Christian L. E. Franzke

Stochastic climate theory and modeling

Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as subgrid-scale parameterizations (SSPs) as well as for model error representation, uncertainty quantification, data assimilation, and ensemble prediction. The need to use stochastic approaches in weather and climate models arises because we still cannot resolve all necessary processes and scales in comprehensive numerical weather and climate prediction models. In many practical applications one is mainly interested in the largest and potentially predictable scales and not necessarily in the small and fast scales. For instance, reduced order models can simulate and predict large-scale modes. Statistical mechanics and dynamical systems theory suggest that in reduced order models the impact of unresolved degrees of freedom can be represented by suitable combinations of deterministic and stochastic components and non-Markovian (memory) terms. Stochastic approaches in numerical weather and climate prediction models also lead to the reduction of model biases. Hence, there is a clear need for systematic stochastic approaches in weather and climate modeling. In this review, we present evidence for stochastic effects in laboratory experiments. Then we provide an overview of stochastic climate theory from an applied mathematics perspective. We also survey the current use of stochastic methods in comprehensive weather and climate prediction models and show that stochastic parameterizations have the potential to remedy many of the current biases in these comprehensive models.

Stochastic parameterization: Towards a new view of weather and climate models

AbstractThe last decade has seen the success of stochastic parameterizations in short-term, medium-range, and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to represent model inadequacy better and to improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides better estimates of uncertainty, but it is also extremely promising for reducing long-standing climate biases and is relevant for determining the climate response to external forcing. This article highlights recent developments from different research groups that show that the stochastic representation of unresolved processes in the atmosphere, oceans, land surface, and cryosphere of comprehensive weather and climate models 1) gives rise to more reliable probabilistic forecasts of weather and climate and 2) reduces systematic model bias. We make a case that the use of mathematically stri...

Contrasting interannual and multidecadal NAO variability

Decadal and longer timescale variability in the winter North Atlantic Oscillation (NAO) has considerable impact on regional climate, yet it remains unclear what fraction of this variability is potentially predictable. This study takes a new approach to this question by demonstrating clear physical differences between NAO variability on interannual-decadal (<30 year) and multidecadal (>30 year) timescales. It is shown that on the shorter timescale the NAO is dominated by variations in the latitude of the North Atlantic jet and storm track, whereas on the longer timescale it represents changes in their strength instead. NAO variability on the two timescales is associated with different dynamical behaviour in terms of eddy-mean flow interaction, Rossby wave breaking and blocking. The two timescales also exhibit different regional impacts on temperature and precipitation and different relationships to sea surface temperatures. These results are derived from linear regression analysis of the Twentieth Century and NCEP-NCAR reanalyses and of a high-resolution HiGEM General Circulation Model control simulation, with additional analysis of a long sea level pressure reconstruction. Evidence is presented for an influence of the ocean circulation on the longer timescale variability of the NAO, which is particularly clear in the model data. As well as providing new evidence of potential predictability, these findings are shown to have implications for the reconstruction and interpretation of long climate records.

The role of the Sun in long‐term change in the F2 peak ionosphere: New insights from EEMD and numerical modeling

We applied Ensemble Empirical Mode Decomposition (EEMD) for the first time to ionosonde data to study trends in the critical frequency of the F2 peak, foF2, and its height, hmF2, from 1959 to 2005. EEMD decomposes a time series into several quasi-cyclical components, called Intrinsic Mode Functions (IMFs), and a residual, which can be interpreted as a long-term trend. In contrast to the more commonly used linear regression-based trend analysis, EEMD makes no assumptions on the functional form of the trend and no separate correction for the influence of solar activity variations is needed. We also adopted a more rigorous significance testing procedure with less restrictive underlying assumptions than the F-test, which is normally used as part of a linear regression-based trend analysis. EEMD analysis shows that trends in hmF2 and foF2 between 1959 and 2005 are mostly highly linear, but the F-test tends to overestimate the significance of trends in hmF2 and foF2 in 30% and 25% of cases, respectively. EEMD-based trends are consistently more negative than linear regression-based trends, by 30-35% for hmF2 and about 50% for foF2. This may be due to the different treatment of the influence of a long-term decrease in solar activity from 1959 to 2005. We estimate the effect of this decrease in solar activity with two different data-based methods as well as using numerical model simulations. While these estimates vary, all three methods demonstrate a larger relative influence of the Sun on trends in foF2 than on trends in hmF2.

Low-frequency nonlinearity and regime behavior in the Northern Hemisphere extratropical atmosphere

The extra-tropical atmosphere is characterized by robust circulations which have time scales longer than that associated with developing baroclinic systems but shorter than a season. Such low frequency variability is governed to a large extent by non-linear dynamics, and hence is chaotic. A useful aspect of this low-frequency circulation is that it can often be described by just a few quasi-stationary regime states, broadly defined as recurrent or persistent large scale structures, that exert a significant impact on the probability of experiencing extreme surface weather conditions. We review a variety of techniques for identifying circulation regimes from reanalysis and numerical model output. While various techniques often yield similar regime circulation patterns, they offer different perspectives on the regimes. The regimes themselves are manifest in planetary scale patterns. They affect the structure of synoptic scale patterns. Extra-tropical flow regimes have been identified in simplified atmospheric models and comprehensive coupled climate models and in reanalysis data sets. It is an ongoing challenge to accurately model these regime states and high horizontal resolutions are often needed to accurately reproduce them. The regime paradigm helps to understand the response to external forcing on a variety of time scales, has been helpful in categorizing a large number of weather types and their effect on local conditions, and is useful in downscaling. Despite their usefulness, there is a debate on the non-equivocal and systematic existence of these nonlinear circulation regimes. We review our current understanding of the nonlinear and regime paradigms and suggest future research.

On the dynamics of persistent states and their secular trends in the waveguides of the Southern Hemisphere troposphere

We identify the dynamical drivers of systematic changes in persistent quasi-stationary states (regimes) of the Southern Hemisphere troposphere and their secular trends. We apply a purely data-driven approach, whereby a multiscale approximation to nonstationary dynamical processes is achieved through optimal sequences of locally stationary fast vector autoregressive factor processes, to examine a high resolution atmospheric reanalysis over the period encompassing 1958–2013. This approach identifies regimes and their secular trends in terms of the predictability of the flow and is Granger causal. A comprehensive set of diagnostics on both isentropic and isobaric surfaces is employed to examine teleconnections over the full hemisphere and for a set of regional domains. Composite states for the hemisphere obtained from nonstationary nonparametric cluster analysis reveal patterns consistent with a circumglobal wave 3 (polar)–wave 5 (subtropical) pattern, while regional composites reveal the Pacific South American pattern and blocking modes. The respective roles of potential vorticity sources, stationary Rossby waves and baroclinic instability on the dynamics of these circulation modes are shown to be reflected by the seasonal variations of the waveguides, where Rossby wave sources and baroclinic disturbances are largely contained within the waveguides and with little direct evidence of sustained remote tropical influences on persistent synoptic features. Warm surface temperature anomalies are strongly connected with regions of upper level divergence and anticyclonic Rossby wave sources. The persistent states identified reveal significant variability on interannual to decadal time scales with large secular trends identified in all sectors apart from a region close to South America.

Systematic physics constrained parameter estimation of stochastic differential equations

A systematic Bayesian framework is developed for physics constrained parameter inference of stochastic differential equations (SDE) from partial observations. Physical constraints are derived for stochastic climate models but are applicable for many fluid systems. A condition is derived for global stability of stochastic climate models based on energy conservation. Stochastic climate models are globally stable when a quadratic form, which is related to the cubic nonlinear operator, is negative definite. A new algorithm for the efficient sampling of such negative definite matrices is developed and also for imputing unobserved data which improve the accuracy of the parameter estimates. The performance of this framework is evaluated on two conceptual climate models.

Research Article. On memory, dimension, and atmospheric teleconnections

Abstract Using reanalysed atmospheric data and applying a data-driven multiscale approximation to non-stationary dynamical processes, we undertake a systematic examination of the role of memory and dimensionality in defining the quasi-stationary states of the troposphere over the recent decades. We focus on the role of teleconnections characterised by either zonally-oriented wave trains or meridional dipolar structures. We consider the impact of various strategies for dimension reduction based on principal component analysis, diagonalization and truncation.We include the impact of memory by consideration of Bernoulli, Markovian and non-Markovian processes. We a priori explicitly separate barotropic and baroclinic processes and then implement a comprehensive sensitivity analysis to the number and type of retained modes. Our results show the importance of explicitly mitigating the deleterious impacts of signal degradation through ill-conditioning and under sampling in preference to simple strategies based on thresholds in terms of explained variance. In both hemispheres, the results obtained for the dominant tropospheric modes depend critically on the extent to which the higher order modes are retained, the number of free model parameters to be fitted, and whether memory effects are taken into account. Our study identifies the primary role of the circumglobal teleconnection pattern in both hemispheres for Bernoulli and Markov processes, and the transient nature and zonal structure of the Southern Hemisphere patterns in relation to their Northern Hemisphere counterparts. For both hemispheres, overfitted models yield structures consistent with the major teleconnection modes (NAO, PNA and SAM), which give way to zonally oriented wavetrains when either memory effects are ignored or where the dimension is reduced via diagonalising. Where baroclinic processes are emphasised, circumpolar wavetrains are manifest.

Systematic decomposition of the Madden-Julian Oscillation into balanced and inertio-gravity components

We present a new method for the three-dimensional multivariate decomposition of the MJO into balanced and inertio-gravity (IG) components. The method analyzes global fields with no filtering involved and it provides a quantitative comparison between the contribution of the Rossby, Kelvin and other balanced and IG modes to the MJO circulation and its teleconnections. n nResults based on the ERA Interim reanalysis data and the multivariate MJO index show that the Rossby mode with the lowest meridional index is the largest contributor to the MJO circulation over the Pacific. A smaller role of the Kelvin mode is diagnosed over the Indian ocean and the maritime continent. The MJO teleconnections in the polar stratosphere appear associated with the leading balanced vertical modes. n nThe presented method shows new ways of evaluating the MJO structure and its global impacts in weather and climate models.

Local trend disparities of European minimum and maximum temperature extremes

Ecosystems and societies are highly vulnerable to extreme temperatures and to changes in the range of temperatures at local scales. Here I will show how trends in warm and cold extremes have evolved over the last six decades in Europe on local scales. Comparing the slopes of two extreme quantiles demonstrates that there are significant disparities in trends of cold and warm temperature extremes at many locations in Europe. At some locations the range of extreme cold and hot temperatures increases, while at other locations it decreases. These results suggest that at some locations both warm and cold extremes intensify which seems to be contradictory to the prevailing view of global warming in which both cold and warm temperatures are expected to increase.