attention has been paid to the interaction between the baroclinic and barotropic flows within the planetary geostrophic scaling. This is the focus of the present study, which utilizes planetary geostrophic equations for a Boussinesq fluid supplemented by a novel evolution equation for the barotropic flow. The latter is affected by meridional momentum flux due to baroclinic flow and drag by the surface wind. The barotropic wind, on the other hand, affects the baroclinic flow through buoyancy advection. Via a relaxation towards a prescribed buoyancy profile the model produces realistic major features of the zonally symmetric wind and temperature fields. We show that there is considerable cancellation between the barotropic and the baroclinic surface zonal mean zonal winds. Linear and nonlinear model responses to steady diabatic zonally asymmetric forcing are investigated, and the arising stationary waves are interpreted in terms of analytical solutions. We also study the problem of baroclinic instability on the sphere within the present model. © 2019 The Authors. Quarterly Journal of the Royal Meteorological Society published by John Wiley Sons Ltd on behalf of the Royal Meteorological Society