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Jeremiah P. Sjoberg and Thomas Birner

Abstract

The amplitude of upward-propagating tropospherically forced planetary waves is known to be of first-order importance in producing sudden stratospheric warmings (SSWs). This forcing amplitude is observed to undergo strong temporal fluctuations. Characteristics of the resulting transient forcing leading to SSWs are studied in reanalysis data and in highly truncated simple models of stratospheric wave–mean flow interaction. It is found in both the reanalysis data and the simple models that SSWs are preferentially generated by transient forcing of sufficiently long time scales (on the order of 1 week or longer). The time scale of the transient forcing is found to play a stronger role in producing SSWs than the strength of the forcing. In the simple models it is possible to fix the amplitude of the tropospheric forcing but to vary the time scale of the forcing. The resulting frequency of occurrence of SSWs shows dramatic reductions for decreasing forcing time scales.

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Jeremiah P. Sjoberg and Thomas Birner

Abstract

A classic result of studying stratospheric wave–mean flow interactions presented by Holton and Mass is that, for constant incoming wave forcing (at a notional tropopause), a vacillating stratospheric response may ensue. Simple models, such as the Holton–Mass model, typically prescribe the incoming wave forcing in terms of geopotential perturbation, which is not a proxy for upward wave activity flux. Here, the authors reformulate the Holton–Mass model such that incoming upward wave activity flux is prescribed. The Holton–Mass model contains a positive wave–mean flow feedback whereby wave forcing decelerates the mean flow, allowing enhanced wave propagation, which then further decelerates the mean flow, etc., until the mean flow no longer supports wave propagation. By specifying incoming wave activity flux, this feedback is constrained to the model interior. Bistability—where the zonal wind may exist at one of two distinct steady states for a given incoming wave forcing—is maintained in this reformulated model. The model is perturbed with transient pulses of upward wave activity flux to produce transitions between the two stable states. A minimum of integrated incoming wave activity flux necessary to force these sudden stratospheric warming–like transitions exists for pulses with time scales on the order of 10 days, arising from a wave time scale internal to the model at which forcing produces the strongest mean-flow response. The authors examine how the tropopause affects the internal feedback for this model setup and find that the tropopause inversion layer may potentially provide an important source of wave activity in the lower stratosphere.

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Jeremiah P. Sjoberg, Richard A. Anthes, and Therese Rieckh

Abstract

The three-cornered hat (3CH) method, which was originally developed to assess the random errors of atomic clocks, is a means for estimating the error variances of three different data sets. Here we give an overview of the historical development of the 3CH and select other methods for estimating error variances that use either two or three data sets. We discuss similarities and differences between these methods and the 3CH method.

This study assesses the sensitivity of the 3CH method to the factors that limit its accuracy, including sample size, outliers, different magnitudes of errors between the data sets, biases, and unknown error correlations. Using simulated data sets for which the errors and their correlations among the data sets are known, this analysis shows the conditions under which the 3CH method provides the most and least accurate estimates. The effect of representativeness errors caused by differences in vertical resolution of data sets is investigated. These representativeness errors are generally small relative to the magnitude of the random errors in the data sets, and the impact of this source of errors can be reduced by appropriate filtering.

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