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- ItemCascade-based disaggregation of continuous rainfall time series: The influence of climate(Göttingen : Copernicus GmbH, 2001) Güntner, A.; Olsson, J.; Calver, A.; Gannon, B.Rainfall data of high temporal resolution are required in a multitude of hydrological applications. In the present paper, a temporal rainfall disaggregation model is applied to convert daily time series into an hourly resolution. The model is based on the principles of random multiplicative cascade processes. Its parameters are dependent on (1) the volume and (2) the position in the rainfall sequence of the time interval with rainfall to be disaggregated. The aim is to compare parameters and performance of the model between two contrasting climates with different rainfall generating mechanisms, a semi-arid tropical (Brazil) and a temperate (United Kingdom) climate. In the range of time scales studied, the scale-invariant assumptions of the model are approximately equally well fulfilled for both climates. The model parameters differ distinctly between climates, reflecting the dominance of convective processes in the Brazilian rainfall and of advective processes associated with frontal passages in the British rainfall. In the British case, the parameters exhibit a slight seasonal variation consistent with the higher frequency of convection during summer. When applied for disaggregation, the model reproduces a range of hourly rainfall characteristics with a high accuracy in both climates. However, the overall model performance is somewhat better for the semi-arid tropical rainfall. In particular, extreme rainfall in the UK is overestimated whereas extreme rainfall in Brazil is well reproduced. Transferability of parameters in time is associated with larger uncertainty in the semi-arid climate due to its higher interannual variability and lower percentage of rainy intervals. For parameter transferability in space, no restrictions are found between the Brazilian stations whereas in the UK regional differences are more pronounced. The overall high accuracy of disaggregated data supports the potential usefulness of the model in hydrological applications.
- ItemIdentification of dynamical transitions in marine palaeoclimate records by recurrence network analysis(Göttingen : Copernicus GmbH, 2011) Donges, J.F.; Donner, R.V.; Rehfeld, K.; Marwan, N.; Trauth, M.H.; Kurths, J.The analysis of palaeoclimate time series is usually affected by severe methodological problems, resulting primarily from non-equidistant sampling and uncertain age models. As an alternative to existing methods of time series analysis, in this paper we argue that the statistical properties of recurrence networks - a recently developed approach - are promising candidates for characterising the system's nonlinear dynamics and quantifying structural changes in its reconstructed phase space as time evolves. In a first order approximation, the results of recurrence network analysis are invariant to changes in the age model and are not directly affected by non-equidistant sampling of the data. Specifically, we investigate the behaviour of recurrence network measures for both paradigmatic model systems with non-stationary parameters and four marine records of long-term palaeoclimate variations. We show that the obtained results are qualitatively robust under changes of the relevant parameters of our method, including detrending, size of the running window used for analysis, and embedding delay. We demonstrate that recurrence network analysis is able to detect relevant regime shifts in synthetic data as well as in problematic geoscientific time series. This suggests its application as a general exploratory tool of time series analysis complementing existing methods.
- ItemSpatial structures and directionalities in Monsoonal precipitation over South Asia(Göttingen : Copernicus GmbH, 2010) Malik, N.; Marwan, N.; Kurths, J.Precipitation during the monsoon season over the Indian subcontinent occurs in form of enormously complex spatiotemporal patterns due to the underlying dynamics of atmospheric circulation and varying topography. Employing methods from nonlinear time series analysis, we study spatial structures of the rainfall field during the summer monsoon and identify principle regions where the dynamics of monsoonal rainfall is more coherent or homogenous. Moreover, we estimate the time delay patterns of rain events. Here we present an analysis of two separate high resolution gridded data sets of daily rainfall covering the Indian subcontinent. Using the method of event synchronization (ES), we estimate regions where heavy rain events during monsoon happen in some lag synchronised form. Further using the delay behaviour of rainfall events, we estimate the directionalities related to the progress of such type of rainfall events. The Active (break) phase of a monsoon is characterised by an increase(decrease) of rainfall over certain regions of the Indian subcontinent. We show that our method is able to identify regions of such coherent rainfall activity.
- ItemComparison of correlation analysis techniques for irregularly sampled time series(Göttingen : Copernicus GmbH, 2011) Rehfeld, K.; Marwan, N.; Heitzig, J.; Kurths, J.Geoscientific measurements often provide time series with irregular time sampling, requiring either data reconstruction (interpolation) or sophisticated methods to handle irregular sampling. We compare the linear interpolation technique and different approaches for analyzing the correlation functions and persistence of irregularly sampled time series, as Lomb-Scargle Fourier transformation and kernel-based methods. In a thorough benchmark test we investigate the performance of these techniques. All methods have comparable root mean square errors (RMSEs) for low skewness of the inter-observation time distribution. For high skewness, very irregular data, interpolation bias and RMSE increase strongly. We find a 40 % lower RMSE for the lag-1 autocorrelation function (ACF) for the Gaussian kernel method vs. the linear interpolation scheme,in the analysis of highly irregular time series. For the cross correlation function (CCF) the RMSE is then lower by 60 %. The application of the Lomb-Scargle technique gave results comparable to the kernel methods for the univariate, but poorer results in the bivariate case. Especially the high-frequency components of the signal, where classical methods show a strong bias in ACF and CCF magnitude, are preserved when using the kernel methods. We illustrate the performances of interpolation vs. Gaussian kernel method by applying both to paleo-data from four locations, reflecting late Holocene Asian monsoon variability as derived from speleothem δ18O measurements. Cross correlation results are similar for both methods, which we attribute to the long time scales of the common variability. The persistence time (memory) is strongly overestimated when using the standard, interpolation-based, approach. Hence, the Gaussian kernel is a reliable and more robust estimator with significant advantages compared to other techniques and suitable for large scale application to paleo-data.
- ItemAn extended singular spectrum transformation (SST) for the investigation of Kenyan precipitation data(Göttingen : Copernicus GmbH, 2013) Itoh, N.; Marwan, N.In this paper a change-point detection method is proposed by extending the singular spectrum transformation (SST) developed as one of the capabilities of singular spectrum analysis (SSA). The method uncovers change points related with trends and periodicities. The potential of the proposed method is demonstrated by analysing simple model time series including linear functions and sine functions as well as real world data (precipitation data in Kenya). A statistical test of the results is proposed based on a Monte Carlo simulation with surrogate methods. As a result, the successful estimation of change points as inherent properties in the representative time series of both trend and harmonics is shown. With regards to the application, we find change points in the precipitation data of Kenyan towns (Nakuru, Naivasha, Narok, and Kisumu) which coincide with the variability of the Indian Ocean Dipole (IOD) suggesting its impact of extreme climate in East Africa.
- ItemLong-term changes in the north-south asymmetry of solar activity: A nonlinear dynamics characterization using visibility graphs(Göttingen : Copernicus GmbH, 2014) Zou, Y.; Donner, R.V.; Marwan, N.; Small, M.; Kurths, J.Solar activity is characterized by complex dynamics superimposed onto an almost periodic, approximately 11-year cycle. One of its main features is the presence of a marked, time-varying hemispheric asymmetry, the deeper reasons for which have not yet been completely uncovered. Traditionally, this asymmetry has been studied by considering amplitude and phase differences. Here, we use visibility graphs, a novel tool of nonlinear time series analysis, to obtain complementary information on hemispheric asymmetries in dynamical properties. Our analysis provides deep insights into the potential and limitations of this method, revealing a complex interplay between factors relating to statistical and dynamical properties, i.e., effects due to the probability distribution and the regularity of observed fluctuations. We demonstrate that temporal changes in the hemispheric predominance of the graph properties lag those directly associated with the total hemispheric sunspot areas. Our findings open a new dynamical perspective on studying the north-south sunspot asymmetry, which is to be further explored in future work.
- ItemCorrelation-Based characterisation of time-Varying dynamical complexity in the Earth's magnetosphere(Göttingen : Copernicus GmbH, 2013) Donner, R.V.; Balasis, G.The dynamical behaviour of the magnetosphere is known to be a sensitive indicator for the response of the system to solar wind coupling. Since the solar activity commonly displays very interesting non-stationary and multi-scale dynamics, the magnetospheric response also exhibits a high degree of dynamical complexity associated with fundamentally different characteristics during periods of quiescence and magnetic storms. The resulting temporal complexity profile has been explored using several approaches from applied statistics, dynamical systems theory and statistical mechanics. Here, we propose an alternative way of looking at time-varying dynamical complexity of nonlinear geophysical time series utilising subtle but significant changes in the linear autocorrelation structure of the recorded data. Our approach is demonstrated to sensitively trace the dynamic signatures associated with intense magnetic storms, and to display reasonable skills in distinguishing between quiescence and storm periods. The potentials and methodological limitations of this new viewpoint are discussed in some detail.