# A01 - Coupling a multiscale stochastic precipitation model to large scale atmospheric flow dynamics

### Project Details

**Status:**In Progress**Head(s):**Prof. Ulbrich, Dr. Névir, Dr. Rust**Project member(s):**Anette Müller, Christoph Ritschel, Sarah Jödicke, Dr. René Preusker, Dr. Klaus Müller, Jannick Fischer**Participating Institution(s):**FU Berlin**Area:**A: Efficient modelling of macro scales**Positions available?:**

### Project Summary

Global and regional climate models (GCMs and RCMs) have difficulties to simulate precipitation, particularly on small spatial and temporal scales (~1km, <1h); the scales of extreme convective events. As relevant processes are not (or not adequately) resolved on the grid-scale of the models, so called “parametrizations” are typically used to replace the unresolved processes. A parametrization maps grid-scale variables on the effects that sub-gridscale processes will have on the grid-scale. Based on the current grid-scale flow situation, they thus calculate the feedback to the grid scale, e.g., the latent heat release due to condensation and the associated formation of precipitation. Parametrizations are based on idealized and highly simplified models of the sub-grid-scale processes; recent ideas include stochasticity to account for the observed variability. If these parametrizations do not adequately mimic the sub-grid-scale processes and their feedback to the grid-sccale, neither small scale precipitation nor the synoptic (super-grid) scale flow can be expected to be captured in a realistic way.

Ranging from synoptic scale frontal lifting to convective scale precipitation events, precipitation itself is a phenomenon spanning multiple scales [8]. Furthermore, synoptic scale processes can lead to conditions favoring or inhibiting small scale convective precipitation and, vice versa, intensive convective events effect meso and synoptic scale circulation. Precipitation and circulation are thus connected across several scales in the sense of the CRC. Here, we aim at developing a stochastic precipitation model particular suitable for small and meso scale convective events which will be two-way-nested into a GCM, i.e., the GCM drives the precipitation model and it’s results (realization of precipitation) are fed back to the GCM. As such, this hybrid model is on the one hand meant to be strong in simulating realistic precipitation events – as extreme intensities or intensity-duration relations – and reproducing statistics of meso to small scale precipitation events for climate projections. On the other hand, it allows for an effective feedback of the effects of sub-grid-scale precipitation to the grid scale.

A multi-level stochastic process representing convective cells, cell clusters and rain events is the basis of the precipitation model. Coherent set analyses supports the model building process with respect to identifying the relevant precipitation structures and their dynamics. Model parameters thus characterize different scales and consequently depend on the flow model (GCM) in a multi-scale way. To identify variables and scales driving the stochastic model, we use a multi-scale analysis of precipitation related variables in the primitive equations governing the atmospheric flow. In the focus is a novel stability parameter, the Dynamic State Index (DSI), developed at the FU.

The main challenges are thus (1) to build a stochastic precipitation model on the basis of a multi-level stochastic process with parameters dependent on the large scale flow, (2) to derive relations between precipitation characteristics and large scale flow to link parameters of the stochastic model to variables of the atmospheric flow and (3) to establish an effective feedback mechanism from the stochastic model to the grid-scale flow. We thus aim at improving the simulation of the large scale flow model (GCM) while simultaneously give a more realistic description of the associated small scale precipitation. Ultimately, this stochastic precipitation model replaces part of the current sub-grid-scale parametrizations.

### Project publications

Banisch, R. and Trstanova, Z. and Bittracher, A. and Klus, S. and Koltai, P. (2020) *Diffusion maps tailored to arbitrary non-degenerate Ito processes.* SciendeDirect, 48 (1). pp. 242-265.

Müller, Annette and Névir, Peter (2019) *Using the concept of the Dynamic State Index for a scale-dependent analysis of atmospheric blocking.* Meteorologische Zeitschrift, 28 (6). pp. 487-498.

Miron, P. and Beron-Vera, F.J. and Olascoaga, M.J. and Koltai, P. (2019) *Markov-chain-inspired search for MH370.* Chaos: An Interdisciplinary Journal of Nonlinear Science, 29 (4). ISSN 1054-1500 (print); 1089-7682 (online)

Fackeldey, K. and Koltai, P. and Névir, P. and Rust, H.W. and Schild, A and Weber, M. (2019) *From Metastable to Coherent Sets – time-discretization schemes.* Chaos: An Interdisciplinary Journal of Nonlinear Science, 29 (1). 012101. ISSN 1054-1500 (print); 1089-7682 (online)

Müller, A. and Névir, P. and Klein, R. (2018) *Scale Dependent Analytical Investigation of the Dynamic State Index Concerning the Quasi-Geostrophic Theory.* Mathematics of Climate and Weather Forecasting, 4 (1). pp. 1-22. ISSN 2353-6438 (online)

Koltai, P. and Lie, Han Cheng and Plonka, M. (2018) *Fréchet differentiable drift dependence of Perron--Frobenius and Koopman operators for non-deterministic dynamics.* SFB 1114 Preprint in arXiv:1805.06719 . pp. 1-24. (Submitted)

Koltai, P. and Schütte, Ch. (2018) *A multiscale perturbation expansion approach for Markov state modeling of non-stationary molecular dynamics.* Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 16 (4). pp. 1455-1485. ISSN 1540-3459

Fischer, M. and Ulbrich, U. and Rust, H.W. (2017) *A spatial and seasonal climatology of extreme precipitation return-levels: A case study.* Spatial Statistics . pp. 1-25. (In Press)

Hittmeir, S. and Klein, R. and Müller, A. and Névir, P. (2017) *The Dynamic State Index with Moisture and Phase Changes.* SFB 1114 Preprint . pp. 1-12. (Unpublished)

Nissen, K.M. and Ulbrich, U. (2017) *Increasing frequencies and changing characteristics of heavy precipitation events threatening infrastructure in Europe under climate change.* Nat. Hazards Earth Syst. Sci., 17 . pp. 1177-1190.

Mazza, E. and Ulbrich, U. and Klein, R. (2017) *The Tropical Transition of the October 1996 Medicane in the Western Mediterranean Sea: A Warm Seclusion Event.* Monthly Weather Review, 145 . pp. 2575-2595. ISSN Online: 1520-0493 Print: 0027-0644

Ritschel, C. and Rust, H.W. and Ulbrich, U. (2017) *Precipitation extremes on multiple time scales -- Bartlett-Lewis Rectangular Pulse Model and Intensity-Duration-Frequency curves.* Hydrol. Earth Syst. Sci. . pp. 1-20. (Submitted)

O'Kane, T.J. and Monselesan, D.P. and Risbey, J.S. and Horenko, I. and Franzke, Ch.L.E. (2017) *On memory, dimension, and atmospheric teleconnection patterns.* Math. Clim. Weather Forecast, 3 (1). pp. 1-27.

Horenko, I. and Gerber, S. and O'Kane, T.J. and Risbey, J.S. and Monselesan, D.P. (2017) *On inference and validation of causality relations in climate teleconnections.* In: Nonlinear and Stochastic Climate Dynamics. Cambridge University Press, pp. 184-208. ISBN 9781107118140

Hirt, M. and Schielicke, L. and Müller, A. and Névir, P. (2017) *Statistical and dynamical analyses of atmospheric blocking with an idealized point vortex model.* Tellus A . pp. 1-22. (Submitted)

Fischer, M. and Rust, H.W. and Ulbrich, U. (2016) *Seasonal Cycle in German Daily Precipitation Extremes.* Meteorologische Zeitschrift . pp. 1-11. ISSN 0941-2948 (Submitted)

Horenko, I. and Gerber, S. (2015) *Improving clustering by imposing network information.* Science Advances, 1 (7). ISSN 2375-2548

O’Kane, T.J. and Risbey, J.S. and Monselesan, D.P. and Horenko, I. and Franzke, Ch.L.E. (2015) *On the dynamics of persistent states and their secular trends in the waveguides of the Southern Hemisphere troposphere.* Climate Dynamics . ISSN Print: 0930-7575, Online: 1432-0894