Wavelet analysis for non-stationary, non-linear time series

Methods for detecting and quantifying nonlinearities in nonstationary time series are introduced and developed. In particular, higher-order wavelet analysis was applied to an ideal time series and the Quasi-biennial Oscillation (QBO) time series. Multiple-testing problems inherent in wavelet analysis were addressed by controlling the false discovery rate. A new local autobicoherence spectrum facilitated the detection of local nonlinearities and the quantification of cycle geometry. The local autobicoherence spectrum of the QBO time series showed that the QBO time series contained a mode with a period of 28 months that was phase-coupled to a harmonic with a period of 14 months. An additional nonlinearly interacting triad was found among modes with periods of 10, 16, 26 months. Local biphase spectra determined that the nonlinear interactions were not quadratic and that the effect of the nonlinearities was to produce non-smoothly varying oscillations. The oscillations were found to be skewed so that negative QBO regimes were preferred, and also asymmetric in the sense that phase transitions between the easterly and westerly phases occurred more rapidly than those from westerly to easterly regimes.

Theoretical comparison of subgrid turbulence in the atmosphere and ocean

Due to the massive disparity between the largest and smallest eddies in the atmosphere and ocean, it is not possible to simulate these flows by explicitly resolving all scales on a computational grid. Instead the large scales are explicitly resolved, and the interactions between the unresolved subgrid turbulence and large resolved scales are parameterised. If these interactions are not properly represented then an increase in resolution will not necessarily improve the accuracy of the large scales. This has been a significant and long standing problem since the earliest climate simulations. Historically subgrid models for the atmosphere and ocean have been developed in isolation, with the structure of each motivated by different physical phenomena. Here we solve the turbulence closure problem by determining the parameterisation coefficients (eddy viscosities) from the subgrid statistics of high resolution quasi-geostrophic atmospheric and oceanic simulations. These subgrid coefficients are characterised into a set of simple unifying scaling laws, for truncations made within the enstrophy cascading inertial range. The ocean additionally has an inverse energy cascading range, within which the subgrid model coefficients have alternative scaling properties. Simulations adopting these scaling laws are shown to reproduce the statistics of the reference benchmark simulations across resolved scales, with orders of magnitude improvement in computational efficiency. This reduction in both resolution dependence and computational effort will improve the efficiency and accuracy of geophysical research and operational activities that require data generated by general circulation models, including: weather, seasonal and climate prediction; transport studies; and understanding natural variability and extreme events.

Static behaviour of induced seismicity

The standard paradigm to describe seismicity induced by fluid injection is to apply nonlinear diffusion dynamics in a poroelastic medium. I show that the spatiotemporal behaviour and rate evolution of induced seismicity can, instead, be expressed by geometric operations on a static stress field produced by volume change at depth. I obtain laws similar in form to the ones derived from poroelasticity while requiring a lower description length. Although fluid flow is known to occur in the ground, it is not pertinent to the behaviour of induced seismicity. The proposed model is equivalent to the static stress model for tectonic foreshocks generated by the Non-Critical Precursory Accelerating Seismicity Theory. This study hence verifies the explanatory power of this theory outside of its original scope.

A local particle filter for high dimensional geophysical systems

A local particle filter (LPF) is introduced that outperforms traditional ensemble Kalman filters in highly nonlinear/non-Gaussian scenarios, both in accuracy and computational cost. The standard Sampling Importance Resampling (SIR) particle filter is augmented with an observation-space localization approach, for which an independent analysis is computed locally at each gridpoint. The deterministic resampling approach of Kitagawa is adapted for application locally and combined with interpolation of the analysis weights to smooth the transition between neighboring points. Gaussian noise is applied with magnitude equal to the local analysis spread to prevent particle degeneracy while maintaining the estimate of the growing dynamical instabilities. The approach is validated against the Local Ensemble Transform Kalman Filter (LETKF) using the 40-variable Lorenz-96 model. The results show that: (1) the accuracy of LPF surpasses LETKF as the forecast length increases (thus increasing the degree of nonlinearity), (2) the cost of LPF is significantly lower than LETKF as the ensemble size increases, and (3) LPF prevents filter divergence experienced by LETKF in cases with non-Gaussian observation error distributions.

Recent seismic activity at Cephalonia island (Greece): a study through candidate electromagnetic precursors in terms of nonlinear dynamics

The preparation process of two recent earthquakes (EQs) occurred in Cephalonia (Kefalonia) island, Greece, (38.22° N, 20.53° E), 26 January 2014, Mw =6.0, depth =21 km, and (38.25° N, 20.39° E), 3 February 2014, Mw =5.9, depth =10 km, respectively, is studied in terms of the critical dynamics revealed in observables of the involved non-linear processes. Specifically, we show, by means of the method of critical fluctuations (MCF), that signatures of critical, as well as tricritical, dynamics were embedded in the fracture-induced electromagnetic emissions (EME) recorded by two stations in locations near the epicenters of these two EQs. It is worth noting that both, the MHz EME recorded by the telemetric stations on the island of Cephalonia and the neighboring island of Zante (Zakynthos), reached simultaneously critical condition a few days before the occurrence of each earthquake. The critical characteristics embedded in the EME signals were further verified using the natural time (NT) method. Moreover, we show, in terms of the NT method, that the foreshock seismic activity also presented critical characteristics before each one of these events. Importantly, the revealed critical process seems to be focused on the area corresponding to the west Cephalonia zone, following the seismotectonic and hazard zoning of the Ionian Islands area near Cephalonia.

Power law distributions of wildfires across Europe: benchmarking a land surface model with observed data

Monthly wildfire burned area frequency is here modeled with a power law distribution and scaling exponent across different European biomes are estimated. Data sets, spanning from 2000 to 2009, comprehend the inventory of monthly burned areas from the European Forest Fire Information System (EFFIS) and simulated monthly burned areas from a recent parameterization of a Land Surface Model (LSM), that is the Community Land Model (CLM). Power law exponents are estimated with a Maximum Likelihood Estimation (MLE) for different European biomes. The characteristic fire size (CFS), i.e. the area that most contributes to the total burned area, was also calculated both from EFFIS and CLM data set. We used the power law fitting and the CFS analysis to benchmark CLM model against the EFFIS observational wildfires data set available for Europe. Results for the EFFIS data showed that power law fittings holds for 2–3 orders of magnitude in the Boreal and Continental ecoregions, whereas the distribution of the Alpine, Atlantic are fitted only in the upper tail. Power law instead is not a suitable model for fitting CLM simulations. CLM benchmarking analysis showed that the model strongly overestimates burned areas and fails in reproducing size-frequency distribution of observed EFFIS wildfires. This benchmarking analysis showed that some refinements in CLM structure (in particular regarding the anthropogenic influence) are needed for predicting future wildfires scenarios, since the low spatial resolution of the model and differences in relative frequency of small and large fires can affect the reliability of the predictions.

Study of the overturning length scales at the Spanish planetary boundary layer

The focus of this paper is to analyze the behaviour of the maximum Thorpe displacement (dT)max and the Thorpe scale LT at the atmospheric boundary layer (ABL), extending previous research with new data and improving our studies related to the novel use of the Thorpe method applied to ABL. The maximum Thorpe displacements varies between −900 and 950 m for the different field campaigns. The Thorpe scale LT ranges between 0.2 and 680 m for the different data sets which cover different stratified mixing conditions (turbulence sher-driven and convective regions). We analyze the relation between dT)max and the Thorpe scale LT and we deduce that they verify a power law. We also deduce that there is a difference in exponents of the power laws for convective conditions and shear-driven conditions. This different power laws could identify overturns created under different mechanisms.

Complex environmental beta-plane turbulence: laboratory experiments with altimetric imaging velocimetry

Results from the spectral analyses of the flows in two experiments where turbulent flows were generated in a rotating tank with topographic β-effect, are presented. The flows were forced either by heating water from below or supplying fresh water at the top of saline layer. The flow was essentially barotropic in the first experiment and baroclinic in the second experiment. The gradient of the surface elevation was measured using optical altimetry (Altimetric Imaging Velocimetry). Multiple zonal jets of alternating direction were observed in both experiments. Turbulent cascades of energy exhibit certain universal properties in spite of the different nature of flows in the experiments.

Predicting climate extremes – a complex network approach

Regional decadal predictions have emerged in the past few years as a research field with high application potential, especially for extremes like heat and drought periods. However, up to now the prediction skill of decadal hindcasts, as evaluated with standard methods is moderate, and for extreme values even rarely investigated. In this study, we use hindcast data from a regional climate model (CCLM) for 8 regions in Europe to construct time evolving climate networks and use the network correlation threshold (link strength) as a predictor for heat periods. We show that the skill of the network measure to predict the low frequency dynamics of heat periods is similar to the one of the standard approach, with the potential of being even better in some regions.

Wavelet analysis of the singular spectral reconstructed time series to study the imprints of Solar–ENSO–Geomagnetic activity on Indian climate

In order to study the imprints of solar–ENSO–geomagnetic activity on the Indian Subcontinent, we have applied the Singular Spectral Analysis (SSA) and wavelet analysis to the tree ring temperature variability record from the western Himalayas. The data used in the present study are the Solar Sunspot Number (SSN), Geomagnetic Indices (aa Index), Southern Oscillation Index (SOI) and tree ring temperature record from western Himalayas (WH), for the period of 1876–2000. The SSA and wavelet spectra reveal the presence of 5 years short term ENSO variations to 11 year solar cycle indicating the influence of both the solar–geomagnetic and ENSO imprints in the tree ring data. The presence of 33-year cycle periodicity suggests the Sun-temperature variability probably involving the induced changes in the basic state of the atmosphere. Our wavelet analysis for the SSA reconstructed time series agrees with our previous results and also enhance the amplitude of the signals by removing the noise and showing a strong influence of solar–geomagnetic and ENSO patterns throughout the record. The solar flares are considered to be responsible for cause in the circulation patterns in the atmosphere. The net effect of solar–geomagnetic processes on temperature record thus appears to be the result of counteracting influences on shorter (about 5–6 years) and longer (about 11–12 years) time scales. The present analysis thus suggests that the influence of solar processes on Indian temperature variability operates in part indirectly through ENSO, but on more than one time scale. The analyses hence provides credible evidence for teleconnections of tropical pacific climatic variability with Indian climate ranging from interannual-decadal time scales and also demonstrate the possible role of exogenic triggering in reorganizing the global earth–ocean–atmospheric systems.