Many scientists have made use of the wavelet method in analyzing time series, often using popular free software. However, at present there are no similar easy to use wavelet packages for analyzing two time series together. We discuss the cross wavelet transform and wavelet coher- ence for examining relationships in time frequency space be- tween two time series. We demonstrate how phase angle statistics can be used to gain confidence in causal relation- ships and test mechanistic models of physical relationships between the time series. As an example of typical data where such analyses have proven useful, we apply the methods to the Arctic Oscillation index and the Baltic maximum sea ice extent record. Monte Carlo methods are used to assess the statistical significance against red noise backgrounds. A software package has been developed that allows users to perform the cross wavelet transform and wavelet coherence (http://www.pol.ac.uk/home/research/waveletcoherence/). As we are interested in extracting low s/n ratio signals in time series we discuss only CWT in this paper. While CWT is a common tool for analyzing localized intermittent os- cillations in a time series, it is very often desirable to ex- amine two time series together that may be expected to be linked in some way. In particular, to examine whether re- gions in time frequency space with large common power have a consistent phase relationship and therefore are sug- gestive of causality between the time series. Many geophys- ical time series are not Normally distributed and we suggest methods of applying the CWT to such time series. From two CWTs we construct the Cross Wavelet Transform (XWT) which will expose their common power and relative phase in time-frequency space. We will further define a measure of Wavelet Coherence (WTC) between two CWT, which can find significant coherence even though the common power is low, and show how confidence levels against red noise back- grounds are calculated. We will present the basic CWT theory before we move on to XWT and WTC. New developments such as quanti- fying the phase relationship and calculating the WTC sig- nificance level will be treated more fully. When using the methods on time series it is important to have solid mecha- nistic foundations on which to base any relationships found, and we caution against using the methods in a "scatter-gun" approach (particularly if the time series probability density functions are modified). To illustrate how the various meth- ods are used we apply them to two data sets from meteo- rology and glaciology. Finally, we will provide links to a MatLab software package.

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Application of the cross wavelet transform and wavelet coherence to geophysical time series

The Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2), is the latest atmospheric reanalysis of the modern satellite era produced by NASA’s Global Modeling and Assimilation Office (GMAO). MERRA-2 assimilates observation types not available to its predecessor, MERRA, and includes updates to the Goddard Earth Observing System (GEOS) model and analysis scheme so as to provide a viable ongoing climate analysis beyond MERRA’s terminus. While addressing known limitations of MERRA, MERRA-2 is also intended to be a development milestone for a future integrated Earth system analysis (IESA) currently under development at GMAO. This paper provides an overview of the MERRA-2 system and various performance metrics. Among the advances in MERRA-2 relevant to IESA are the assimilation of aerosol observations, several improvements to the representation of the stratosphere including ozone, and improved representations of cryospheric processes. Other improvements in the quality of M...

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The Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2)

The NCEP Climate Forecast System Reanalysis (CFSR) was completed for the 31-yr period from 1979 to 2009, in January 2010. The CFSR was designed and executed as a global, high-resolution coupled atmosphere–ocean–land surface–sea ice system to provide the best estimate of the state of these coupled domains over this period. The current CFSR will be extended as an operational, real-time product into the future. New features of the CFSR include 1) coupling of the atmosphere and ocean during the generation of the 6-h guess field, 2) an interactive sea ice model, and 3) assimilation of satellite radiances by the Gridpoint Statistical Interpolation (GSI) scheme over the entire period. The CFSR global atmosphere resolution is ~38 km (T382) with 64 levels extending from the surface to 0.26 hPa. The global ocean's latitudinal spacing is 0.25° at the equator, extending to a global 0.5° beyond the tropics, with 40 levels to a depth of 4737 m. The global land surface model has four soil levels and the global sea ice m...

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The NCEP Climate Forecast System Reanalysis

A simple analytic model is constructed to elucidate some basic features of the response of the tropical atmosphere to diabatic heating. In particular, there is considerable east-west asymmetry which can be illustrated by solutions for heating concentrated in an area of finite extent. This is of more than academic interest because heating in practice tends to be concentrated in specific areas. For instance, a model with heating symmetric about the equator at Indonesian longitudes produces low-level easterly flow over the Pacific through propagation of Kelvin waves into the region. It also produces low-level westerly inflow over the Indian Ocean (but in a smaller region) because planetary waves propagate there. In the heating region itself the low-level flow is away from the equator as required by the vorticity equation. The return flow toward the equator is farther west because of planetary wave propagation, and so cyclonic flow is obtained around lows which form on the western margins of the heating zone. Another model solution with the heating displaced north of the equator provides a flow similar to the monsoon circulation of July and a simple model solution can also be found for heating concentrated along an inter-tropical convergence line.

Some simple solutions for heat-induced tropical circulation.

This chapter should be cited as: Myhre, G., D. Shindell, F.-M. Bréon, W. Collins, J. Fuglestvedt, J. Huang, D. Koch, J.-F. Lamarque, D. Lee, B. Mendoza, T. Nakajima, A. Robock, G. Stephens, T. Takemura and H. Zhang, 2013: Anthropogenic and Natural Radiative Forcing. In: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Stocker, T.F., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex and P.M. Midgley (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA. Coordinating Lead Authors: Gunnar Myhre (Norway), Drew Shindell (USA)

Anthropogenic and Natural Radiative Forcing

The instructor's manual to a work which introduces the fundamental principles of meteorology, explaining storm dynamics and the dynamics of climate and its global implications.

An introduction to dynamic meteorology

In the past, studies of stratosphere-troposphere exchange of mass and chemical species have mainly emphasized the synoptic- and small-scale mechanisms of exchange This review, however, includes also the global-scale aspects of exchange, such as the transport across an isentropic surface (potential temperature about 380 K) that in the tropics lies just above the tropopause, near the 100-hPa pressure level Such a surface divides the stratosphere into an “overworld” and an extratropical “lowermost stratosphere” that for transport purposes need to be sharply distinguished This approach places stratosphere-troposphere exchange in the framework of the general circulation and helps to clarify the roles of the different mechanisms involved and the interplay between large and small scales The role of waves and eddies in the extratropical overworld is emphasized There, wave-induced forces drive a kind of global-scale extratropical “fluid-dynamical suction pump,” which withdraws air upward and poleward from the tropical lower stratosphere and pushes it poleward and downward into the extratropical troposphere The resulting global-scale circulation drives the stratosphere away from radiative equilibrium conditions Wave-induced forces may be considered to exert a nonlocal control, mainly downward in the extratropics but reaching laterally into the tropics, over the transport of mass across lower stratospheric isentropic surfaces This mass transport is for many purposes a useful measure of global-scale stratosphere-troposphere exchange, especially on seasonal or longer timescales Because the strongest wave-induced forces occur in the northern hemisphere winter season, the exchange rate is also a maximum at that season The global exchange rate is not determined by details of near-tropopause phenomena such as penetrative cumulus convection or small-scale mixing associated with upper level fronts and cyclones These smaller-scale processes must be considered, however, in order to understand the finer details of exchange Moist convection appears to play an important role in the tropics in accounting for the extreme dehydration of air entering the stratosphere Stratospheric air finds its way back into the troposphere through a vast variety of irreversible eddy exchange phenomena, including tropopause folding and the formation of so-called tropical upper tropospheric troughs and consequent irreversible exchange General circulation models are able to simulate the mean global-scale mass exchange and its seasonal cycle but are not able to properly resolve the tropical dehydration process Two-dimensional (height-latitude) models commonly used for assessment of human impact on the ozone layer include representation of stratosphere-troposphere exchange that is adequate to allow reasonable simulation of photochemical processes occurring in the overworld However, for assessing changes in the lowermost stratosphere, the strong longitudinal asymmetries in stratosphere-troposphere exchange render current two-dimensional models inadequate Either current transport parameterizations must be improved, or else, more likely, such changes can be adequately assessed only by three-dimensional models

Stratosphere‐troposphere exchange

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Middle atmosphere dynamics.

The quasi-biennial oscillation (QBO) dominates the variability of the equatorial stratosphere (∼16–50 km) and is easily seen as downward propagating easterly and westerly wind regimes, with a variable period averaging approximately 28 months. From a fluid dynamical perspective, the QBO is a fascinating example of a coherent, oscillating mean flow that is driven by propagating waves with periods unrelated to that of the resulting oscillation. Although the QBO is a tropical phenomenon, it affects the stratospheric flow from pole to pole by modulating the effects of extratropical waves. Indeed, study of the QBO is inseparable from the study of atmospheric wave motions that drive it and are modulated by it. The QBO affects variability in the mesosphere near 85 km by selectively filtering waves that propagate upward through the equatorial stratosphere, and may also affect the strength of Atlantic hurricanes. The effects of the QBO are not confined to atmospheric dynamics. Chemical constituents, such as ozone, water vapor, and methane, are affected by circulation changes induced by the QBO. There are also substantial QBO signals in many of the shorter-lived chemical constituents. Through modulation of extratropical wave propagation, the QBO has an effect on the breakdown of the wintertime stratospheric polar vortices and the severity of high-latitude ozone depletion. The polar vortex in the stratosphere affects surface weather patterns, providing a mechanism for the QBO to have an effect at the Earth's surface. As more data sources (e.g., wind and temperature measurements from both ground-based systems and satellites) become available, the effects of the QBO can be more precisely assessed. This review covers the current state of knowledge of the tropical QBO, its extratropical dynamical effects, chemical constituent transport, and effects of the QBO in the troposphere (∼0–16 km) and mesosphere (∼50–100 km). It is intended to provide a broad overview of the QBO and its effects to researchers outside the field, as well as a source of information and references for specialists. The history of research on the QBO is discussed only briefly, and the reader is referred to several historical review papers. The basic theory of the QBO is summarized, and tutorial references are provided.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1999RG000073

James R. Holton

Papers

An introduction to dynamic meteorology

Stratosphere‐troposphere exchange

An introduction to dynamic meteorology

Middle atmosphere dynamics.

The quasi-biennial oscillation