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In atmospheric sciences, sizes of data sets grow continuously due to increasing resolutions. A central task is the comparison of spatiotemporal fields, to assess different simulations and to compare simulations with observations. A significant information reduction is possible by focusing on geometric-topological features of the fields or on derived meteorological objects. Due to the huge size of the data sets, spatial features have to be extracted in time slices and traced over time. Fields with chaotic component, i.e. without 1:1 spatiotemporal correspondences, can be compared by looking upon statistics of feature properties. Feature extraction, however, requires a clear mathematical definition of the features - which many meteorological objects still lack. Traditionally, object extractions are often heuristic, defined only by implemented algorithms, and thus are not comparable. This work surveys our framework designed for efficient development of feature tracking methods and for testing new feature definitions. The framework supports well-established visualization practices and is being used by atmospheric researchers to diagnose and compare data.

Given a time-dependent stochastic process with trajectories x(t) in a space $\Omega$, there may be sets such that the corresponding trajectories only very rarely cross the boundaries of these sets. We can analyze such a process in terms of metastability or coherence. Metastable sets M are defined in space $M\subset\Omega$, coherent sets $M(t)\subset\Omega$ are defined in space and time. Hence, if we extend the space by the time-variable t, coherent sets are metastable sets in $\Omega\times[0,\infty]$. This relation can be exploited, because there already exist spectral algorithms for the identification of metastable sets. In this article we show that these well-established spectral algorithms (like PCCA+) also identify coherent sets of non-autonomous dynamical systems. For the identification of coherent sets, one has to compute a discretization (a matrix T) of the transfer operator of the process using a space-timediscretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application.

In atmospheric sciences, sizes of data sets grow continuously due to increasing resolutions. A central task is the comparison of spatiotemporal fields, to assess different simulations and to compare simulations with observations. A significant information reduction is possible by focusing on geometric-topological features of the fields or on derived meteorological objects. Due to the huge size of the data sets, spatial features have to be extracted in time slices and traced over time. Fields with chaotic component, i.e. without 1:1 spatiotemporal correspondences, can be compared by looking upon statistics of feature properties. Feature extraction, however, requires a clear mathematical definition of the features – which many meteorological objects still lack. Traditionally, object extractions are often heuristic, defined only by implemented algorithms, and thus are not comparable. This work surveys our framework designed for efficient development of feature tracking methods and for testing new feature definitions. The framework supports well-established visualization practices and is being used by atmospheric researchers to diagnose and compare data.

In this article, we show that these well-established spectral algorithms (like PCCA+, Perron Cluster Cluster Analysis) also identify coherent sets of non-autonomous dynamical systems. For the identification of coherent sets, one has to compute a discretization (a matrix T) of the transfer operator of the process using a space-time-discretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application.

Evaluation of forecasts by accuracy and spread in the MiKlip decadal climate prediction system
(2016)

We present the evaluation of temperature and precipitation forecasts obtained with the MiKlip decadal climate prediction system. These decadal hindcast experiments are verified with respect to the accuracy of the ensemble mean and the ensemble spread as a representative for the forecast uncertainty. The skill assessment follows the verification framework already used by the decadal prediction community, but enhanced with additional evaluation techniques like the logarithmic ensemble spread score. The core of the MiKlip system is the coupled Max Planck Institute Earth System Model. An ensemble of 10 members is initialized annually with ocean and atmosphere reanalyses of the European Centre for Medium-Range Weather Forecasts. For assessing the effect of the initialization, we compare these predictions to uninitialized climate projections with the same model system. Initialization improves the accuracy of temperature and precipitation forecasts in year 1, particularly in the Pacific region. The ensemble spread well represents the forecast uncertainty in lead year 1, except in the tropics. This estimate of prediction skill creates confidence in the respective 2014 forecasts, which depict less precipitation in the tropics and a warming almost everywhere. However, large cooling patterns appear in the Northern Hemisphere, the Pacific South America and the Southern Ocean. Forecasts for 2015 to 2022 show even warmer temperatures than for 2014, especially over the continents. The evaluation of lead years 2 to 9 for temperature shows skill globally with the exception of the eastern Pacific. The ensemble spread can again be used as an estimate of the forecast uncertainty in many regions: It improves over the tropics compared to lead year 1. Due to a reduction of the conditional bias, the decadal predictions of the initialized system gain skill in the accuracy compared to the uninitialized simulations in the lead years 2 to 9. Furthermore, we show that increasing the ensemble size improves the MiKlip decadal climate prediction system for all lead years.