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Extreme convective precipitation events are among the most severe hazards in central Europe and are expected to intensify under global warming. However, the degree of intensification and the underlying processes are still uncertain. In this thesis, recent advances in continuous, radar-based precipitation monitoring and convection-permitting climate modeling are used to investigate Lagrangian properties of convective rain cells such as precipitation intensity, cell area, and precipitation sum and their relationship to large-scale, environmental conditions.
Firstly, convective precipitation objects are tracked in a gauge-adjusted radar-data set and the properties of these cells are related to large-scale environmental variables to investigate the observed super-Clausius-Clapeyron (CC) scaling of convective extreme precipitation. The Lagrangian precipitation sum of convective cells increases with dew point temperature at rates well above the CC-rate with increasing rates for higher dew point temperatures. These varying, high rates are caused by a covarying increase of CAPE with dew point temperature as well as the effect of high vertical wind shear causing an increase in cell area and thus precipitation sum. At the same time, cells move faster at high vertical wind shear so that Eulerian scaling rates are lower than Lagrangian but still above the CC-rate. The results show that wind shear and static instability need to be taken into account when transferring precipitation scaling under current climate conditions to future conditions. Secondly, the representation of convective cell properties in the convection-permitting climate model COSMO-CLM is evaluated. The model can simulate the observed frequency distributions of cell properties such as lifetime, area, mean and maximum intensity, and precipitation sum. The increase of area and intensity with lifetime is also well captured despite an underestimation of the intensity of the most severe cells. Furthermore, the model can represent the temperature scaling of intensity, area, and precipitation sum but fails to simulate the observed increase of lifetime. Thus, the model is suitable to study climatologies of convective storms in Germany. Thirdly, two COSMO-CLM projections at the end of the century under emission scenario RCP8.5 were investigated. While the number of convective cells and their lifetime remain approximately constant compared to present conditions, intensity and area increase strongly. The relative increase of intensity and area is largest for the highest percentiles meaning that extreme events intensify the most. The characteristic afternoon maximum of convective precipitation is damped, and shifted to later times of day which leads to an increase of nighttime precipitation in the future. Scaling rates of cell properties with dew point temperature are nearly identical in present and future in the simulation driven by the EC-Earth model which means that the upper limit of cell properties like intensity, area, and precipitation sum could be predicted from near-surface dew point temperature. However, this result could not be reproduced by the simulation driven by MIROC5 and needs further investigation.
Derivation and characterization of a new filter for nonlinear high-dimensional data assimilation
(2015)
Data assimilation (DA) combines model forecasts with real-world observations to achieve an optimal estimate of the state of a dynamical system. The quality of predictions in nonlinear and chaotic systems such as atmospheric or oceanic circulation is strongly sensitive to the initial conditions. Therefore, beyond the consistent reconstruction of past states, a primary relevance of advanced DA methods concerns the proper model initialization. The ensemble Kalman filter (EnKF) and its deterministic variants, mostly square root filters such as the ensemble transform Kalman filter (ETKF), represent a popular alternative to variational DA schemes. They are applied in a wide range of research and operations. Their forecast step employs an ensemble integration that fully respects the nonlinear nature of the analyzed system. In the analysis step, they implicitly assume the prior state and observation errors to be Gaussian. Consequently, in nonlinear systems, the mean and covariance of the analysis ensemble are biased and these filters remain suboptimal. In contrast, the fully nonlinear, non-Gaussian particle filter (PF) relies on Bayes' theorem without further assumptions, which guarantees an exact asymptotic behavior. However, it is exposed to weight collapse, particularly in higher-dimensional settings, known as the curse of dimensionality.
This work presents a new method to obtain an analysis ensemble with mean and covariance that exactly match the corresponding Bayesian estimates. This is achieved by a deterministic matrix square root transformation of the forecast ensemble, and subsequently a suitable random rotation that significantly contributes to filter stability while preserving the required second-order statistics. The forecast step remains as in the ETKF. The algorithm, which is fairly easy to implement and computationally efficient, is referred to as the nonlinear ensemble transform filter (NETF). The limitation with respect to fully-nonlinear filtering is that the NETF only considers the mean and covariance of the Bayesian analysis density, neglecting higher-order moments.
The properties and performance of the proposed algorithm are investigated via a set of experiments. The results indicate that such a filter formulation can increase the analysis quality, even for relatively small ensemble sizes, compared to other ensemble filters in nonlinear, non-Gaussian scenarios. They also confirm that localization enhances the applicability of this PF-inspired scheme in larger-dimensional systems. Finally, the novel filter is coupled to a large-scale ocean general circulation model with a realistic observation scenario. The NETF remains stable with a small ensemble size and shows a consistent behavior. Additionally, its analyses exhibit low estimation errors, as revealed by a comparison with a free ensemble integration and the ETKF. The results confirm that, in principle, the filter can be applied successfully and as simple as the ETKF in high-dimensional problems. No further modifications are needed, even though the algorithm is only based on the particle weights. Thus, it is able to overcome the curse of dimensionality, even in deterministic systems. This proves that the NETF constitutes a promising and user-friendly method for nonlinear high-dimensional DA.
The climate system is one of the classical examples of a complex dynamical system consisting of interacting sub-systems through mass, momentum, and energy exchange across various spatial and temporal scales. This thesis aims to detect and quantify sub-component interactions from an information exchange (IE) perspective. For this purpose, IE estimators derived from information theory are explored and applied to the available climate data obtained from observations, reanalysis, global and regional climate models. Specifically, this thesis investigates the usefulness of information theory methods for process-oriented climate model evaluation.
Firstly, methods derived from the concepts of information theory such as transfer entropy and information flow along with their linear and non-linear estimation techniques are initially tested and applied to idealized two-dimensional dynamical systems. The results revealed an expected direction and magnitude of IE providing insights into underlying dynamics. However, as expected the linear estimators are robust for linear systems but fail for non-linear systems. Though the non-linear estimators (kernel and kraskov) showed expected results for all the idealized systems, their free tuning parameters are to be tested for consistent results. Moreover, these methods are sensitive to the available time series length.
A real world example case study involving the dynamics between the Indian and Pacific oceans revealed a physically consistent bi-directional IE. However, unexpected IE was detected in the example of North Atlantic and European air temperatures indicating hidden drivers. Though IE provides insights into system dynamics, the availability of time series length and the system at hand must be carefully taken into account before inferring any possible interpretations of the results.
Quantifying the IE from El-Ni\~{n}o southern oscillation (ENSO) and Indian Ocean Dipole (IOD) to the Indian Summer Monsoon Rainfall (ISMR) with the observational and reanalysis data sets revealed that both ENSO and IOD are synergistic predictors for the inter-annual variability of the ISMR over central India i.e., the monsoon core region. Though the investigated three Global Climate Models (GCM) could not reveal the underlying IE dynamics of ENSO, IOD, and ISMR, a Regional Climate Model (RCM) simulation downscaling one of the GCMs with realistic large scale signals across the lateral boundaries showed good agreement with the observations.
Evaluating a coupled regional climate modeling system driven by two different global data sets with IE estimators revealed significant differences between the process chains linking the north-west Mediterranean sea surface temperatures, evaporation, wind speed, and the Vb-cyclone induced precipitation over Danube, Odra, and Elbe catchments in the historical period (1951-2005). Detailed investigation revealed that the north-west Mediterranean Sea in the coupled regional simulation driven by ERA-20C reanalysis corresponded to the Vb-cyclone precipitation over the three catchments while no such correspondence is noted in the EC-EARTH driven simulation. This discrepancy is attributed to the inheritance of the simulation biases from GCM into the RCM. In the future period (1965-2099), no significant changes in the processes are noted from the simulation.
Overall, this thesis used IE estimators in investigating the underlying dynamics of climate system and climate models. The estimators proved useful in providing insights into climate system dynamics assisting in a process based climate model evaluation.