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Tobias Kremer, Elmar Schömer, Christian Euler, and Michael Riemer

trajectories in TCs. We then describe our strategy to handle the very large amount of trajectories that underlies our analysis and our choice of cluster algorithm. Finally, we discuss the representation of the obtained clusters in physical space, which is a nontrivial task in our case because clustering is performed in a transformed, normalized space (see below) and trajectories in the same cluster thus do not necessarily form coherent bundles of trajectories in physical space. a. Defining similarity of

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Peter Vogel, Peter Knippertz, Andreas H. Fink, Andreas Schlueter, and Tilmann Gneiting

forecasting ( Alley et al. 2019 ). Why is there so little progress in tropical weather forecasting, although many challenges have been realized for decades (e.g., Smith et al. 2001 )? First, initial uncertainties tend to be largest in equatorial regions ( Žagar 2017 ). This is caused by an insufficient observational network, data assimilation algorithms optimized for midlatitude conditions, and large model errors, which also contribute to a fast degradation of forecast quality ( Privé and Errico 2013

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Volkmar Wirth, Michael Riemer, Edmund K. M. Chang, and Olivia Martius

latitude band, with the weighting function being proportional to the zonal variance of the meridional wind. This algorithm self-adjusts to the optimum range of latitudes and avoids the need to predetermine a fixed latitude band. Another algorithm makes the latitudinal band depend even on longitude with the aim to follow the main waveguide ( Martius et al. 2006 ). A systematic comparison between different types of Hovmöller diagrams shows that the refinements are beneficial in situations where otherwise

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Stephan Rasp and Sebastian Lerch

networks are a flexible and user-friendly machine learning algorithm that can model arbitrary nonlinear functions ( Nielsen 2015 ). They consist of several layers of interconnected nodes that are modulated with simple nonlinearities ( Fig. 1 ; section 4 ). Over the past decade many fields, most notably computer vision and natural language processing ( LeCun et al. 2015 ), but also biology, physics, and chemistry ( Angermueller et al. 2016 ; Goh et al. 2017 ), have been transformed by neural networks

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Paolo Ghinassi, Georgios Fragkoulidis, and Volkmar Wirth

simulation with a barotropic model on the sphere. Our paper is organized as follows. Section 2 contains a brief summary of the theory of LWA and its extension to the primitive equations framework, including a description of our algorithm for the identification of RWPs. In section 3 the new diagnostic is applied to an observed case of RWP propagation and breaking, and we compare our results with the envelope of meridional wind diagnostic. To support the interpretation of this comparison, we apply

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Jacopo Riboldi, Christian M. Grams, Michael Riemer, and Heather M. Archambault

on its degree of interaction with an upstream trough (e.g., Evans and Hart 2003 ; Studholme et al. 2015 ). The nearest trough upstream of the TC at is identified and tracked. All the cases have been manually inspected to avoid two TCs recurving at the same time also having the same maximum interaction point and to make sure that the correct upstream trough at is tracked. b. Trough tracking A tracking algorithm is implemented to diagnose the zonal propagation of upper-level troughs. The

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Stephan Rasp, Tobias Selz, and George C. Craig

found by Scheufele (2014) ]. We therefore separate the cloud objects using a local maximum filter in combination with a watershed algorithm ( Beucher and Meyer 1992 ). For the local maximum filter, we use a search footprint of 3 × 3 grid points. All subsequently presented analysis is done using the separated objects unless otherwise stated. For further information and sensitivity tests of the cloud separation algorithm, see the aforementioned Jupyter notebook cloud

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Thomas Engel, Andreas H. Fink, Peter Knippertz, Gregor Pante, and Jan Bliefernicht

these events: 1) most importantly, ~100-yr-long time series of daily rainfall with very few gaps are available at both locations—a very rare situation in Africa, and 2) recently, the Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks–Climate Data Record (PERSIANN-CDR; Ashouri et al. 2015 ), a homogenized, 32-yr-long (1983–2014) SRFE dataset, was released. The PERSIANN-CDR algorithm uses homogenized infrared brightness temperatures and was trained in a neural

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Tobias Selz, Lotte Bierdel, and George C. Craig

grid points were discarded to minimize inflow artifacts and to render the number of grid points a multiple of 5 (convenient for the algorithm to distinguish wet and dry segments as described below). For each time step and pressure level, the one-dimensional spectral KE density (the KE spectrum) is defined by the integral where k is the one-dimensional wavenumber and is the domain-averaged kinetic energy. Discrete cosine transforms (DCT; Denis et al. 2002 ) of the wind components are used to

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Gabriel Wolf and Volkmar Wirth

; Grazzini and Vitart 2015 ). Despite some obvious advantages in comparison with Hovmöller diagrams, diagnosing and tracking of RWPs is far from straightforward and may occasionally yield misleading results. In particular, diagnosing RWP objects on a longitude–latitude map requires a number of choices, like for instance choosing an algorithm to compute the envelope of a wave packet and picking a threshold. Neither Hovmöller diagrams nor RWP tracking inherently provides information about the propagation

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